7385 lines
217 KiB
C++
7385 lines
217 KiB
C++
// This code is in the public domain -- castanyo@yahoo.es
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#include "xatlas.h"
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#include <assert.h>
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#include <float.h>
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#include <math.h>
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#include <stdarg.h>
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#include <stdint.h>
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#include <stdio.h>
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#include <string.h>
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#include <time.h>
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#include <algorithm>
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#include <cmath>
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#include <memory>
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#include <unordered_map>
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#include <vector>
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#undef min
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#undef max
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#ifndef xaAssert
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#define xaAssert(exp) \
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if (!(exp)) { \
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xaPrint("%s %s %s\n", #exp, __FILE__, __LINE__); \
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}
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#endif
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#ifndef xaDebugAssert
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#define xaDebugAssert(exp) assert(exp)
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#endif
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#ifndef xaPrint
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#define xaPrint(...) \
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if (xatlas::internal::s_print) { \
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xatlas::internal::s_print(__VA_ARGS__); \
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}
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#endif
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#ifdef _MSC_VER
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// Ignore gcc attributes.
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#define __attribute__(X)
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#endif
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#ifdef _MSC_VER
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#define restrict
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#define NV_FORCEINLINE __forceinline
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#else
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#define restrict __restrict__
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#define NV_FORCEINLINE __attribute__((always_inline)) inline
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#endif
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#define NV_UINT32_MAX 0xffffffff
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#define NV_FLOAT_MAX 3.402823466e+38F
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#ifndef PI
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#define PI float(3.1415926535897932384626433833)
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#endif
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#define NV_EPSILON (0.0001f)
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#define NV_NORMAL_EPSILON (0.001f)
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namespace xatlas {
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namespace internal {
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static PrintFunc s_print = NULL;
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static int align(int x, int a) {
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return (x + a - 1) & ~(a - 1);
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}
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static bool isAligned(int x, int a) {
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return (x & (a - 1)) == 0;
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}
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/// Return the maximum of the three arguments.
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template <typename T>
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static T max3(const T &a, const T &b, const T &c) {
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return std::max(a, std::max(b, c));
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}
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/// Return the maximum of the three arguments.
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template <typename T>
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static T min3(const T &a, const T &b, const T &c) {
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return std::min(a, std::min(b, c));
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}
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/// Clamp between two values.
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template <typename T>
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static T clamp(const T &x, const T &a, const T &b) {
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return std::min(std::max(x, a), b);
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}
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static float saturate(float f) {
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return clamp(f, 0.0f, 1.0f);
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}
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// Robust floating point comparisons:
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// http://realtimecollisiondetection.net/blog/?p=89
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static bool equal(const float f0, const float f1, const float epsilon = NV_EPSILON) {
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//return fabs(f0-f1) <= epsilon;
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return fabs(f0 - f1) <= epsilon * max3(1.0f, fabsf(f0), fabsf(f1));
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}
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NV_FORCEINLINE static int ftoi_floor(float val) {
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return (int)val;
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}
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NV_FORCEINLINE static int ftoi_ceil(float val) {
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return (int)ceilf(val);
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}
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NV_FORCEINLINE static int ftoi_round(float f) {
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return int(floorf(f + 0.5f));
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}
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static bool isZero(const float f, const float epsilon = NV_EPSILON) {
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return fabs(f) <= epsilon;
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}
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static float lerp(float f0, float f1, float t) {
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const float s = 1.0f - t;
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return f0 * s + f1 * t;
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}
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static float square(float f) {
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return f * f;
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}
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static int square(int i) {
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return i * i;
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}
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/** Return the next power of two.
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* @see http://graphics.stanford.edu/~seander/bithacks.html
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* @warning Behaviour for 0 is undefined.
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* @note isPowerOfTwo(x) == true -> nextPowerOfTwo(x) == x
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* @note nextPowerOfTwo(x) = 2 << log2(x-1)
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*/
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static uint32_t nextPowerOfTwo(uint32_t x) {
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xaDebugAssert(x != 0);
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// On modern CPUs this is supposed to be as fast as using the bsr instruction.
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x--;
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x |= x >> 1;
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x |= x >> 2;
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x |= x >> 4;
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x |= x >> 8;
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x |= x >> 16;
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return x + 1;
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}
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static uint64_t nextPowerOfTwo(uint64_t x) {
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xaDebugAssert(x != 0);
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uint32_t p = 1;
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while (x > p) {
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p += p;
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}
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return p;
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}
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static uint32_t sdbmHash(const void *data_in, uint32_t size, uint32_t h = 5381) {
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const uint8_t *data = (const uint8_t *)data_in;
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uint32_t i = 0;
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while (i < size) {
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h = (h << 16) + (h << 6) - h + (uint32_t)data[i++];
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}
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return h;
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}
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// Note that this hash does not handle NaN properly.
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static uint32_t sdbmFloatHash(const float *f, uint32_t count, uint32_t h = 5381) {
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for (uint32_t i = 0; i < count; i++) {
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union {
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float f;
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uint32_t i;
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} x = { f[i] };
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if (x.i == 0x80000000) x.i = 0;
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h = sdbmHash(&x, 4, h);
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}
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return h;
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}
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template <typename T>
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static uint32_t hash(const T &t, uint32_t h = 5381) {
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return sdbmHash(&t, sizeof(T), h);
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}
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static uint32_t hash(const float &f, uint32_t h) {
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return sdbmFloatHash(&f, 1, h);
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}
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// Functors for hash table:
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template <typename Key>
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struct Hash {
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uint32_t operator()(const Key &k) const { return hash(k); }
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};
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template <typename Key>
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struct Equal {
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bool operator()(const Key &k0, const Key &k1) const { return k0 == k1; }
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};
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class Vector2 {
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public:
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typedef Vector2 const &Arg;
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Vector2() {}
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explicit Vector2(float f) :
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x(f),
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y(f) {}
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Vector2(float x, float y) :
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x(x),
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y(y) {}
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Vector2(Vector2::Arg v) :
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x(v.x),
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y(v.y) {}
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const Vector2 &operator=(Vector2::Arg v) {
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x = v.x;
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y = v.y;
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return *this;
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}
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const float *ptr() const { return &x; }
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void set(float _x, float _y) {
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x = _x;
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y = _y;
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}
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Vector2 operator-() const {
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return Vector2(-x, -y);
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}
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void operator+=(Vector2::Arg v) {
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x += v.x;
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y += v.y;
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}
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void operator-=(Vector2::Arg v) {
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x -= v.x;
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y -= v.y;
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}
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void operator*=(float s) {
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x *= s;
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y *= s;
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}
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void operator*=(Vector2::Arg v) {
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x *= v.x;
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y *= v.y;
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}
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friend bool operator==(Vector2::Arg a, Vector2::Arg b) {
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return a.x == b.x && a.y == b.y;
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}
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friend bool operator!=(Vector2::Arg a, Vector2::Arg b) {
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return a.x != b.x || a.y != b.y;
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}
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union {
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#ifdef _MSC_VER
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#pragma warning(push)
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#pragma warning(disable : 4201)
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#endif
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struct
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{
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float x, y;
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};
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#ifdef _MSC_VER
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#pragma warning(pop)
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#endif
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float component[2];
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};
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};
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Vector2 operator+(Vector2::Arg a, Vector2::Arg b) {
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return Vector2(a.x + b.x, a.y + b.y);
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}
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Vector2 operator-(Vector2::Arg a, Vector2::Arg b) {
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return Vector2(a.x - b.x, a.y - b.y);
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}
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Vector2 operator*(Vector2::Arg v, float s) {
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return Vector2(v.x * s, v.y * s);
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}
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Vector2 operator*(Vector2::Arg v1, Vector2::Arg v2) {
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return Vector2(v1.x * v2.x, v1.y * v2.y);
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}
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Vector2 operator/(Vector2::Arg v, float s) {
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return Vector2(v.x / s, v.y / s);
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}
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Vector2 lerp(Vector2::Arg v1, Vector2::Arg v2, float t) {
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const float s = 1.0f - t;
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return Vector2(v1.x * s + t * v2.x, v1.y * s + t * v2.y);
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}
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float dot(Vector2::Arg a, Vector2::Arg b) {
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return a.x * b.x + a.y * b.y;
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}
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float lengthSquared(Vector2::Arg v) {
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return v.x * v.x + v.y * v.y;
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}
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float length(Vector2::Arg v) {
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return sqrtf(lengthSquared(v));
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}
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float distance(Vector2::Arg a, Vector2::Arg b) {
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return length(a - b);
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}
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bool isNormalized(Vector2::Arg v, float epsilon = NV_NORMAL_EPSILON) {
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return equal(length(v), 1, epsilon);
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}
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Vector2 normalize(Vector2::Arg v, float epsilon = NV_EPSILON) {
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float l = length(v);
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xaDebugAssert(!isZero(l, epsilon));
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#ifdef NDEBUG
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epsilon = 0; // silence unused parameter warning
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#endif
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Vector2 n = v * (1.0f / l);
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xaDebugAssert(isNormalized(n));
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return n;
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}
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Vector2 normalizeSafe(Vector2::Arg v, Vector2::Arg fallback, float epsilon = NV_EPSILON) {
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float l = length(v);
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if (isZero(l, epsilon)) {
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return fallback;
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}
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return v * (1.0f / l);
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}
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bool equal(Vector2::Arg v1, Vector2::Arg v2, float epsilon = NV_EPSILON) {
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return equal(v1.x, v2.x, epsilon) && equal(v1.y, v2.y, epsilon);
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}
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Vector2 max(Vector2::Arg a, Vector2::Arg b) {
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return Vector2(std::max(a.x, b.x), std::max(a.y, b.y));
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}
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bool isFinite(Vector2::Arg v) {
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return std::isfinite(v.x) && std::isfinite(v.y);
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}
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// Note, this is the area scaled by 2!
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float triangleArea(Vector2::Arg v0, Vector2::Arg v1) {
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return (v0.x * v1.y - v0.y * v1.x); // * 0.5f;
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}
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float triangleArea(Vector2::Arg a, Vector2::Arg b, Vector2::Arg c) {
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// IC: While it may be appealing to use the following expression:
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//return (c.x * a.y + a.x * b.y + b.x * c.y - b.x * a.y - c.x * b.y - a.x * c.y); // * 0.5f;
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// That's actually a terrible idea. Small triangles far from the origin can end up producing fairly large floating point
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// numbers and the results becomes very unstable and dependent on the order of the factors.
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// Instead, it's preferable to subtract the vertices first, and multiply the resulting small values together. The result
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// in this case is always much more accurate (as long as the triangle is small) and less dependent of the location of
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// the triangle.
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//return ((a.x - c.x) * (b.y - c.y) - (a.y - c.y) * (b.x - c.x)); // * 0.5f;
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return triangleArea(a - c, b - c);
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}
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float triangleArea2(Vector2::Arg v1, Vector2::Arg v2, Vector2::Arg v3) {
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return 0.5f * (v3.x * v1.y + v1.x * v2.y + v2.x * v3.y - v2.x * v1.y - v3.x * v2.y - v1.x * v3.y);
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}
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static uint32_t hash(const Vector2 &v, uint32_t h) {
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return sdbmFloatHash(v.component, 2, h);
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}
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class Vector3 {
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public:
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typedef Vector3 const &Arg;
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Vector3() {}
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explicit Vector3(float f) :
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x(f),
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y(f),
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z(f) {}
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Vector3(float x, float y, float z) :
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x(x),
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y(y),
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z(z) {}
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Vector3(Vector2::Arg v, float z) :
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x(v.x),
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y(v.y),
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z(z) {}
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Vector3(Vector3::Arg v) :
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x(v.x),
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y(v.y),
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z(v.z) {}
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const Vector3 &operator=(Vector3::Arg v) {
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x = v.x;
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y = v.y;
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z = v.z;
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return *this;
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}
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Vector2 xy() const {
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return Vector2(x, y);
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}
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const float *ptr() const { return &x; }
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void set(float _x, float _y, float _z) {
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x = _x;
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y = _y;
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z = _z;
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}
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Vector3 operator-() const {
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return Vector3(-x, -y, -z);
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}
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void operator+=(Vector3::Arg v) {
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x += v.x;
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y += v.y;
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z += v.z;
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}
|
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void operator-=(Vector3::Arg v) {
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x -= v.x;
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y -= v.y;
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z -= v.z;
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}
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|
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void operator*=(float s) {
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x *= s;
|
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y *= s;
|
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z *= s;
|
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}
|
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|
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void operator/=(float s) {
|
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float is = 1.0f / s;
|
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x *= is;
|
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y *= is;
|
||
z *= is;
|
||
}
|
||
|
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void operator*=(Vector3::Arg v) {
|
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x *= v.x;
|
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y *= v.y;
|
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z *= v.z;
|
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}
|
||
|
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void operator/=(Vector3::Arg v) {
|
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x /= v.x;
|
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y /= v.y;
|
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z /= v.z;
|
||
}
|
||
|
||
friend bool operator==(Vector3::Arg a, Vector3::Arg b) {
|
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return a.x == b.x && a.y == b.y && a.z == b.z;
|
||
}
|
||
|
||
friend bool operator!=(Vector3::Arg a, Vector3::Arg b) {
|
||
return a.x != b.x || a.y != b.y || a.z != b.z;
|
||
}
|
||
|
||
union {
|
||
#ifdef _MSC_VER
|
||
#pragma warning(push)
|
||
#pragma warning(disable : 4201)
|
||
#endif
|
||
struct
|
||
{
|
||
float x, y, z;
|
||
};
|
||
#ifdef _MSC_VER
|
||
#pragma warning(pop)
|
||
#endif
|
||
|
||
float component[3];
|
||
};
|
||
};
|
||
|
||
Vector3 add(Vector3::Arg a, Vector3::Arg b) {
|
||
return Vector3(a.x + b.x, a.y + b.y, a.z + b.z);
|
||
}
|
||
Vector3 add(Vector3::Arg a, float b) {
|
||
return Vector3(a.x + b, a.y + b, a.z + b);
|
||
}
|
||
Vector3 operator+(Vector3::Arg a, Vector3::Arg b) {
|
||
return add(a, b);
|
||
}
|
||
Vector3 operator+(Vector3::Arg a, float b) {
|
||
return add(a, b);
|
||
}
|
||
|
||
Vector3 sub(Vector3::Arg a, Vector3::Arg b) {
|
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return Vector3(a.x - b.x, a.y - b.y, a.z - b.z);
|
||
}
|
||
|
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Vector3 sub(Vector3::Arg a, float b) {
|
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return Vector3(a.x - b, a.y - b, a.z - b);
|
||
}
|
||
|
||
Vector3 operator-(Vector3::Arg a, Vector3::Arg b) {
|
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return sub(a, b);
|
||
}
|
||
|
||
Vector3 operator-(Vector3::Arg a, float b) {
|
||
return sub(a, b);
|
||
}
|
||
|
||
Vector3 cross(Vector3::Arg a, Vector3::Arg b) {
|
||
return Vector3(a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x);
|
||
}
|
||
|
||
Vector3 operator*(Vector3::Arg v, float s) {
|
||
return Vector3(v.x * s, v.y * s, v.z * s);
|
||
}
|
||
|
||
Vector3 operator*(float s, Vector3::Arg v) {
|
||
return Vector3(v.x * s, v.y * s, v.z * s);
|
||
}
|
||
|
||
Vector3 operator*(Vector3::Arg v, Vector3::Arg s) {
|
||
return Vector3(v.x * s.x, v.y * s.y, v.z * s.z);
|
||
}
|
||
|
||
Vector3 operator/(Vector3::Arg v, float s) {
|
||
return v * (1.0f / s);
|
||
}
|
||
|
||
Vector3 lerp(Vector3::Arg v1, Vector3::Arg v2, float t) {
|
||
const float s = 1.0f - t;
|
||
return Vector3(v1.x * s + t * v2.x, v1.y * s + t * v2.y, v1.z * s + t * v2.z);
|
||
}
|
||
|
||
float dot(Vector3::Arg a, Vector3::Arg b) {
|
||
return a.x * b.x + a.y * b.y + a.z * b.z;
|
||
}
|
||
|
||
float lengthSquared(Vector3::Arg v) {
|
||
return v.x * v.x + v.y * v.y + v.z * v.z;
|
||
}
|
||
|
||
float length(Vector3::Arg v) {
|
||
return sqrtf(lengthSquared(v));
|
||
}
|
||
|
||
float distance(Vector3::Arg a, Vector3::Arg b) {
|
||
return length(a - b);
|
||
}
|
||
|
||
float distanceSquared(Vector3::Arg a, Vector3::Arg b) {
|
||
return lengthSquared(a - b);
|
||
}
|
||
|
||
bool isNormalized(Vector3::Arg v, float epsilon = NV_NORMAL_EPSILON) {
|
||
return equal(length(v), 1, epsilon);
|
||
}
|
||
|
||
Vector3 normalize(Vector3::Arg v, float epsilon = NV_EPSILON) {
|
||
float l = length(v);
|
||
xaDebugAssert(!isZero(l, epsilon));
|
||
#ifdef NDEBUG
|
||
epsilon = 0; // silence unused parameter warning
|
||
#endif
|
||
Vector3 n = v * (1.0f / l);
|
||
xaDebugAssert(isNormalized(n));
|
||
return n;
|
||
}
|
||
|
||
Vector3 normalizeSafe(Vector3::Arg v, Vector3::Arg fallback, float epsilon = NV_EPSILON) {
|
||
float l = length(v);
|
||
if (isZero(l, epsilon)) {
|
||
return fallback;
|
||
}
|
||
return v * (1.0f / l);
|
||
}
|
||
|
||
bool equal(Vector3::Arg v1, Vector3::Arg v2, float epsilon = NV_EPSILON) {
|
||
return equal(v1.x, v2.x, epsilon) && equal(v1.y, v2.y, epsilon) && equal(v1.z, v2.z, epsilon);
|
||
}
|
||
|
||
Vector3 min(Vector3::Arg a, Vector3::Arg b) {
|
||
return Vector3(std::min(a.x, b.x), std::min(a.y, b.y), std::min(a.z, b.z));
|
||
}
|
||
|
||
Vector3 max(Vector3::Arg a, Vector3::Arg b) {
|
||
return Vector3(std::max(a.x, b.x), std::max(a.y, b.y), std::max(a.z, b.z));
|
||
}
|
||
|
||
Vector3 clamp(Vector3::Arg v, float min, float max) {
|
||
return Vector3(clamp(v.x, min, max), clamp(v.y, min, max), clamp(v.z, min, max));
|
||
}
|
||
|
||
Vector3 saturate(Vector3::Arg v) {
|
||
return Vector3(saturate(v.x), saturate(v.y), saturate(v.z));
|
||
}
|
||
|
||
Vector3 floor(Vector3::Arg v) {
|
||
return Vector3(floorf(v.x), floorf(v.y), floorf(v.z));
|
||
}
|
||
|
||
bool isFinite(Vector3::Arg v) {
|
||
return std::isfinite(v.x) && std::isfinite(v.y) && std::isfinite(v.z);
|
||
}
|
||
|
||
static uint32_t hash(const Vector3 &v, uint32_t h) {
|
||
return sdbmFloatHash(v.component, 3, h);
|
||
}
|
||
|
||
/// Basis class to compute tangent space basis, ortogonalizations and to
|
||
/// transform vectors from one space to another.
|
||
class Basis {
|
||
public:
|
||
/// Create a null basis.
|
||
Basis() :
|
||
tangent(0, 0, 0),
|
||
bitangent(0, 0, 0),
|
||
normal(0, 0, 0) {}
|
||
|
||
void buildFrameForDirection(Vector3::Arg d, float angle = 0) {
|
||
xaAssert(isNormalized(d));
|
||
normal = d;
|
||
// Choose minimum axis.
|
||
if (fabsf(normal.x) < fabsf(normal.y) && fabsf(normal.x) < fabsf(normal.z)) {
|
||
tangent = Vector3(1, 0, 0);
|
||
} else if (fabsf(normal.y) < fabsf(normal.z)) {
|
||
tangent = Vector3(0, 1, 0);
|
||
} else {
|
||
tangent = Vector3(0, 0, 1);
|
||
}
|
||
// Ortogonalize
|
||
tangent -= normal * dot(normal, tangent);
|
||
tangent = normalize(tangent);
|
||
bitangent = cross(normal, tangent);
|
||
// Rotate frame around normal according to angle.
|
||
if (angle != 0.0f) {
|
||
float c = cosf(angle);
|
||
float s = sinf(angle);
|
||
Vector3 tmp = c * tangent - s * bitangent;
|
||
bitangent = s * tangent + c * bitangent;
|
||
tangent = tmp;
|
||
}
|
||
}
|
||
|
||
Vector3 tangent;
|
||
Vector3 bitangent;
|
||
Vector3 normal;
|
||
};
|
||
|
||
// Simple bit array.
|
||
class BitArray {
|
||
public:
|
||
BitArray() :
|
||
m_size(0) {}
|
||
BitArray(uint32_t sz) {
|
||
resize(sz);
|
||
}
|
||
|
||
uint32_t size() const {
|
||
return m_size;
|
||
}
|
||
|
||
void clear() {
|
||
resize(0);
|
||
}
|
||
|
||
void resize(uint32_t new_size) {
|
||
m_size = new_size;
|
||
m_wordArray.resize((m_size + 31) >> 5);
|
||
}
|
||
|
||
/// Get bit.
|
||
bool bitAt(uint32_t b) const {
|
||
xaDebugAssert(b < m_size);
|
||
return (m_wordArray[b >> 5] & (1 << (b & 31))) != 0;
|
||
}
|
||
|
||
// Set a bit.
|
||
void setBitAt(uint32_t idx) {
|
||
xaDebugAssert(idx < m_size);
|
||
m_wordArray[idx >> 5] |= (1 << (idx & 31));
|
||
}
|
||
|
||
// Toggle a bit.
|
||
void toggleBitAt(uint32_t idx) {
|
||
xaDebugAssert(idx < m_size);
|
||
m_wordArray[idx >> 5] ^= (1 << (idx & 31));
|
||
}
|
||
|
||
// Set a bit to the given value. @@ Rename modifyBitAt?
|
||
void setBitAt(uint32_t idx, bool b) {
|
||
xaDebugAssert(idx < m_size);
|
||
m_wordArray[idx >> 5] = setBits(m_wordArray[idx >> 5], 1 << (idx & 31), b);
|
||
xaDebugAssert(bitAt(idx) == b);
|
||
}
|
||
|
||
// Clear all the bits.
|
||
void clearAll() {
|
||
memset(m_wordArray.data(), 0, m_wordArray.size() * sizeof(uint32_t));
|
||
}
|
||
|
||
// Set all the bits.
|
||
void setAll() {
|
||
memset(m_wordArray.data(), 0xFF, m_wordArray.size() * sizeof(uint32_t));
|
||
}
|
||
|
||
private:
|
||
// See "Conditionally set or clear bits without branching" at http://graphics.stanford.edu/~seander/bithacks.html
|
||
uint32_t setBits(uint32_t w, uint32_t m, bool b) {
|
||
return (w & ~m) | (-int(b) & m);
|
||
}
|
||
|
||
// Number of bits stored.
|
||
uint32_t m_size;
|
||
|
||
// Array of bits.
|
||
std::vector<uint32_t> m_wordArray;
|
||
};
|
||
|
||
/// Bit map. This should probably be called BitImage.
|
||
class BitMap {
|
||
public:
|
||
BitMap() :
|
||
m_width(0),
|
||
m_height(0) {}
|
||
BitMap(uint32_t w, uint32_t h) :
|
||
m_width(w),
|
||
m_height(h),
|
||
m_bitArray(w * h) {}
|
||
|
||
uint32_t width() const {
|
||
return m_width;
|
||
}
|
||
uint32_t height() const {
|
||
return m_height;
|
||
}
|
||
|
||
void resize(uint32_t w, uint32_t h, bool initValue) {
|
||
BitArray tmp(w * h);
|
||
if (initValue)
|
||
tmp.setAll();
|
||
else
|
||
tmp.clearAll();
|
||
// @@ Copying one bit at a time. This could be much faster.
|
||
for (uint32_t y = 0; y < m_height; y++) {
|
||
for (uint32_t x = 0; x < m_width; x++) {
|
||
//tmp.setBitAt(y*w + x, bitAt(x, y));
|
||
if (bitAt(x, y) != initValue) tmp.toggleBitAt(y * w + x);
|
||
}
|
||
}
|
||
std::swap(m_bitArray, tmp);
|
||
m_width = w;
|
||
m_height = h;
|
||
}
|
||
|
||
bool bitAt(uint32_t x, uint32_t y) const {
|
||
xaDebugAssert(x < m_width && y < m_height);
|
||
return m_bitArray.bitAt(y * m_width + x);
|
||
}
|
||
|
||
void setBitAt(uint32_t x, uint32_t y) {
|
||
xaDebugAssert(x < m_width && y < m_height);
|
||
m_bitArray.setBitAt(y * m_width + x);
|
||
}
|
||
|
||
void clearAll() {
|
||
m_bitArray.clearAll();
|
||
}
|
||
|
||
private:
|
||
uint32_t m_width;
|
||
uint32_t m_height;
|
||
BitArray m_bitArray;
|
||
};
|
||
|
||
// Axis Aligned Bounding Box.
|
||
class Box {
|
||
public:
|
||
Box() {}
|
||
Box(const Box &b) :
|
||
minCorner(b.minCorner),
|
||
maxCorner(b.maxCorner) {}
|
||
Box(const Vector3 &mins, const Vector3 &maxs) :
|
||
minCorner(mins),
|
||
maxCorner(maxs) {}
|
||
|
||
operator const float *() const {
|
||
return reinterpret_cast<const float *>(this);
|
||
}
|
||
|
||
// Clear the bounds.
|
||
void clearBounds() {
|
||
minCorner.set(FLT_MAX, FLT_MAX, FLT_MAX);
|
||
maxCorner.set(-FLT_MAX, -FLT_MAX, -FLT_MAX);
|
||
}
|
||
|
||
// Return extents of the box.
|
||
Vector3 extents() const {
|
||
return (maxCorner - minCorner) * 0.5f;
|
||
}
|
||
|
||
// Add a point to this box.
|
||
void addPointToBounds(const Vector3 &p) {
|
||
minCorner = min(minCorner, p);
|
||
maxCorner = max(maxCorner, p);
|
||
}
|
||
|
||
// Get the volume of the box.
|
||
float volume() const {
|
||
Vector3 d = extents();
|
||
return 8.0f * (d.x * d.y * d.z);
|
||
}
|
||
|
||
Vector3 minCorner;
|
||
Vector3 maxCorner;
|
||
};
|
||
|
||
class Fit {
|
||
public:
|
||
static Vector3 computeCentroid(int n, const Vector3 *__restrict points) {
|
||
Vector3 centroid(0.0f);
|
||
for (int i = 0; i < n; i++) {
|
||
centroid += points[i];
|
||
}
|
||
centroid /= float(n);
|
||
return centroid;
|
||
}
|
||
|
||
static Vector3 computeCovariance(int n, const Vector3 *__restrict points, float *__restrict covariance) {
|
||
// compute the centroid
|
||
Vector3 centroid = computeCentroid(n, points);
|
||
// compute covariance matrix
|
||
for (int i = 0; i < 6; i++) {
|
||
covariance[i] = 0.0f;
|
||
}
|
||
for (int i = 0; i < n; i++) {
|
||
Vector3 v = points[i] - centroid;
|
||
covariance[0] += v.x * v.x;
|
||
covariance[1] += v.x * v.y;
|
||
covariance[2] += v.x * v.z;
|
||
covariance[3] += v.y * v.y;
|
||
covariance[4] += v.y * v.z;
|
||
covariance[5] += v.z * v.z;
|
||
}
|
||
return centroid;
|
||
}
|
||
|
||
static bool isPlanar(int n, const Vector3 *points, float epsilon = NV_EPSILON) {
|
||
// compute the centroid and covariance
|
||
float matrix[6];
|
||
computeCovariance(n, points, matrix);
|
||
float eigenValues[3];
|
||
Vector3 eigenVectors[3];
|
||
if (!eigenSolveSymmetric3(matrix, eigenValues, eigenVectors)) {
|
||
return false;
|
||
}
|
||
return eigenValues[2] < epsilon;
|
||
}
|
||
|
||
// Tridiagonal solver from Charles Bloom.
|
||
// Householder transforms followed by QL decomposition.
|
||
// Seems to be based on the code from Numerical Recipes in C.
|
||
static bool eigenSolveSymmetric3(const float matrix[6], float eigenValues[3], Vector3 eigenVectors[3]) {
|
||
xaDebugAssert(matrix != NULL && eigenValues != NULL && eigenVectors != NULL);
|
||
float subd[3];
|
||
float diag[3];
|
||
float work[3][3];
|
||
work[0][0] = matrix[0];
|
||
work[0][1] = work[1][0] = matrix[1];
|
||
work[0][2] = work[2][0] = matrix[2];
|
||
work[1][1] = matrix[3];
|
||
work[1][2] = work[2][1] = matrix[4];
|
||
work[2][2] = matrix[5];
|
||
EigenSolver3_Tridiagonal(work, diag, subd);
|
||
if (!EigenSolver3_QLAlgorithm(work, diag, subd)) {
|
||
for (int i = 0; i < 3; i++) {
|
||
eigenValues[i] = 0;
|
||
eigenVectors[i] = Vector3(0);
|
||
}
|
||
return false;
|
||
}
|
||
for (int i = 0; i < 3; i++) {
|
||
eigenValues[i] = (float)diag[i];
|
||
}
|
||
// eigenvectors are the columns; make them the rows :
|
||
for (int i = 0; i < 3; i++) {
|
||
for (int j = 0; j < 3; j++) {
|
||
eigenVectors[j].component[i] = (float)work[i][j];
|
||
}
|
||
}
|
||
// shuffle to sort by singular value :
|
||
if (eigenValues[2] > eigenValues[0] && eigenValues[2] > eigenValues[1]) {
|
||
std::swap(eigenValues[0], eigenValues[2]);
|
||
std::swap(eigenVectors[0], eigenVectors[2]);
|
||
}
|
||
if (eigenValues[1] > eigenValues[0]) {
|
||
std::swap(eigenValues[0], eigenValues[1]);
|
||
std::swap(eigenVectors[0], eigenVectors[1]);
|
||
}
|
||
if (eigenValues[2] > eigenValues[1]) {
|
||
std::swap(eigenValues[1], eigenValues[2]);
|
||
std::swap(eigenVectors[1], eigenVectors[2]);
|
||
}
|
||
xaDebugAssert(eigenValues[0] >= eigenValues[1] && eigenValues[0] >= eigenValues[2]);
|
||
xaDebugAssert(eigenValues[1] >= eigenValues[2]);
|
||
return true;
|
||
}
|
||
|
||
private:
|
||
static void EigenSolver3_Tridiagonal(float mat[3][3], float *diag, float *subd) {
|
||
// Householder reduction T = Q^t M Q
|
||
// Input:
|
||
// mat, symmetric 3x3 matrix M
|
||
// Output:
|
||
// mat, orthogonal matrix Q
|
||
// diag, diagonal entries of T
|
||
// subd, subdiagonal entries of T (T is symmetric)
|
||
const float epsilon = 1e-08f;
|
||
float a = mat[0][0];
|
||
float b = mat[0][1];
|
||
float c = mat[0][2];
|
||
float d = mat[1][1];
|
||
float e = mat[1][2];
|
||
float f = mat[2][2];
|
||
diag[0] = a;
|
||
subd[2] = 0.f;
|
||
if (fabsf(c) >= epsilon) {
|
||
const float ell = sqrtf(b * b + c * c);
|
||
b /= ell;
|
||
c /= ell;
|
||
const float q = 2 * b * e + c * (f - d);
|
||
diag[1] = d + c * q;
|
||
diag[2] = f - c * q;
|
||
subd[0] = ell;
|
||
subd[1] = e - b * q;
|
||
mat[0][0] = 1;
|
||
mat[0][1] = 0;
|
||
mat[0][2] = 0;
|
||
mat[1][0] = 0;
|
||
mat[1][1] = b;
|
||
mat[1][2] = c;
|
||
mat[2][0] = 0;
|
||
mat[2][1] = c;
|
||
mat[2][2] = -b;
|
||
} else {
|
||
diag[1] = d;
|
||
diag[2] = f;
|
||
subd[0] = b;
|
||
subd[1] = e;
|
||
mat[0][0] = 1;
|
||
mat[0][1] = 0;
|
||
mat[0][2] = 0;
|
||
mat[1][0] = 0;
|
||
mat[1][1] = 1;
|
||
mat[1][2] = 0;
|
||
mat[2][0] = 0;
|
||
mat[2][1] = 0;
|
||
mat[2][2] = 1;
|
||
}
|
||
}
|
||
|
||
static bool EigenSolver3_QLAlgorithm(float mat[3][3], float *diag, float *subd) {
|
||
// QL iteration with implicit shifting to reduce matrix from tridiagonal
|
||
// to diagonal
|
||
const int maxiter = 32;
|
||
for (int ell = 0; ell < 3; ell++) {
|
||
int iter;
|
||
for (iter = 0; iter < maxiter; iter++) {
|
||
int m;
|
||
for (m = ell; m <= 1; m++) {
|
||
float dd = fabsf(diag[m]) + fabsf(diag[m + 1]);
|
||
if (fabsf(subd[m]) + dd == dd)
|
||
break;
|
||
}
|
||
if (m == ell)
|
||
break;
|
||
float g = (diag[ell + 1] - diag[ell]) / (2 * subd[ell]);
|
||
float r = sqrtf(g * g + 1);
|
||
if (g < 0)
|
||
g = diag[m] - diag[ell] + subd[ell] / (g - r);
|
||
else
|
||
g = diag[m] - diag[ell] + subd[ell] / (g + r);
|
||
float s = 1, c = 1, p = 0;
|
||
for (int i = m - 1; i >= ell; i--) {
|
||
float f = s * subd[i], b = c * subd[i];
|
||
if (fabsf(f) >= fabsf(g)) {
|
||
c = g / f;
|
||
r = sqrtf(c * c + 1);
|
||
subd[i + 1] = f * r;
|
||
c *= (s = 1 / r);
|
||
} else {
|
||
s = f / g;
|
||
r = sqrtf(s * s + 1);
|
||
subd[i + 1] = g * r;
|
||
s *= (c = 1 / r);
|
||
}
|
||
g = diag[i + 1] - p;
|
||
r = (diag[i] - g) * s + 2 * b * c;
|
||
p = s * r;
|
||
diag[i + 1] = g + p;
|
||
g = c * r - b;
|
||
for (int k = 0; k < 3; k++) {
|
||
f = mat[k][i + 1];
|
||
mat[k][i + 1] = s * mat[k][i] + c * f;
|
||
mat[k][i] = c * mat[k][i] - s * f;
|
||
}
|
||
}
|
||
diag[ell] -= p;
|
||
subd[ell] = g;
|
||
subd[m] = 0;
|
||
}
|
||
if (iter == maxiter)
|
||
// should not get here under normal circumstances
|
||
return false;
|
||
}
|
||
return true;
|
||
}
|
||
};
|
||
|
||
/// Fixed size vector class.
|
||
class FullVector {
|
||
public:
|
||
FullVector(uint32_t dim) { m_array.resize(dim); }
|
||
FullVector(const FullVector &v) :
|
||
m_array(v.m_array) {}
|
||
|
||
const FullVector &operator=(const FullVector &v) {
|
||
xaAssert(dimension() == v.dimension());
|
||
m_array = v.m_array;
|
||
return *this;
|
||
}
|
||
|
||
uint32_t dimension() const { return m_array.size(); }
|
||
const float &operator[](uint32_t index) const { return m_array[index]; }
|
||
float &operator[](uint32_t index) { return m_array[index]; }
|
||
|
||
void fill(float f) {
|
||
const uint32_t dim = dimension();
|
||
for (uint32_t i = 0; i < dim; i++) {
|
||
m_array[i] = f;
|
||
}
|
||
}
|
||
|
||
void operator+=(const FullVector &v) {
|
||
xaDebugAssert(dimension() == v.dimension());
|
||
const uint32_t dim = dimension();
|
||
for (uint32_t i = 0; i < dim; i++) {
|
||
m_array[i] += v.m_array[i];
|
||
}
|
||
}
|
||
|
||
void operator-=(const FullVector &v) {
|
||
xaDebugAssert(dimension() == v.dimension());
|
||
const uint32_t dim = dimension();
|
||
for (uint32_t i = 0; i < dim; i++) {
|
||
m_array[i] -= v.m_array[i];
|
||
}
|
||
}
|
||
|
||
void operator*=(const FullVector &v) {
|
||
xaDebugAssert(dimension() == v.dimension());
|
||
const uint32_t dim = dimension();
|
||
for (uint32_t i = 0; i < dim; i++) {
|
||
m_array[i] *= v.m_array[i];
|
||
}
|
||
}
|
||
|
||
void operator+=(float f) {
|
||
const uint32_t dim = dimension();
|
||
for (uint32_t i = 0; i < dim; i++) {
|
||
m_array[i] += f;
|
||
}
|
||
}
|
||
|
||
void operator-=(float f) {
|
||
const uint32_t dim = dimension();
|
||
for (uint32_t i = 0; i < dim; i++) {
|
||
m_array[i] -= f;
|
||
}
|
||
}
|
||
|
||
void operator*=(float f) {
|
||
const uint32_t dim = dimension();
|
||
for (uint32_t i = 0; i < dim; i++) {
|
||
m_array[i] *= f;
|
||
}
|
||
}
|
||
|
||
private:
|
||
std::vector<float> m_array;
|
||
};
|
||
|
||
namespace halfedge {
|
||
class Face;
|
||
class Vertex;
|
||
|
||
class Edge {
|
||
public:
|
||
uint32_t id;
|
||
Edge *next;
|
||
Edge *prev; // This is not strictly half-edge, but makes algorithms easier and faster.
|
||
Edge *pair;
|
||
Vertex *vertex;
|
||
Face *face;
|
||
|
||
// Default constructor.
|
||
Edge(uint32_t id) :
|
||
id(id),
|
||
next(NULL),
|
||
prev(NULL),
|
||
pair(NULL),
|
||
vertex(NULL),
|
||
face(NULL) {}
|
||
|
||
// Vertex queries.
|
||
const Vertex *from() const {
|
||
return vertex;
|
||
}
|
||
|
||
Vertex *from() {
|
||
return vertex;
|
||
}
|
||
|
||
const Vertex *to() const {
|
||
return pair->vertex; // This used to be 'next->vertex', but that changed often when the connectivity of the mesh changes.
|
||
}
|
||
|
||
Vertex *to() {
|
||
return pair->vertex;
|
||
}
|
||
|
||
// Edge queries.
|
||
void setNext(Edge *e) {
|
||
next = e;
|
||
if (e != NULL) e->prev = this;
|
||
}
|
||
void setPrev(Edge *e) {
|
||
prev = e;
|
||
if (e != NULL) e->next = this;
|
||
}
|
||
|
||
// @@ It would be more simple to only check m_pair == NULL
|
||
// Face queries.
|
||
bool isBoundary() const {
|
||
return !(face && pair->face);
|
||
}
|
||
|
||
// @@ This is not exactly accurate, we should compare the texture coordinates...
|
||
bool isSeam() const {
|
||
return vertex != pair->next->vertex || next->vertex != pair->vertex;
|
||
}
|
||
|
||
bool isNormalSeam() const;
|
||
bool isTextureSeam() const;
|
||
|
||
bool isValid() const {
|
||
// null face is OK.
|
||
if (next == NULL || prev == NULL || pair == NULL || vertex == NULL) return false;
|
||
if (next->prev != this) return false;
|
||
if (prev->next != this) return false;
|
||
if (pair->pair != this) return false;
|
||
return true;
|
||
}
|
||
|
||
float length() const;
|
||
|
||
// Return angle between this edge and the previous one.
|
||
float angle() const;
|
||
};
|
||
|
||
class Vertex {
|
||
public:
|
||
uint32_t id;
|
||
uint32_t original_id;
|
||
Edge *edge;
|
||
Vertex *next;
|
||
Vertex *prev;
|
||
Vector3 pos;
|
||
Vector3 nor;
|
||
Vector2 tex;
|
||
|
||
Vertex(uint32_t id) :
|
||
id(id),
|
||
original_id(id),
|
||
edge(NULL),
|
||
pos(0.0f),
|
||
nor(0.0f),
|
||
tex(0.0f) {
|
||
next = this;
|
||
prev = this;
|
||
}
|
||
|
||
// Set first edge of all colocals.
|
||
void setEdge(Edge *e) {
|
||
for (VertexIterator it(colocals()); !it.isDone(); it.advance()) {
|
||
it.current()->edge = e;
|
||
}
|
||
}
|
||
|
||
// Update position of all colocals.
|
||
void setPos(const Vector3 &p) {
|
||
for (VertexIterator it(colocals()); !it.isDone(); it.advance()) {
|
||
it.current()->pos = p;
|
||
}
|
||
}
|
||
|
||
bool isFirstColocal() const {
|
||
return firstColocal() == this;
|
||
}
|
||
|
||
const Vertex *firstColocal() const {
|
||
uint32_t firstId = id;
|
||
const Vertex *vertex = this;
|
||
for (ConstVertexIterator it(colocals()); !it.isDone(); it.advance()) {
|
||
if (it.current()->id < firstId) {
|
||
firstId = vertex->id;
|
||
vertex = it.current();
|
||
}
|
||
}
|
||
return vertex;
|
||
}
|
||
|
||
Vertex *firstColocal() {
|
||
Vertex *vertex = this;
|
||
uint32_t firstId = id;
|
||
for (VertexIterator it(colocals()); !it.isDone(); it.advance()) {
|
||
if (it.current()->id < firstId) {
|
||
firstId = vertex->id;
|
||
vertex = it.current();
|
||
}
|
||
}
|
||
return vertex;
|
||
}
|
||
|
||
bool isColocal(const Vertex *v) const {
|
||
if (this == v) return true;
|
||
if (pos != v->pos) return false;
|
||
for (ConstVertexIterator it(colocals()); !it.isDone(); it.advance()) {
|
||
if (v == it.current()) {
|
||
return true;
|
||
}
|
||
}
|
||
return false;
|
||
}
|
||
|
||
void linkColocal(Vertex *v) {
|
||
next->prev = v;
|
||
v->next = next;
|
||
next = v;
|
||
v->prev = this;
|
||
}
|
||
void unlinkColocal() {
|
||
next->prev = prev;
|
||
prev->next = next;
|
||
next = this;
|
||
prev = this;
|
||
}
|
||
|
||
// @@ Note: This only works if linkBoundary has been called.
|
||
bool isBoundary() const {
|
||
return (edge && !edge->face);
|
||
}
|
||
|
||
// Iterator that visits the edges around this vertex in counterclockwise order.
|
||
class EdgeIterator //: public Iterator<Edge *>
|
||
{
|
||
public:
|
||
EdgeIterator(Edge *e) :
|
||
m_end(NULL),
|
||
m_current(e) {}
|
||
|
||
virtual void advance() {
|
||
if (m_end == NULL) m_end = m_current;
|
||
m_current = m_current->pair->next;
|
||
//m_current = m_current->prev->pair;
|
||
}
|
||
|
||
virtual bool isDone() const {
|
||
return m_end == m_current;
|
||
}
|
||
virtual Edge *current() const {
|
||
return m_current;
|
||
}
|
||
Vertex *vertex() const {
|
||
return m_current->vertex;
|
||
}
|
||
|
||
private:
|
||
Edge *m_end;
|
||
Edge *m_current;
|
||
};
|
||
|
||
EdgeIterator edges() {
|
||
return EdgeIterator(edge);
|
||
}
|
||
EdgeIterator edges(Edge *e) {
|
||
return EdgeIterator(e);
|
||
}
|
||
|
||
// Iterator that visits the edges around this vertex in counterclockwise order.
|
||
class ConstEdgeIterator //: public Iterator<Edge *>
|
||
{
|
||
public:
|
||
ConstEdgeIterator(const Edge *e) :
|
||
m_end(NULL),
|
||
m_current(e) {}
|
||
ConstEdgeIterator(EdgeIterator it) :
|
||
m_end(NULL),
|
||
m_current(it.current()) {}
|
||
|
||
virtual void advance() {
|
||
if (m_end == NULL) m_end = m_current;
|
||
m_current = m_current->pair->next;
|
||
//m_current = m_current->prev->pair;
|
||
}
|
||
|
||
virtual bool isDone() const {
|
||
return m_end == m_current;
|
||
}
|
||
virtual const Edge *current() const {
|
||
return m_current;
|
||
}
|
||
const Vertex *vertex() const {
|
||
return m_current->to();
|
||
}
|
||
|
||
private:
|
||
const Edge *m_end;
|
||
const Edge *m_current;
|
||
};
|
||
|
||
ConstEdgeIterator edges() const {
|
||
return ConstEdgeIterator(edge);
|
||
}
|
||
ConstEdgeIterator edges(const Edge *e) const {
|
||
return ConstEdgeIterator(e);
|
||
}
|
||
|
||
// Iterator that visits all the colocal vertices.
|
||
class VertexIterator //: public Iterator<Edge *>
|
||
{
|
||
public:
|
||
VertexIterator(Vertex *v) :
|
||
m_end(NULL),
|
||
m_current(v) {}
|
||
|
||
virtual void advance() {
|
||
if (m_end == NULL) m_end = m_current;
|
||
m_current = m_current->next;
|
||
}
|
||
|
||
virtual bool isDone() const {
|
||
return m_end == m_current;
|
||
}
|
||
virtual Vertex *current() const {
|
||
return m_current;
|
||
}
|
||
|
||
private:
|
||
Vertex *m_end;
|
||
Vertex *m_current;
|
||
};
|
||
|
||
VertexIterator colocals() {
|
||
return VertexIterator(this);
|
||
}
|
||
|
||
// Iterator that visits all the colocal vertices.
|
||
class ConstVertexIterator //: public Iterator<Edge *>
|
||
{
|
||
public:
|
||
ConstVertexIterator(const Vertex *v) :
|
||
m_end(NULL),
|
||
m_current(v) {}
|
||
|
||
virtual void advance() {
|
||
if (m_end == NULL) m_end = m_current;
|
||
m_current = m_current->next;
|
||
}
|
||
|
||
virtual bool isDone() const {
|
||
return m_end == m_current;
|
||
}
|
||
virtual const Vertex *current() const {
|
||
return m_current;
|
||
}
|
||
|
||
private:
|
||
const Vertex *m_end;
|
||
const Vertex *m_current;
|
||
};
|
||
|
||
ConstVertexIterator colocals() const {
|
||
return ConstVertexIterator(this);
|
||
}
|
||
};
|
||
|
||
bool Edge::isNormalSeam() const {
|
||
return (vertex->nor != pair->next->vertex->nor || next->vertex->nor != pair->vertex->nor);
|
||
}
|
||
|
||
bool Edge::isTextureSeam() const {
|
||
return (vertex->tex != pair->next->vertex->tex || next->vertex->tex != pair->vertex->tex);
|
||
}
|
||
|
||
float Edge::length() const {
|
||
return internal::length(to()->pos - from()->pos);
|
||
}
|
||
|
||
float Edge::angle() const {
|
||
Vector3 p = vertex->pos;
|
||
Vector3 a = prev->vertex->pos;
|
||
Vector3 b = next->vertex->pos;
|
||
Vector3 v0 = a - p;
|
||
Vector3 v1 = b - p;
|
||
return acosf(dot(v0, v1) / (internal::length(v0) * internal::length(v1)));
|
||
}
|
||
|
||
class Face {
|
||
public:
|
||
uint32_t id;
|
||
uint16_t group;
|
||
uint16_t material;
|
||
Edge *edge;
|
||
|
||
Face(uint32_t id) :
|
||
id(id),
|
||
group(uint16_t(~0)),
|
||
material(uint16_t(~0)),
|
||
edge(NULL) {}
|
||
|
||
float area() const {
|
||
float area = 0;
|
||
const Vector3 &v0 = edge->from()->pos;
|
||
for (ConstEdgeIterator it(edges(edge->next)); it.current() != edge->prev; it.advance()) {
|
||
const Edge *e = it.current();
|
||
const Vector3 &v1 = e->vertex->pos;
|
||
const Vector3 &v2 = e->next->vertex->pos;
|
||
area += length(cross(v1 - v0, v2 - v0));
|
||
}
|
||
return area * 0.5f;
|
||
}
|
||
|
||
float parametricArea() const {
|
||
float area = 0;
|
||
const Vector2 &v0 = edge->from()->tex;
|
||
for (ConstEdgeIterator it(edges(edge->next)); it.current() != edge->prev; it.advance()) {
|
||
const Edge *e = it.current();
|
||
const Vector2 &v1 = e->vertex->tex;
|
||
const Vector2 &v2 = e->next->vertex->tex;
|
||
area += triangleArea(v0, v1, v2);
|
||
}
|
||
return area * 0.5f;
|
||
}
|
||
|
||
Vector3 normal() const {
|
||
Vector3 n(0);
|
||
const Vertex *vertex0 = NULL;
|
||
for (ConstEdgeIterator it(edges()); !it.isDone(); it.advance()) {
|
||
const Edge *e = it.current();
|
||
xaAssert(e != NULL);
|
||
if (vertex0 == NULL) {
|
||
vertex0 = e->vertex;
|
||
} else if (e->next->vertex != vertex0) {
|
||
const halfedge::Vertex *vertex1 = e->from();
|
||
const halfedge::Vertex *vertex2 = e->to();
|
||
const Vector3 &p0 = vertex0->pos;
|
||
const Vector3 &p1 = vertex1->pos;
|
||
const Vector3 &p2 = vertex2->pos;
|
||
Vector3 v10 = p1 - p0;
|
||
Vector3 v20 = p2 - p0;
|
||
n += cross(v10, v20);
|
||
}
|
||
}
|
||
return normalizeSafe(n, Vector3(0, 0, 1), 0.0f);
|
||
}
|
||
|
||
Vector3 centroid() const {
|
||
Vector3 sum(0.0f);
|
||
uint32_t count = 0;
|
||
for (ConstEdgeIterator it(edges()); !it.isDone(); it.advance()) {
|
||
const Edge *e = it.current();
|
||
sum += e->from()->pos;
|
||
count++;
|
||
}
|
||
return sum / float(count);
|
||
}
|
||
|
||
// Unnormalized face normal assuming it's a triangle.
|
||
Vector3 triangleNormal() const {
|
||
Vector3 p0 = edge->vertex->pos;
|
||
Vector3 p1 = edge->next->vertex->pos;
|
||
Vector3 p2 = edge->next->next->vertex->pos;
|
||
Vector3 e0 = p2 - p0;
|
||
Vector3 e1 = p1 - p0;
|
||
return normalizeSafe(cross(e0, e1), Vector3(0), 0.0f);
|
||
}
|
||
|
||
Vector3 triangleNormalAreaScaled() const {
|
||
Vector3 p0 = edge->vertex->pos;
|
||
Vector3 p1 = edge->next->vertex->pos;
|
||
Vector3 p2 = edge->next->next->vertex->pos;
|
||
Vector3 e0 = p2 - p0;
|
||
Vector3 e1 = p1 - p0;
|
||
return cross(e0, e1);
|
||
}
|
||
|
||
// Average of the edge midpoints weighted by the edge length.
|
||
// I want a point inside the triangle, but closer to the cirumcenter.
|
||
Vector3 triangleCenter() const {
|
||
Vector3 p0 = edge->vertex->pos;
|
||
Vector3 p1 = edge->next->vertex->pos;
|
||
Vector3 p2 = edge->next->next->vertex->pos;
|
||
float l0 = length(p1 - p0);
|
||
float l1 = length(p2 - p1);
|
||
float l2 = length(p0 - p2);
|
||
Vector3 m0 = (p0 + p1) * l0 / (l0 + l1 + l2);
|
||
Vector3 m1 = (p1 + p2) * l1 / (l0 + l1 + l2);
|
||
Vector3 m2 = (p2 + p0) * l2 / (l0 + l1 + l2);
|
||
return m0 + m1 + m2;
|
||
}
|
||
|
||
bool isValid() const {
|
||
uint32_t count = 0;
|
||
for (ConstEdgeIterator it(edges()); !it.isDone(); it.advance()) {
|
||
const Edge *e = it.current();
|
||
if (e->face != this) return false;
|
||
if (!e->isValid()) return false;
|
||
if (!e->pair->isValid()) return false;
|
||
count++;
|
||
}
|
||
if (count < 3) return false;
|
||
return true;
|
||
}
|
||
|
||
bool contains(const Edge *e) const {
|
||
for (ConstEdgeIterator it(edges()); !it.isDone(); it.advance()) {
|
||
if (it.current() == e) return true;
|
||
}
|
||
return false;
|
||
}
|
||
|
||
uint32_t edgeCount() const {
|
||
uint32_t count = 0;
|
||
for (ConstEdgeIterator it(edges()); !it.isDone(); it.advance()) {
|
||
++count;
|
||
}
|
||
return count;
|
||
}
|
||
|
||
// The iterator that visits the edges of this face in clockwise order.
|
||
class EdgeIterator //: public Iterator<Edge *>
|
||
{
|
||
public:
|
||
EdgeIterator(Edge *e) :
|
||
m_end(NULL),
|
||
m_current(e) {}
|
||
|
||
virtual void advance() {
|
||
if (m_end == NULL) m_end = m_current;
|
||
m_current = m_current->next;
|
||
}
|
||
|
||
virtual bool isDone() const {
|
||
return m_end == m_current;
|
||
}
|
||
virtual Edge *current() const {
|
||
return m_current;
|
||
}
|
||
Vertex *vertex() const {
|
||
return m_current->vertex;
|
||
}
|
||
|
||
private:
|
||
Edge *m_end;
|
||
Edge *m_current;
|
||
};
|
||
|
||
EdgeIterator edges() {
|
||
return EdgeIterator(edge);
|
||
}
|
||
EdgeIterator edges(Edge *e) {
|
||
xaDebugAssert(contains(e));
|
||
return EdgeIterator(e);
|
||
}
|
||
|
||
// The iterator that visits the edges of this face in clockwise order.
|
||
class ConstEdgeIterator //: public Iterator<const Edge *>
|
||
{
|
||
public:
|
||
ConstEdgeIterator(const Edge *e) :
|
||
m_end(NULL),
|
||
m_current(e) {}
|
||
ConstEdgeIterator(const EdgeIterator &it) :
|
||
m_end(NULL),
|
||
m_current(it.current()) {}
|
||
|
||
virtual void advance() {
|
||
if (m_end == NULL) m_end = m_current;
|
||
m_current = m_current->next;
|
||
}
|
||
|
||
virtual bool isDone() const {
|
||
return m_end == m_current;
|
||
}
|
||
virtual const Edge *current() const {
|
||
return m_current;
|
||
}
|
||
const Vertex *vertex() const {
|
||
return m_current->vertex;
|
||
}
|
||
|
||
private:
|
||
const Edge *m_end;
|
||
const Edge *m_current;
|
||
};
|
||
|
||
ConstEdgeIterator edges() const {
|
||
return ConstEdgeIterator(edge);
|
||
}
|
||
ConstEdgeIterator edges(const Edge *e) const {
|
||
xaDebugAssert(contains(e));
|
||
return ConstEdgeIterator(e);
|
||
}
|
||
};
|
||
|
||
/// Simple half edge mesh designed for dynamic mesh manipulation.
|
||
class Mesh {
|
||
public:
|
||
Mesh() :
|
||
m_colocalVertexCount(0) {}
|
||
|
||
Mesh(const Mesh *mesh) {
|
||
// Copy mesh vertices.
|
||
const uint32_t vertexCount = mesh->vertexCount();
|
||
m_vertexArray.resize(vertexCount);
|
||
for (uint32_t v = 0; v < vertexCount; v++) {
|
||
const Vertex *vertex = mesh->vertexAt(v);
|
||
xaDebugAssert(vertex->id == v);
|
||
m_vertexArray[v] = new Vertex(v);
|
||
m_vertexArray[v]->pos = vertex->pos;
|
||
m_vertexArray[v]->nor = vertex->nor;
|
||
m_vertexArray[v]->tex = vertex->tex;
|
||
}
|
||
m_colocalVertexCount = vertexCount;
|
||
// Copy mesh faces.
|
||
const uint32_t faceCount = mesh->faceCount();
|
||
std::vector<uint32_t> indexArray;
|
||
indexArray.reserve(3);
|
||
for (uint32_t f = 0; f < faceCount; f++) {
|
||
const Face *face = mesh->faceAt(f);
|
||
for (Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const Vertex *vertex = it.current()->from();
|
||
indexArray.push_back(vertex->id);
|
||
}
|
||
addFace(indexArray);
|
||
indexArray.clear();
|
||
}
|
||
}
|
||
|
||
~Mesh() {
|
||
clear();
|
||
}
|
||
|
||
void clear() {
|
||
for (size_t i = 0; i < m_vertexArray.size(); i++)
|
||
delete m_vertexArray[i];
|
||
m_vertexArray.clear();
|
||
for (auto it = m_edgeMap.begin(); it != m_edgeMap.end(); it++)
|
||
delete it->second;
|
||
m_edgeArray.clear();
|
||
m_edgeMap.clear();
|
||
for (size_t i = 0; i < m_faceArray.size(); i++)
|
||
delete m_faceArray[i];
|
||
m_faceArray.clear();
|
||
}
|
||
|
||
Vertex *addVertex(const Vector3 &pos) {
|
||
xaDebugAssert(isFinite(pos));
|
||
Vertex *v = new Vertex(m_vertexArray.size());
|
||
v->pos = pos;
|
||
m_vertexArray.push_back(v);
|
||
return v;
|
||
}
|
||
|
||
/// Link colocal vertices based on geometric location only.
|
||
void linkColocals() {
|
||
xaPrint("--- Linking colocals:\n");
|
||
const uint32_t vertexCount = this->vertexCount();
|
||
std::unordered_map<Vector3, Vertex *, Hash<Vector3>, Equal<Vector3> > vertexMap;
|
||
vertexMap.reserve(vertexCount);
|
||
for (uint32_t v = 0; v < vertexCount; v++) {
|
||
Vertex *vertex = vertexAt(v);
|
||
Vertex *colocal = vertexMap[vertex->pos];
|
||
if (colocal) {
|
||
colocal->linkColocal(vertex);
|
||
} else {
|
||
vertexMap[vertex->pos] = vertex;
|
||
}
|
||
}
|
||
m_colocalVertexCount = vertexMap.size();
|
||
xaPrint("--- %d vertex positions.\n", m_colocalVertexCount);
|
||
// @@ Remove duplicated vertices? or just leave them as colocals?
|
||
}
|
||
|
||
void linkColocalsWithCanonicalMap(const std::vector<uint32_t> &canonicalMap) {
|
||
xaPrint("--- Linking colocals:\n");
|
||
uint32_t vertexMapSize = 0;
|
||
for (uint32_t i = 0; i < canonicalMap.size(); i++) {
|
||
vertexMapSize = std::max(vertexMapSize, canonicalMap[i] + 1);
|
||
}
|
||
std::vector<Vertex *> vertexMap;
|
||
vertexMap.resize(vertexMapSize, NULL);
|
||
m_colocalVertexCount = 0;
|
||
const uint32_t vertexCount = this->vertexCount();
|
||
for (uint32_t v = 0; v < vertexCount; v++) {
|
||
Vertex *vertex = vertexAt(v);
|
||
Vertex *colocal = vertexMap[canonicalMap[v]];
|
||
if (colocal != NULL) {
|
||
xaDebugAssert(vertex->pos == colocal->pos);
|
||
colocal->linkColocal(vertex);
|
||
} else {
|
||
vertexMap[canonicalMap[v]] = vertex;
|
||
m_colocalVertexCount++;
|
||
}
|
||
}
|
||
xaPrint("--- %d vertex positions.\n", m_colocalVertexCount);
|
||
}
|
||
|
||
Face *addFace() {
|
||
Face *f = new Face(m_faceArray.size());
|
||
m_faceArray.push_back(f);
|
||
return f;
|
||
}
|
||
|
||
Face *addFace(uint32_t v0, uint32_t v1, uint32_t v2) {
|
||
uint32_t indexArray[3];
|
||
indexArray[0] = v0;
|
||
indexArray[1] = v1;
|
||
indexArray[2] = v2;
|
||
return addFace(indexArray, 3, 0, 3);
|
||
}
|
||
|
||
Face *addUniqueFace(uint32_t v0, uint32_t v1, uint32_t v2) {
|
||
|
||
int base_vertex = m_vertexArray.size();
|
||
|
||
uint32_t ids[3] = { v0, v1, v2 };
|
||
|
||
Vector3 base[3] = {
|
||
m_vertexArray[v0]->pos,
|
||
m_vertexArray[v1]->pos,
|
||
m_vertexArray[v2]->pos,
|
||
};
|
||
|
||
//make sure its not a degenerate
|
||
bool degenerate = distanceSquared(base[0], base[1]) < NV_EPSILON || distanceSquared(base[0], base[2]) < NV_EPSILON || distanceSquared(base[1], base[2]) < NV_EPSILON;
|
||
xaDebugAssert(!degenerate);
|
||
|
||
float min_x = 0;
|
||
|
||
for (int i = 0; i < 3; i++) {
|
||
if (i == 0 || m_vertexArray[v0]->pos.x < min_x) {
|
||
min_x = m_vertexArray[v0]->pos.x;
|
||
}
|
||
}
|
||
|
||
float max_x = 0;
|
||
|
||
for (int j = 0; j < m_vertexArray.size(); j++) {
|
||
if (j == 0 || m_vertexArray[j]->pos.x > max_x) { //vertex already exists
|
||
max_x = m_vertexArray[j]->pos.x;
|
||
}
|
||
}
|
||
|
||
//separate from everything else, in x axis
|
||
for (int i = 0; i < 3; i++) {
|
||
|
||
base[i].x -= min_x;
|
||
base[i].x += max_x + 10.0;
|
||
}
|
||
|
||
for (int i = 0; i < 3; i++) {
|
||
Vertex *v = new Vertex(m_vertexArray.size());
|
||
v->pos = base[i];
|
||
v->nor = m_vertexArray[ids[i]]->nor,
|
||
v->tex = m_vertexArray[ids[i]]->tex,
|
||
|
||
v->original_id = ids[i];
|
||
m_vertexArray.push_back(v);
|
||
}
|
||
|
||
uint32_t indexArray[3];
|
||
indexArray[0] = base_vertex + 0;
|
||
indexArray[1] = base_vertex + 1;
|
||
indexArray[2] = base_vertex + 2;
|
||
return addFace(indexArray, 3, 0, 3);
|
||
}
|
||
|
||
Face *addFace(uint32_t v0, uint32_t v1, uint32_t v2, uint32_t v3) {
|
||
uint32_t indexArray[4];
|
||
indexArray[0] = v0;
|
||
indexArray[1] = v1;
|
||
indexArray[2] = v2;
|
||
indexArray[3] = v3;
|
||
return addFace(indexArray, 4, 0, 4);
|
||
}
|
||
|
||
Face *addFace(const std::vector<uint32_t> &indexArray) {
|
||
return addFace(indexArray, 0, indexArray.size());
|
||
}
|
||
|
||
Face *addFace(const std::vector<uint32_t> &indexArray, uint32_t first, uint32_t num) {
|
||
return addFace(indexArray.data(), (uint32_t)indexArray.size(), first, num);
|
||
}
|
||
|
||
Face *addFace(const uint32_t *indexArray, uint32_t indexCount, uint32_t first, uint32_t num) {
|
||
xaDebugAssert(first < indexCount);
|
||
xaDebugAssert(num <= indexCount - first);
|
||
xaDebugAssert(num > 2);
|
||
if (!canAddFace(indexArray, first, num)) {
|
||
return NULL;
|
||
}
|
||
Face *f = new Face(m_faceArray.size());
|
||
Edge *firstEdge = NULL;
|
||
Edge *last = NULL;
|
||
Edge *current = NULL;
|
||
for (uint32_t i = 0; i < num - 1; i++) {
|
||
current = addEdge(indexArray[first + i], indexArray[first + i + 1]);
|
||
xaAssert(current != NULL && current->face == NULL);
|
||
current->face = f;
|
||
if (last != NULL)
|
||
last->setNext(current);
|
||
else
|
||
firstEdge = current;
|
||
last = current;
|
||
}
|
||
current = addEdge(indexArray[first + num - 1], indexArray[first]);
|
||
xaAssert(current != NULL && current->face == NULL);
|
||
current->face = f;
|
||
last->setNext(current);
|
||
current->setNext(firstEdge);
|
||
f->edge = firstEdge;
|
||
m_faceArray.push_back(f);
|
||
return f;
|
||
}
|
||
|
||
// These functions disconnect the given element from the mesh and delete it.
|
||
|
||
// @@ We must always disconnect edge pairs simultaneously.
|
||
void disconnect(Edge *edge) {
|
||
xaDebugAssert(edge != NULL);
|
||
// Remove from edge list.
|
||
if ((edge->id & 1) == 0) {
|
||
xaDebugAssert(m_edgeArray[edge->id / 2] == edge);
|
||
m_edgeArray[edge->id / 2] = NULL;
|
||
}
|
||
// Remove edge from map. @@ Store map key inside edge?
|
||
xaDebugAssert(edge->from() != NULL && edge->to() != NULL);
|
||
size_t removed = m_edgeMap.erase(Key(edge->from()->id, edge->to()->id));
|
||
xaDebugAssert(removed == 1);
|
||
#ifdef NDEBUG
|
||
removed = 0; // silence unused parameter warning
|
||
#endif
|
||
// Disconnect from vertex.
|
||
if (edge->vertex != NULL) {
|
||
if (edge->vertex->edge == edge) {
|
||
if (edge->prev && edge->prev->pair) {
|
||
edge->vertex->edge = edge->prev->pair;
|
||
} else if (edge->pair && edge->pair->next) {
|
||
edge->vertex->edge = edge->pair->next;
|
||
} else {
|
||
edge->vertex->edge = NULL;
|
||
// @@ Remove disconnected vertex?
|
||
}
|
||
}
|
||
}
|
||
// Disconnect from face.
|
||
if (edge->face != NULL) {
|
||
if (edge->face->edge == edge) {
|
||
if (edge->next != NULL && edge->next != edge) {
|
||
edge->face->edge = edge->next;
|
||
} else if (edge->prev != NULL && edge->prev != edge) {
|
||
edge->face->edge = edge->prev;
|
||
} else {
|
||
edge->face->edge = NULL;
|
||
// @@ Remove disconnected face?
|
||
}
|
||
}
|
||
}
|
||
// Disconnect from previous.
|
||
if (edge->prev) {
|
||
if (edge->prev->next == edge) {
|
||
edge->prev->setNext(NULL);
|
||
}
|
||
//edge->setPrev(NULL);
|
||
}
|
||
// Disconnect from next.
|
||
if (edge->next) {
|
||
if (edge->next->prev == edge) {
|
||
edge->next->setPrev(NULL);
|
||
}
|
||
//edge->setNext(NULL);
|
||
}
|
||
}
|
||
|
||
void remove(Edge *edge) {
|
||
xaDebugAssert(edge != NULL);
|
||
disconnect(edge);
|
||
delete edge;
|
||
}
|
||
|
||
void remove(Vertex *vertex) {
|
||
xaDebugAssert(vertex != NULL);
|
||
// Remove from vertex list.
|
||
m_vertexArray[vertex->id] = NULL;
|
||
// Disconnect from colocals.
|
||
vertex->unlinkColocal();
|
||
// Disconnect from edges.
|
||
if (vertex->edge != NULL) {
|
||
// @@ Removing a connected vertex is asking for trouble...
|
||
if (vertex->edge->vertex == vertex) {
|
||
// @@ Connect edge to a colocal?
|
||
vertex->edge->vertex = NULL;
|
||
}
|
||
vertex->setEdge(NULL);
|
||
}
|
||
delete vertex;
|
||
}
|
||
|
||
void remove(Face *face) {
|
||
xaDebugAssert(face != NULL);
|
||
// Remove from face list.
|
||
m_faceArray[face->id] = NULL;
|
||
// Disconnect from edges.
|
||
if (face->edge != NULL) {
|
||
xaDebugAssert(face->edge->face == face);
|
||
face->edge->face = NULL;
|
||
face->edge = NULL;
|
||
}
|
||
delete face;
|
||
}
|
||
|
||
// Triangulate in place.
|
||
void triangulate() {
|
||
bool all_triangles = true;
|
||
const uint32_t faceCount = m_faceArray.size();
|
||
for (uint32_t f = 0; f < faceCount; f++) {
|
||
Face *face = m_faceArray[f];
|
||
if (face->edgeCount() != 3) {
|
||
all_triangles = false;
|
||
break;
|
||
}
|
||
}
|
||
if (all_triangles) {
|
||
return;
|
||
}
|
||
// Do not touch vertices, but rebuild edges and faces.
|
||
std::vector<Edge *> edgeArray;
|
||
std::vector<Face *> faceArray;
|
||
std::swap(edgeArray, m_edgeArray);
|
||
std::swap(faceArray, m_faceArray);
|
||
m_edgeMap.clear();
|
||
for (uint32_t f = 0; f < faceCount; f++) {
|
||
Face *face = faceArray[f];
|
||
// Trivial fan-like triangulation.
|
||
const uint32_t v0 = face->edge->vertex->id;
|
||
uint32_t v2, v1 = (uint32_t)-1;
|
||
for (Face::EdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
Edge *edge = it.current();
|
||
v2 = edge->to()->id;
|
||
if (v2 == v0) break;
|
||
if (v1 != -1) addFace(v0, v1, v2);
|
||
v1 = v2;
|
||
}
|
||
}
|
||
xaDebugAssert(m_faceArray.size() > faceCount); // triangle count > face count
|
||
linkBoundary();
|
||
for (size_t i = 0; i < edgeArray.size(); i++)
|
||
delete edgeArray[i];
|
||
for (size_t i = 0; i < faceArray.size(); i++)
|
||
delete faceArray[i];
|
||
}
|
||
|
||
/// Link boundary edges once the mesh has been created.
|
||
void linkBoundary() {
|
||
xaPrint("--- Linking boundaries:\n");
|
||
int num = 0;
|
||
// Create boundary edges.
|
||
uint32_t edgeCount = this->edgeCount();
|
||
for (uint32_t e = 0; e < edgeCount; e++) {
|
||
Edge *edge = edgeAt(e);
|
||
if (edge != NULL && edge->pair == NULL) {
|
||
Edge *pair = new Edge(edge->id + 1);
|
||
uint32_t i = edge->from()->id;
|
||
uint32_t j = edge->next->from()->id;
|
||
Key key(j, i);
|
||
xaAssert(m_edgeMap.find(key) == m_edgeMap.end());
|
||
pair->vertex = m_vertexArray[j];
|
||
m_edgeMap[key] = pair;
|
||
edge->pair = pair;
|
||
pair->pair = edge;
|
||
num++;
|
||
}
|
||
}
|
||
// Link boundary edges.
|
||
for (uint32_t e = 0; e < edgeCount; e++) {
|
||
Edge *edge = edgeAt(e);
|
||
if (edge != NULL && edge->pair->face == NULL) {
|
||
linkBoundaryEdge(edge->pair);
|
||
}
|
||
}
|
||
xaPrint("--- %d boundary edges.\n", num);
|
||
}
|
||
|
||
/*
|
||
Fixing T-junctions.
|
||
|
||
- Find T-junctions. Find vertices that are on an edge.
|
||
- This test is approximate.
|
||
- Insert edges on a spatial index to speedup queries.
|
||
- Consider only open edges, that is edges that have no pairs.
|
||
- Consider only vertices on boundaries.
|
||
- Close T-junction.
|
||
- Split edge.
|
||
|
||
*/
|
||
bool splitBoundaryEdges() // Returns true if any split was made.
|
||
{
|
||
std::vector<Vertex *> boundaryVertices;
|
||
for (uint32_t i = 0; i < m_vertexArray.size(); i++) {
|
||
Vertex *v = m_vertexArray[i];
|
||
if (v->isBoundary()) {
|
||
boundaryVertices.push_back(v);
|
||
}
|
||
}
|
||
xaPrint("Fixing T-junctions:\n");
|
||
int splitCount = 0;
|
||
for (uint32_t v = 0; v < boundaryVertices.size(); v++) {
|
||
Vertex *vertex = boundaryVertices[v];
|
||
Vector3 x0 = vertex->pos;
|
||
// Find edges that this vertex overlaps with.
|
||
for (uint32_t e = 0; e < m_edgeArray.size(); e++) {
|
||
Edge *edge = m_edgeArray[e];
|
||
if (edge != NULL && edge->isBoundary()) {
|
||
if (edge->from() == vertex || edge->to() == vertex) {
|
||
continue;
|
||
}
|
||
Vector3 x1 = edge->from()->pos;
|
||
Vector3 x2 = edge->to()->pos;
|
||
Vector3 v01 = x0 - x1;
|
||
Vector3 v21 = x2 - x1;
|
||
float l = length(v21);
|
||
float d = length(cross(v01, v21)) / l;
|
||
if (isZero(d)) {
|
||
float t = dot(v01, v21) / (l * l);
|
||
if (t > 0.0f + NV_EPSILON && t < 1.0f - NV_EPSILON) {
|
||
xaDebugAssert(equal(lerp(x1, x2, t), x0));
|
||
Vertex *splitVertex = splitBoundaryEdge(edge, t, x0);
|
||
vertex->linkColocal(splitVertex); // @@ Should we do this here?
|
||
splitCount++;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
xaPrint(" - %d edges split.\n", splitCount);
|
||
xaDebugAssert(isValid());
|
||
return splitCount != 0;
|
||
}
|
||
|
||
// Vertices
|
||
uint32_t vertexCount() const {
|
||
return m_vertexArray.size();
|
||
}
|
||
const Vertex *vertexAt(int i) const {
|
||
return m_vertexArray[i];
|
||
}
|
||
Vertex *vertexAt(int i) {
|
||
return m_vertexArray[i];
|
||
}
|
||
|
||
uint32_t colocalVertexCount() const {
|
||
return m_colocalVertexCount;
|
||
}
|
||
|
||
// Faces
|
||
uint32_t faceCount() const {
|
||
return m_faceArray.size();
|
||
}
|
||
const Face *faceAt(int i) const {
|
||
return m_faceArray[i];
|
||
}
|
||
Face *faceAt(int i) {
|
||
return m_faceArray[i];
|
||
}
|
||
|
||
// Edges
|
||
uint32_t edgeCount() const {
|
||
return m_edgeArray.size();
|
||
}
|
||
const Edge *edgeAt(int i) const {
|
||
return m_edgeArray[i];
|
||
}
|
||
Edge *edgeAt(int i) {
|
||
return m_edgeArray[i];
|
||
}
|
||
|
||
class ConstVertexIterator;
|
||
|
||
class VertexIterator {
|
||
friend class ConstVertexIterator;
|
||
|
||
public:
|
||
VertexIterator(Mesh *mesh) :
|
||
m_mesh(mesh),
|
||
m_current(0) {}
|
||
|
||
virtual void advance() {
|
||
m_current++;
|
||
}
|
||
virtual bool isDone() const {
|
||
return m_current == m_mesh->vertexCount();
|
||
}
|
||
virtual Vertex *current() const {
|
||
return m_mesh->vertexAt(m_current);
|
||
}
|
||
|
||
private:
|
||
halfedge::Mesh *m_mesh;
|
||
uint32_t m_current;
|
||
};
|
||
VertexIterator vertices() {
|
||
return VertexIterator(this);
|
||
}
|
||
|
||
class ConstVertexIterator {
|
||
public:
|
||
ConstVertexIterator(const Mesh *mesh) :
|
||
m_mesh(mesh),
|
||
m_current(0) {}
|
||
ConstVertexIterator(class VertexIterator &it) :
|
||
m_mesh(it.m_mesh),
|
||
m_current(it.m_current) {}
|
||
|
||
virtual void advance() {
|
||
m_current++;
|
||
}
|
||
virtual bool isDone() const {
|
||
return m_current == m_mesh->vertexCount();
|
||
}
|
||
virtual const Vertex *current() const {
|
||
return m_mesh->vertexAt(m_current);
|
||
}
|
||
|
||
private:
|
||
const halfedge::Mesh *m_mesh;
|
||
uint32_t m_current;
|
||
};
|
||
ConstVertexIterator vertices() const {
|
||
return ConstVertexIterator(this);
|
||
}
|
||
|
||
class ConstFaceIterator;
|
||
|
||
class FaceIterator {
|
||
friend class ConstFaceIterator;
|
||
|
||
public:
|
||
FaceIterator(Mesh *mesh) :
|
||
m_mesh(mesh),
|
||
m_current(0) {}
|
||
|
||
virtual void advance() {
|
||
m_current++;
|
||
}
|
||
virtual bool isDone() const {
|
||
return m_current == m_mesh->faceCount();
|
||
}
|
||
virtual Face *current() const {
|
||
return m_mesh->faceAt(m_current);
|
||
}
|
||
|
||
private:
|
||
halfedge::Mesh *m_mesh;
|
||
uint32_t m_current;
|
||
};
|
||
FaceIterator faces() {
|
||
return FaceIterator(this);
|
||
}
|
||
|
||
class ConstFaceIterator {
|
||
public:
|
||
ConstFaceIterator(const Mesh *mesh) :
|
||
m_mesh(mesh),
|
||
m_current(0) {}
|
||
ConstFaceIterator(const FaceIterator &it) :
|
||
m_mesh(it.m_mesh),
|
||
m_current(it.m_current) {}
|
||
|
||
virtual void advance() {
|
||
m_current++;
|
||
}
|
||
virtual bool isDone() const {
|
||
return m_current == m_mesh->faceCount();
|
||
}
|
||
virtual const Face *current() const {
|
||
return m_mesh->faceAt(m_current);
|
||
}
|
||
|
||
private:
|
||
const halfedge::Mesh *m_mesh;
|
||
uint32_t m_current;
|
||
};
|
||
ConstFaceIterator faces() const {
|
||
return ConstFaceIterator(this);
|
||
}
|
||
|
||
class ConstEdgeIterator;
|
||
|
||
class EdgeIterator {
|
||
friend class ConstEdgeIterator;
|
||
|
||
public:
|
||
EdgeIterator(Mesh *mesh) :
|
||
m_mesh(mesh),
|
||
m_current(0) {}
|
||
|
||
virtual void advance() {
|
||
m_current++;
|
||
}
|
||
virtual bool isDone() const {
|
||
return m_current == m_mesh->edgeCount();
|
||
}
|
||
virtual Edge *current() const {
|
||
return m_mesh->edgeAt(m_current);
|
||
}
|
||
|
||
private:
|
||
halfedge::Mesh *m_mesh;
|
||
uint32_t m_current;
|
||
};
|
||
EdgeIterator edges() {
|
||
return EdgeIterator(this);
|
||
}
|
||
|
||
class ConstEdgeIterator {
|
||
public:
|
||
ConstEdgeIterator(const Mesh *mesh) :
|
||
m_mesh(mesh),
|
||
m_current(0) {}
|
||
ConstEdgeIterator(const EdgeIterator &it) :
|
||
m_mesh(it.m_mesh),
|
||
m_current(it.m_current) {}
|
||
|
||
virtual void advance() {
|
||
m_current++;
|
||
}
|
||
virtual bool isDone() const {
|
||
return m_current == m_mesh->edgeCount();
|
||
}
|
||
virtual const Edge *current() const {
|
||
return m_mesh->edgeAt(m_current);
|
||
}
|
||
|
||
private:
|
||
const halfedge::Mesh *m_mesh;
|
||
uint32_t m_current;
|
||
};
|
||
ConstEdgeIterator edges() const {
|
||
return ConstEdgeIterator(this);
|
||
}
|
||
|
||
// @@ Add half-edge iterator.
|
||
|
||
bool isValid() const {
|
||
// Make sure all edges are valid.
|
||
const uint32_t edgeCount = m_edgeArray.size();
|
||
for (uint32_t e = 0; e < edgeCount; e++) {
|
||
Edge *edge = m_edgeArray[e];
|
||
if (edge != NULL) {
|
||
if (edge->id != 2 * e) {
|
||
return false;
|
||
}
|
||
if (!edge->isValid()) {
|
||
return false;
|
||
}
|
||
if (edge->pair->id != 2 * e + 1) {
|
||
return false;
|
||
}
|
||
if (!edge->pair->isValid()) {
|
||
return false;
|
||
}
|
||
}
|
||
}
|
||
// @@ Make sure all faces are valid.
|
||
// @@ Make sure all vertices are valid.
|
||
return true;
|
||
}
|
||
|
||
// Error status:
|
||
|
||
struct ErrorCode {
|
||
enum Enum {
|
||
AlreadyAddedEdge,
|
||
DegenerateColocalEdge,
|
||
DegenerateEdge,
|
||
DuplicateEdge
|
||
};
|
||
};
|
||
|
||
mutable ErrorCode::Enum errorCode;
|
||
mutable uint32_t errorIndex0;
|
||
mutable uint32_t errorIndex1;
|
||
|
||
private:
|
||
// Return true if the face can be added to the manifold mesh.
|
||
bool canAddFace(const std::vector<uint32_t> &indexArray, uint32_t first, uint32_t num) const {
|
||
return canAddFace(indexArray.data(), first, num);
|
||
}
|
||
|
||
bool canAddFace(const uint32_t *indexArray, uint32_t first, uint32_t num) const {
|
||
for (uint32_t j = num - 1, i = 0; i < num; j = i++) {
|
||
if (!canAddEdge(indexArray[first + j], indexArray[first + i])) {
|
||
errorIndex0 = indexArray[first + j];
|
||
errorIndex1 = indexArray[first + i];
|
||
return false;
|
||
}
|
||
}
|
||
// We also have to make sure the face does not have any duplicate edge!
|
||
for (uint32_t i = 0; i < num; i++) {
|
||
int i0 = indexArray[first + i + 0];
|
||
int i1 = indexArray[first + (i + 1) % num];
|
||
for (uint32_t j = i + 1; j < num; j++) {
|
||
int j0 = indexArray[first + j + 0];
|
||
int j1 = indexArray[first + (j + 1) % num];
|
||
if (i0 == j0 && i1 == j1) {
|
||
errorCode = ErrorCode::DuplicateEdge;
|
||
errorIndex0 = i0;
|
||
errorIndex1 = i1;
|
||
return false;
|
||
}
|
||
}
|
||
}
|
||
return true;
|
||
}
|
||
|
||
// Return true if the edge doesn't exist or doesn't have any adjacent face.
|
||
bool canAddEdge(uint32_t i, uint32_t j) const {
|
||
if (i == j) {
|
||
// Skip degenerate edges.
|
||
errorCode = ErrorCode::DegenerateEdge;
|
||
return false;
|
||
}
|
||
// Same check, but taking into account colocal vertices.
|
||
const Vertex *v0 = vertexAt(i);
|
||
const Vertex *v1 = vertexAt(j);
|
||
for (Vertex::ConstVertexIterator it(v0->colocals()); !it.isDone(); it.advance()) {
|
||
if (it.current() == v1) {
|
||
// Skip degenerate edges.
|
||
errorCode = ErrorCode::DegenerateColocalEdge;
|
||
return false;
|
||
}
|
||
}
|
||
// Make sure edge has not been added yet.
|
||
Edge *edge = findEdge(i, j);
|
||
// We ignore edges that don't have an adjacent face yet, since this face could become the edge's face.
|
||
if (!(edge == NULL || edge->face == NULL)) {
|
||
errorCode = ErrorCode::AlreadyAddedEdge;
|
||
return false;
|
||
}
|
||
return true;
|
||
}
|
||
|
||
Edge *addEdge(uint32_t i, uint32_t j) {
|
||
xaAssert(i != j);
|
||
Edge *edge = findEdge(i, j);
|
||
if (edge != NULL) {
|
||
// Edge may already exist, but its face must not be set.
|
||
xaDebugAssert(edge->face == NULL);
|
||
// Nothing else to do!
|
||
} else {
|
||
// Add new edge.
|
||
// Lookup pair.
|
||
Edge *pair = findEdge(j, i);
|
||
if (pair != NULL) {
|
||
// Create edge with same id.
|
||
edge = new Edge(pair->id + 1);
|
||
// Link edge pairs.
|
||
edge->pair = pair;
|
||
pair->pair = edge;
|
||
// @@ I'm not sure this is necessary!
|
||
pair->vertex->setEdge(pair);
|
||
} else {
|
||
// Create edge.
|
||
edge = new Edge(2 * m_edgeArray.size());
|
||
// Add only unpaired edges.
|
||
m_edgeArray.push_back(edge);
|
||
}
|
||
edge->vertex = m_vertexArray[i];
|
||
m_edgeMap[Key(i, j)] = edge;
|
||
}
|
||
// Face and Next are set by addFace.
|
||
return edge;
|
||
}
|
||
|
||
/// Find edge, test all colocals.
|
||
Edge *findEdge(uint32_t i, uint32_t j) const {
|
||
Edge *edge = NULL;
|
||
const Vertex *v0 = vertexAt(i);
|
||
const Vertex *v1 = vertexAt(j);
|
||
// Test all colocal pairs.
|
||
for (Vertex::ConstVertexIterator it0(v0->colocals()); !it0.isDone(); it0.advance()) {
|
||
for (Vertex::ConstVertexIterator it1(v1->colocals()); !it1.isDone(); it1.advance()) {
|
||
Key key(it0.current()->id, it1.current()->id);
|
||
if (edge == NULL) {
|
||
auto edgeIt = m_edgeMap.find(key);
|
||
if (edgeIt != m_edgeMap.end())
|
||
edge = (*edgeIt).second;
|
||
#if !defined(_DEBUG)
|
||
if (edge != NULL) return edge;
|
||
#endif
|
||
} else {
|
||
// Make sure that only one edge is found.
|
||
xaDebugAssert(m_edgeMap.find(key) == m_edgeMap.end());
|
||
}
|
||
}
|
||
}
|
||
return edge;
|
||
}
|
||
|
||
/// Link this boundary edge.
|
||
void linkBoundaryEdge(Edge *edge) {
|
||
xaAssert(edge->face == NULL);
|
||
// Make sure next pointer has not been set. @@ We want to be able to relink boundary edges after mesh changes.
|
||
Edge *next = edge;
|
||
while (next->pair->face != NULL) {
|
||
// Get pair prev
|
||
Edge *e = next->pair->next;
|
||
while (e->next != next->pair) {
|
||
e = e->next;
|
||
}
|
||
next = e;
|
||
}
|
||
edge->setNext(next->pair);
|
||
// Adjust vertex edge, so that it's the boundary edge. (required for isBoundary())
|
||
if (edge->vertex->edge != edge) {
|
||
// Multiple boundaries in the same edge.
|
||
edge->vertex->edge = edge;
|
||
}
|
||
}
|
||
|
||
Vertex *splitBoundaryEdge(Edge *edge, float t, const Vector3 &pos) {
|
||
/*
|
||
We want to go from this configuration:
|
||
|
||
+ +
|
||
| ^
|
||
edge |<->| pair
|
||
v |
|
||
+ +
|
||
|
||
To this one:
|
||
|
||
+ +
|
||
| ^
|
||
e0 |<->| p0
|
||
v |
|
||
vertex + +
|
||
| ^
|
||
e1 |<->| p1
|
||
v |
|
||
+ +
|
||
|
||
*/
|
||
Edge *pair = edge->pair;
|
||
// Make sure boundaries are linked.
|
||
xaDebugAssert(pair != NULL);
|
||
// Make sure edge is a boundary edge.
|
||
xaDebugAssert(pair->face == NULL);
|
||
// Add new vertex.
|
||
Vertex *vertex = addVertex(pos);
|
||
vertex->nor = lerp(edge->from()->nor, edge->to()->nor, t);
|
||
vertex->tex = lerp(edge->from()->tex, edge->to()->tex, t);
|
||
disconnect(edge);
|
||
disconnect(pair);
|
||
// Add edges.
|
||
Edge *e0 = addEdge(edge->from()->id, vertex->id);
|
||
Edge *p0 = addEdge(vertex->id, pair->to()->id);
|
||
Edge *e1 = addEdge(vertex->id, edge->to()->id);
|
||
Edge *p1 = addEdge(pair->from()->id, vertex->id);
|
||
// Link edges.
|
||
e0->setNext(e1);
|
||
p1->setNext(p0);
|
||
e0->setPrev(edge->prev);
|
||
e1->setNext(edge->next);
|
||
p1->setPrev(pair->prev);
|
||
p0->setNext(pair->next);
|
||
xaDebugAssert(e0->next == e1);
|
||
xaDebugAssert(e1->prev == e0);
|
||
xaDebugAssert(p1->next == p0);
|
||
xaDebugAssert(p0->prev == p1);
|
||
xaDebugAssert(p0->pair == e0);
|
||
xaDebugAssert(e0->pair == p0);
|
||
xaDebugAssert(p1->pair == e1);
|
||
xaDebugAssert(e1->pair == p1);
|
||
// Link faces.
|
||
e0->face = edge->face;
|
||
e1->face = edge->face;
|
||
// Link vertices.
|
||
edge->from()->setEdge(e0);
|
||
vertex->setEdge(e1);
|
||
delete edge;
|
||
delete pair;
|
||
return vertex;
|
||
}
|
||
|
||
private:
|
||
std::vector<Vertex *> m_vertexArray;
|
||
std::vector<Edge *> m_edgeArray;
|
||
std::vector<Face *> m_faceArray;
|
||
|
||
struct Key {
|
||
Key() {}
|
||
Key(const Key &k) :
|
||
p0(k.p0),
|
||
p1(k.p1) {}
|
||
Key(uint32_t v0, uint32_t v1) :
|
||
p0(v0),
|
||
p1(v1) {}
|
||
void operator=(const Key &k) {
|
||
p0 = k.p0;
|
||
p1 = k.p1;
|
||
}
|
||
bool operator==(const Key &k) const {
|
||
return p0 == k.p0 && p1 == k.p1;
|
||
}
|
||
|
||
uint32_t p0;
|
||
uint32_t p1;
|
||
};
|
||
|
||
friend struct Hash<Mesh::Key>;
|
||
std::unordered_map<Key, Edge *, Hash<Key>, Equal<Key> > m_edgeMap;
|
||
uint32_t m_colocalVertexCount;
|
||
};
|
||
|
||
class MeshTopology {
|
||
public:
|
||
MeshTopology(const Mesh *mesh) {
|
||
buildTopologyInfo(mesh);
|
||
}
|
||
|
||
/// Determine if the mesh is connected.
|
||
bool isConnected() const {
|
||
return m_connectedCount == 1;
|
||
}
|
||
|
||
/// Determine if the mesh is closed. (Each edge is shared by two faces)
|
||
bool isClosed() const {
|
||
return m_boundaryCount == 0;
|
||
}
|
||
|
||
/// Return true if the mesh has the topology of a disk.
|
||
bool isDisk() const {
|
||
return isConnected() && m_boundaryCount == 1 /* && m_eulerNumber == 1*/;
|
||
}
|
||
|
||
private:
|
||
void buildTopologyInfo(const Mesh *mesh) {
|
||
const uint32_t vertexCount = mesh->colocalVertexCount();
|
||
const uint32_t faceCount = mesh->faceCount();
|
||
const uint32_t edgeCount = mesh->edgeCount();
|
||
xaPrint("--- Building mesh topology:\n");
|
||
std::vector<uint32_t> stack(faceCount);
|
||
BitArray bitFlags(faceCount);
|
||
bitFlags.clearAll();
|
||
// Compute connectivity.
|
||
xaPrint("--- Computing connectivity.\n");
|
||
m_connectedCount = 0;
|
||
for (uint32_t f = 0; f < faceCount; f++) {
|
||
if (bitFlags.bitAt(f) == false) {
|
||
m_connectedCount++;
|
||
stack.push_back(f);
|
||
while (!stack.empty()) {
|
||
const uint32_t top = stack.back();
|
||
xaAssert(top != uint32_t(~0));
|
||
stack.pop_back();
|
||
if (bitFlags.bitAt(top) == false) {
|
||
bitFlags.setBitAt(top);
|
||
const Face *face = mesh->faceAt(top);
|
||
const Edge *firstEdge = face->edge;
|
||
const Edge *edge = firstEdge;
|
||
do {
|
||
const Face *neighborFace = edge->pair->face;
|
||
if (neighborFace != NULL) {
|
||
stack.push_back(neighborFace->id);
|
||
}
|
||
edge = edge->next;
|
||
} while (edge != firstEdge);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
xaAssert(stack.empty());
|
||
xaPrint("--- %d connected components.\n", m_connectedCount);
|
||
// Count boundary loops.
|
||
xaPrint("--- Counting boundary loops.\n");
|
||
m_boundaryCount = 0;
|
||
bitFlags.resize(edgeCount);
|
||
bitFlags.clearAll();
|
||
// Don't forget to link the boundary otherwise this won't work.
|
||
for (uint32_t e = 0; e < edgeCount; e++) {
|
||
const Edge *startEdge = mesh->edgeAt(e);
|
||
if (startEdge != NULL && startEdge->isBoundary() && bitFlags.bitAt(e) == false) {
|
||
xaDebugAssert(startEdge->face != NULL);
|
||
xaDebugAssert(startEdge->pair->face == NULL);
|
||
startEdge = startEdge->pair;
|
||
m_boundaryCount++;
|
||
const Edge *edge = startEdge;
|
||
do {
|
||
bitFlags.setBitAt(edge->id / 2);
|
||
edge = edge->next;
|
||
} while (startEdge != edge);
|
||
}
|
||
}
|
||
xaPrint("--- %d boundary loops found.\n", m_boundaryCount);
|
||
// Compute euler number.
|
||
m_eulerNumber = vertexCount - edgeCount + faceCount;
|
||
xaPrint("--- Euler number: %d.\n", m_eulerNumber);
|
||
// Compute genus. (only valid on closed connected surfaces)
|
||
m_genus = -1;
|
||
if (isClosed() && isConnected()) {
|
||
m_genus = (2 - m_eulerNumber) / 2;
|
||
xaPrint("--- Genus: %d.\n", m_genus);
|
||
}
|
||
}
|
||
|
||
private:
|
||
///< Number of boundary loops.
|
||
int m_boundaryCount;
|
||
|
||
///< Number of connected components.
|
||
int m_connectedCount;
|
||
|
||
///< Euler number.
|
||
int m_eulerNumber;
|
||
|
||
/// Mesh genus.
|
||
int m_genus;
|
||
};
|
||
|
||
float computeSurfaceArea(const halfedge::Mesh *mesh) {
|
||
float area = 0;
|
||
for (halfedge::Mesh::ConstFaceIterator it(mesh->faces()); !it.isDone(); it.advance()) {
|
||
const halfedge::Face *face = it.current();
|
||
area += face->area();
|
||
}
|
||
xaDebugAssert(area >= 0);
|
||
return area;
|
||
}
|
||
|
||
float computeParametricArea(const halfedge::Mesh *mesh) {
|
||
float area = 0;
|
||
for (halfedge::Mesh::ConstFaceIterator it(mesh->faces()); !it.isDone(); it.advance()) {
|
||
const halfedge::Face *face = it.current();
|
||
area += face->parametricArea();
|
||
}
|
||
return area;
|
||
}
|
||
|
||
uint32_t countMeshTriangles(const Mesh *mesh) {
|
||
const uint32_t faceCount = mesh->faceCount();
|
||
uint32_t triangleCount = 0;
|
||
for (uint32_t f = 0; f < faceCount; f++) {
|
||
const Face *face = mesh->faceAt(f);
|
||
uint32_t edgeCount = face->edgeCount();
|
||
xaDebugAssert(edgeCount > 2);
|
||
triangleCount += edgeCount - 2;
|
||
}
|
||
return triangleCount;
|
||
}
|
||
|
||
Mesh *unifyVertices(const Mesh *inputMesh) {
|
||
Mesh *mesh = new Mesh;
|
||
// Only add the first colocal.
|
||
const uint32_t vertexCount = inputMesh->vertexCount();
|
||
for (uint32_t v = 0; v < vertexCount; v++) {
|
||
const Vertex *vertex = inputMesh->vertexAt(v);
|
||
if (vertex->isFirstColocal()) {
|
||
mesh->addVertex(vertex->pos);
|
||
}
|
||
}
|
||
std::vector<uint32_t> indexArray;
|
||
// Add new faces pointing to first colocals.
|
||
uint32_t faceCount = inputMesh->faceCount();
|
||
for (uint32_t f = 0; f < faceCount; f++) {
|
||
const Face *face = inputMesh->faceAt(f);
|
||
indexArray.clear();
|
||
for (Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const Edge *edge = it.current();
|
||
const Vertex *vertex = edge->vertex->firstColocal();
|
||
indexArray.push_back(vertex->id);
|
||
}
|
||
mesh->addFace(indexArray);
|
||
}
|
||
mesh->linkBoundary();
|
||
return mesh;
|
||
}
|
||
|
||
static bool pointInTriangle(const Vector2 &p, const Vector2 &a, const Vector2 &b, const Vector2 &c) {
|
||
return triangleArea(a, b, p) >= 0.00001f &&
|
||
triangleArea(b, c, p) >= 0.00001f &&
|
||
triangleArea(c, a, p) >= 0.00001f;
|
||
}
|
||
|
||
// This is doing a simple ear-clipping algorithm that skips invalid triangles. Ideally, we should
|
||
// also sort the ears by angle, start with the ones that have the smallest angle and proceed in order.
|
||
Mesh *triangulate(const Mesh *inputMesh) {
|
||
Mesh *mesh = new Mesh;
|
||
// Add all vertices.
|
||
const uint32_t vertexCount = inputMesh->vertexCount();
|
||
for (uint32_t v = 0; v < vertexCount; v++) {
|
||
const Vertex *vertex = inputMesh->vertexAt(v);
|
||
mesh->addVertex(vertex->pos);
|
||
}
|
||
std::vector<int> polygonVertices;
|
||
std::vector<float> polygonAngles;
|
||
std::vector<Vector2> polygonPoints;
|
||
const uint32_t faceCount = inputMesh->faceCount();
|
||
for (uint32_t f = 0; f < faceCount; f++) {
|
||
const Face *face = inputMesh->faceAt(f);
|
||
xaDebugAssert(face != NULL);
|
||
const uint32_t edgeCount = face->edgeCount();
|
||
xaDebugAssert(edgeCount >= 3);
|
||
polygonVertices.clear();
|
||
polygonVertices.reserve(edgeCount);
|
||
if (edgeCount == 3) {
|
||
// Simple case for triangles.
|
||
for (Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const Edge *edge = it.current();
|
||
const Vertex *vertex = edge->vertex;
|
||
polygonVertices.push_back(vertex->id);
|
||
}
|
||
int v0 = polygonVertices[0];
|
||
int v1 = polygonVertices[1];
|
||
int v2 = polygonVertices[2];
|
||
mesh->addFace(v0, v1, v2);
|
||
} else {
|
||
// Build 2D polygon projecting vertices onto normal plane.
|
||
// Faces are not necesarily planar, this is for example the case, when the face comes from filling a hole. In such cases
|
||
// it's much better to use the best fit plane.
|
||
const Vector3 fn = face->normal();
|
||
Basis basis;
|
||
basis.buildFrameForDirection(fn);
|
||
polygonPoints.clear();
|
||
polygonPoints.reserve(edgeCount);
|
||
polygonAngles.clear();
|
||
polygonAngles.reserve(edgeCount);
|
||
for (Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const Edge *edge = it.current();
|
||
const Vertex *vertex = edge->vertex;
|
||
polygonVertices.push_back(vertex->id);
|
||
Vector2 p;
|
||
p.x = dot(basis.tangent, vertex->pos);
|
||
p.y = dot(basis.bitangent, vertex->pos);
|
||
polygonPoints.push_back(p);
|
||
}
|
||
polygonAngles.resize(edgeCount);
|
||
while (polygonVertices.size() > 2) {
|
||
uint32_t size = polygonVertices.size();
|
||
// Update polygon angles. @@ Update only those that have changed.
|
||
float minAngle = 2 * PI;
|
||
uint32_t bestEar = 0; // Use first one if none of them is valid.
|
||
bool bestIsValid = false;
|
||
for (uint32_t i = 0; i < size; i++) {
|
||
uint32_t i0 = i;
|
||
uint32_t i1 = (i + 1) % size; // Use Sean's polygon interation trick.
|
||
uint32_t i2 = (i + 2) % size;
|
||
Vector2 p0 = polygonPoints[i0];
|
||
Vector2 p1 = polygonPoints[i1];
|
||
Vector2 p2 = polygonPoints[i2];
|
||
|
||
bool degenerate = distance(p0, p1) < NV_EPSILON || distance(p0, p2) < NV_EPSILON || distance(p1, p2) < NV_EPSILON;
|
||
if (degenerate) {
|
||
continue;
|
||
}
|
||
|
||
float d = clamp(dot(p0 - p1, p2 - p1) / (length(p0 - p1) * length(p2 - p1)), -1.0f, 1.0f);
|
||
float angle = acosf(d);
|
||
float area = triangleArea(p0, p1, p2);
|
||
if (area < 0.0f) angle = 2.0f * PI - angle;
|
||
polygonAngles[i1] = angle;
|
||
if (angle < minAngle || !bestIsValid) {
|
||
// Make sure this is a valid ear, if not, skip this point.
|
||
bool valid = true;
|
||
for (uint32_t j = 0; j < size; j++) {
|
||
if (j == i0 || j == i1 || j == i2) continue;
|
||
Vector2 p = polygonPoints[j];
|
||
if (pointInTriangle(p, p0, p1, p2)) {
|
||
valid = false;
|
||
break;
|
||
}
|
||
}
|
||
if (valid || !bestIsValid) {
|
||
minAngle = angle;
|
||
bestEar = i1;
|
||
bestIsValid = valid;
|
||
}
|
||
}
|
||
}
|
||
if (!bestIsValid)
|
||
break;
|
||
|
||
xaDebugAssert(minAngle <= 2 * PI);
|
||
// Clip best ear:
|
||
uint32_t i0 = (bestEar + size - 1) % size;
|
||
uint32_t i1 = (bestEar + 0) % size;
|
||
uint32_t i2 = (bestEar + 1) % size;
|
||
int v0 = polygonVertices[i0];
|
||
int v1 = polygonVertices[i1];
|
||
int v2 = polygonVertices[i2];
|
||
mesh->addFace(v0, v1, v2);
|
||
polygonVertices.erase(polygonVertices.begin() + i1);
|
||
polygonPoints.erase(polygonPoints.begin() + i1);
|
||
polygonAngles.erase(polygonAngles.begin() + i1);
|
||
}
|
||
}
|
||
}
|
||
mesh->linkBoundary();
|
||
return mesh;
|
||
}
|
||
|
||
} // namespace halfedge
|
||
|
||
/// Mersenne twister random number generator.
|
||
class MTRand {
|
||
public:
|
||
enum time_e { Time };
|
||
enum { N = 624 }; // length of state vector
|
||
enum { M = 397 };
|
||
|
||
/// Constructor that uses the current time as the seed.
|
||
MTRand(time_e) {
|
||
seed((uint32_t)time(NULL));
|
||
}
|
||
|
||
/// Constructor that uses the given seed.
|
||
MTRand(uint32_t s = 0) {
|
||
seed(s);
|
||
}
|
||
|
||
/// Provide a new seed.
|
||
void seed(uint32_t s) {
|
||
initialize(s);
|
||
reload();
|
||
}
|
||
|
||
/// Get a random number between 0 - 65536.
|
||
uint32_t get() {
|
||
// Pull a 32-bit integer from the generator state
|
||
// Every other access function simply transforms the numbers extracted here
|
||
if (left == 0) {
|
||
reload();
|
||
}
|
||
left--;
|
||
uint32_t s1;
|
||
s1 = *next++;
|
||
s1 ^= (s1 >> 11);
|
||
s1 ^= (s1 << 7) & 0x9d2c5680U;
|
||
s1 ^= (s1 << 15) & 0xefc60000U;
|
||
return (s1 ^ (s1 >> 18));
|
||
};
|
||
|
||
/// Get a random number on [0, max] interval.
|
||
uint32_t getRange(uint32_t max) {
|
||
if (max == 0) return 0;
|
||
if (max == NV_UINT32_MAX) return get();
|
||
const uint32_t np2 = nextPowerOfTwo(max + 1); // @@ This fails if max == NV_UINT32_MAX
|
||
const uint32_t mask = np2 - 1;
|
||
uint32_t n;
|
||
do {
|
||
n = get() & mask;
|
||
} while (n > max);
|
||
return n;
|
||
}
|
||
|
||
private:
|
||
void initialize(uint32_t seed) {
|
||
// Initialize generator state with seed
|
||
// See Knuth TAOCP Vol 2, 3rd Ed, p.106 for multiplier.
|
||
// In previous versions, most significant bits (MSBs) of the seed affect
|
||
// only MSBs of the state array. Modified 9 Jan 2002 by Makoto Matsumoto.
|
||
uint32_t *s = state;
|
||
uint32_t *r = state;
|
||
int i = 1;
|
||
*s++ = seed & 0xffffffffUL;
|
||
for (; i < N; ++i) {
|
||
*s++ = (1812433253UL * (*r ^ (*r >> 30)) + i) & 0xffffffffUL;
|
||
r++;
|
||
}
|
||
}
|
||
|
||
void reload() {
|
||
// Generate N new values in state
|
||
// Made clearer and faster by Matthew Bellew (matthew.bellew@home.com)
|
||
uint32_t *p = state;
|
||
int i;
|
||
for (i = N - M; i--; ++p)
|
||
*p = twist(p[M], p[0], p[1]);
|
||
for (i = M; --i; ++p)
|
||
*p = twist(p[M - N], p[0], p[1]);
|
||
*p = twist(p[M - N], p[0], state[0]);
|
||
left = N, next = state;
|
||
}
|
||
|
||
uint32_t hiBit(uint32_t u) const {
|
||
return u & 0x80000000U;
|
||
}
|
||
uint32_t loBit(uint32_t u) const {
|
||
return u & 0x00000001U;
|
||
}
|
||
uint32_t loBits(uint32_t u) const {
|
||
return u & 0x7fffffffU;
|
||
}
|
||
uint32_t mixBits(uint32_t u, uint32_t v) const {
|
||
return hiBit(u) | loBits(v);
|
||
}
|
||
uint32_t twist(uint32_t m, uint32_t s0, uint32_t s1) const {
|
||
return m ^ (mixBits(s0, s1) >> 1) ^ ((~loBit(s1) + 1) & 0x9908b0dfU);
|
||
}
|
||
|
||
uint32_t state[N]; // internal state
|
||
uint32_t *next; // next value to get from state
|
||
int left; // number of values left before reload needed
|
||
};
|
||
|
||
namespace morton {
|
||
// Code from ryg:
|
||
// http://fgiesen.wordpress.com/2009/12/13/decoding-morton-codes/
|
||
|
||
// Inverse of part1By1 - "delete" all odd-indexed bits
|
||
uint32_t compact1By1(uint32_t x) {
|
||
x &= 0x55555555; // x = -f-e -d-c -b-a -9-8 -7-6 -5-4 -3-2 -1-0
|
||
x = (x ^ (x >> 1)) & 0x33333333; // x = --fe --dc --ba --98 --76 --54 --32 --10
|
||
x = (x ^ (x >> 2)) & 0x0f0f0f0f; // x = ---- fedc ---- ba98 ---- 7654 ---- 3210
|
||
x = (x ^ (x >> 4)) & 0x00ff00ff; // x = ---- ---- fedc ba98 ---- ---- 7654 3210
|
||
x = (x ^ (x >> 8)) & 0x0000ffff; // x = ---- ---- ---- ---- fedc ba98 7654 3210
|
||
return x;
|
||
}
|
||
|
||
// Inverse of part1By2 - "delete" all bits not at positions divisible by 3
|
||
uint32_t compact1By2(uint32_t x) {
|
||
x &= 0x09249249; // x = ---- 9--8 --7- -6-- 5--4 --3- -2-- 1--0
|
||
x = (x ^ (x >> 2)) & 0x030c30c3; // x = ---- --98 ---- 76-- --54 ---- 32-- --10
|
||
x = (x ^ (x >> 4)) & 0x0300f00f; // x = ---- --98 ---- ---- 7654 ---- ---- 3210
|
||
x = (x ^ (x >> 8)) & 0xff0000ff; // x = ---- --98 ---- ---- ---- ---- 7654 3210
|
||
x = (x ^ (x >> 16)) & 0x000003ff; // x = ---- ---- ---- ---- ---- --98 7654 3210
|
||
return x;
|
||
}
|
||
|
||
uint32_t decodeMorton2X(uint32_t code) {
|
||
return compact1By1(code >> 0);
|
||
}
|
||
|
||
uint32_t decodeMorton2Y(uint32_t code) {
|
||
return compact1By1(code >> 1);
|
||
}
|
||
|
||
uint32_t decodeMorton3X(uint32_t code) {
|
||
return compact1By2(code >> 0);
|
||
}
|
||
|
||
uint32_t decodeMorton3Y(uint32_t code) {
|
||
return compact1By2(code >> 1);
|
||
}
|
||
|
||
uint32_t decodeMorton3Z(uint32_t code) {
|
||
return compact1By2(code >> 2);
|
||
}
|
||
} // namespace morton
|
||
|
||
// A simple, dynamic proximity grid based on Jon's code.
|
||
// Instead of storing pointers here I store indices.
|
||
struct ProximityGrid {
|
||
void init(const Box &box, uint32_t count) {
|
||
cellArray.clear();
|
||
// Determine grid size.
|
||
float cellWidth;
|
||
Vector3 diagonal = box.extents() * 2.f;
|
||
float volume = box.volume();
|
||
if (equal(volume, 0)) {
|
||
// Degenerate box, treat like a quad.
|
||
Vector2 quad;
|
||
if (diagonal.x < diagonal.y && diagonal.x < diagonal.z) {
|
||
quad.x = diagonal.y;
|
||
quad.y = diagonal.z;
|
||
} else if (diagonal.y < diagonal.x && diagonal.y < diagonal.z) {
|
||
quad.x = diagonal.x;
|
||
quad.y = diagonal.z;
|
||
} else {
|
||
quad.x = diagonal.x;
|
||
quad.y = diagonal.y;
|
||
}
|
||
float cellArea = quad.x * quad.y / count;
|
||
cellWidth = sqrtf(cellArea); // pow(cellArea, 1.0f / 2.0f);
|
||
} else {
|
||
// Ideally we want one cell per point.
|
||
float cellVolume = volume / count;
|
||
cellWidth = powf(cellVolume, 1.0f / 3.0f);
|
||
}
|
||
xaDebugAssert(cellWidth != 0);
|
||
sx = std::max(1, ftoi_ceil(diagonal.x / cellWidth));
|
||
sy = std::max(1, ftoi_ceil(diagonal.y / cellWidth));
|
||
sz = std::max(1, ftoi_ceil(diagonal.z / cellWidth));
|
||
invCellSize.x = float(sx) / diagonal.x;
|
||
invCellSize.y = float(sy) / diagonal.y;
|
||
invCellSize.z = float(sz) / diagonal.z;
|
||
cellArray.resize(sx * sy * sz);
|
||
corner = box.minCorner; // @@ Align grid better?
|
||
}
|
||
|
||
int index_x(float x) const {
|
||
return clamp(ftoi_floor((x - corner.x) * invCellSize.x), 0, sx - 1);
|
||
}
|
||
|
||
int index_y(float y) const {
|
||
return clamp(ftoi_floor((y - corner.y) * invCellSize.y), 0, sy - 1);
|
||
}
|
||
|
||
int index_z(float z) const {
|
||
return clamp(ftoi_floor((z - corner.z) * invCellSize.z), 0, sz - 1);
|
||
}
|
||
|
||
int index(int x, int y, int z) const {
|
||
xaDebugAssert(x >= 0 && x < sx);
|
||
xaDebugAssert(y >= 0 && y < sy);
|
||
xaDebugAssert(z >= 0 && z < sz);
|
||
int idx = (z * sy + y) * sx + x;
|
||
xaDebugAssert(idx >= 0 && uint32_t(idx) < cellArray.size());
|
||
return idx;
|
||
}
|
||
|
||
uint32_t mortonCount() const {
|
||
uint64_t s = uint64_t(max3(sx, sy, sz));
|
||
s = nextPowerOfTwo(s);
|
||
if (s > 1024) {
|
||
return uint32_t(s * s * min3(sx, sy, sz));
|
||
}
|
||
return uint32_t(s * s * s);
|
||
}
|
||
|
||
int mortonIndex(uint32_t code) const {
|
||
uint32_t x, y, z;
|
||
uint32_t s = uint32_t(max3(sx, sy, sz));
|
||
if (s > 1024) {
|
||
// Use layered two-dimensional morton order.
|
||
s = nextPowerOfTwo(s);
|
||
uint32_t layer = code / (s * s);
|
||
code = code % (s * s);
|
||
uint32_t layer_count = uint32_t(min3(sx, sy, sz));
|
||
if (sx == (int)layer_count) {
|
||
x = layer;
|
||
y = morton::decodeMorton2X(code);
|
||
z = morton::decodeMorton2Y(code);
|
||
} else if (sy == (int)layer_count) {
|
||
x = morton::decodeMorton2Y(code);
|
||
y = layer;
|
||
z = morton::decodeMorton2X(code);
|
||
} else { /*if (sz == layer_count)*/
|
||
x = morton::decodeMorton2X(code);
|
||
y = morton::decodeMorton2Y(code);
|
||
z = layer;
|
||
}
|
||
} else {
|
||
x = morton::decodeMorton3X(code);
|
||
y = morton::decodeMorton3Y(code);
|
||
z = morton::decodeMorton3Z(code);
|
||
}
|
||
if (x >= uint32_t(sx) || y >= uint32_t(sy) || z >= uint32_t(sz)) {
|
||
return -1;
|
||
}
|
||
return index(x, y, z);
|
||
}
|
||
|
||
void add(const Vector3 &pos, uint32_t key) {
|
||
int x = index_x(pos.x);
|
||
int y = index_y(pos.y);
|
||
int z = index_z(pos.z);
|
||
uint32_t idx = index(x, y, z);
|
||
cellArray[idx].indexArray.push_back(key);
|
||
}
|
||
|
||
// Gather all points inside the given sphere.
|
||
// Radius is assumed to be small, so we don't bother culling the cells.
|
||
void gather(const Vector3 &position, float radius, std::vector<uint32_t> &indexArray) {
|
||
int x0 = index_x(position.x - radius);
|
||
int x1 = index_x(position.x + radius);
|
||
int y0 = index_y(position.y - radius);
|
||
int y1 = index_y(position.y + radius);
|
||
int z0 = index_z(position.z - radius);
|
||
int z1 = index_z(position.z + radius);
|
||
for (int z = z0; z <= z1; z++) {
|
||
for (int y = y0; y <= y1; y++) {
|
||
for (int x = x0; x <= x1; x++) {
|
||
int idx = index(x, y, z);
|
||
indexArray.insert(indexArray.begin(), cellArray[idx].indexArray.begin(), cellArray[idx].indexArray.end());
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
struct Cell {
|
||
std::vector<uint32_t> indexArray;
|
||
};
|
||
|
||
std::vector<Cell> cellArray;
|
||
|
||
Vector3 corner;
|
||
Vector3 invCellSize;
|
||
int sx, sy, sz;
|
||
};
|
||
|
||
// Based on Pierre Terdiman's and Michael Herf's source code.
|
||
// http://www.codercorner.com/RadixSortRevisited.htm
|
||
// http://www.stereopsis.com/radix.html
|
||
class RadixSort {
|
||
public:
|
||
RadixSort() :
|
||
m_size(0),
|
||
m_ranks(NULL),
|
||
m_ranks2(NULL),
|
||
m_validRanks(false) {}
|
||
~RadixSort() {
|
||
// Release everything
|
||
free(m_ranks2);
|
||
free(m_ranks);
|
||
}
|
||
|
||
RadixSort &sort(const float *input, uint32_t count) {
|
||
if (input == NULL || count == 0) return *this;
|
||
// Resize lists if needed
|
||
if (count != m_size) {
|
||
if (count > m_size) {
|
||
m_ranks2 = (uint32_t *)realloc(m_ranks2, sizeof(uint32_t) * count);
|
||
m_ranks = (uint32_t *)realloc(m_ranks, sizeof(uint32_t) * count);
|
||
}
|
||
m_size = count;
|
||
m_validRanks = false;
|
||
}
|
||
if (count < 32) {
|
||
insertionSort(input, count);
|
||
} else {
|
||
// @@ Avoid touching the input multiple times.
|
||
for (uint32_t i = 0; i < count; i++) {
|
||
FloatFlip((uint32_t &)input[i]);
|
||
}
|
||
radixSort<uint32_t>((const uint32_t *)input, count);
|
||
for (uint32_t i = 0; i < count; i++) {
|
||
IFloatFlip((uint32_t &)input[i]);
|
||
}
|
||
}
|
||
return *this;
|
||
}
|
||
|
||
RadixSort &sort(const std::vector<float> &input) {
|
||
return sort(input.data(), input.size());
|
||
}
|
||
|
||
// Access to results. m_ranks is a list of indices in sorted order, i.e. in the order you may further process your data
|
||
const uint32_t *ranks() const {
|
||
xaDebugAssert(m_validRanks);
|
||
return m_ranks;
|
||
}
|
||
uint32_t *ranks() {
|
||
xaDebugAssert(m_validRanks);
|
||
return m_ranks;
|
||
}
|
||
|
||
private:
|
||
uint32_t m_size;
|
||
uint32_t *m_ranks;
|
||
uint32_t *m_ranks2;
|
||
bool m_validRanks;
|
||
|
||
void FloatFlip(uint32_t &f) {
|
||
int32_t mask = (int32_t(f) >> 31) | 0x80000000; // Warren Hunt, Manchor Ko.
|
||
f ^= mask;
|
||
}
|
||
|
||
void IFloatFlip(uint32_t &f) {
|
||
uint32_t mask = ((f >> 31) - 1) | 0x80000000; // Michael Herf.
|
||
f ^= mask;
|
||
}
|
||
|
||
template <typename T>
|
||
void createHistograms(const T *buffer, uint32_t count, uint32_t *histogram) {
|
||
const uint32_t bucketCount = sizeof(T); // (8 * sizeof(T)) / log2(radix)
|
||
// Init bucket pointers.
|
||
uint32_t *h[bucketCount];
|
||
for (uint32_t i = 0; i < bucketCount; i++) {
|
||
h[i] = histogram + 256 * i;
|
||
}
|
||
// Clear histograms.
|
||
memset(histogram, 0, 256 * bucketCount * sizeof(uint32_t));
|
||
// @@ Add support for signed integers.
|
||
// Build histograms.
|
||
const uint8_t *p = (const uint8_t *)buffer; // @@ Does this break aliasing rules?
|
||
const uint8_t *pe = p + count * sizeof(T);
|
||
while (p != pe) {
|
||
h[0][*p++]++, h[1][*p++]++, h[2][*p++]++, h[3][*p++]++;
|
||
#ifdef _MSC_VER
|
||
#pragma warning(push)
|
||
#pragma warning(disable : 4127)
|
||
#endif
|
||
if (bucketCount == 8) h[4][*p++]++, h[5][*p++]++, h[6][*p++]++, h[7][*p++]++;
|
||
#ifdef _MSC_VER
|
||
#pragma warning(pop)
|
||
#endif
|
||
}
|
||
}
|
||
|
||
template <typename T>
|
||
void insertionSort(const T *input, uint32_t count) {
|
||
if (!m_validRanks) {
|
||
m_ranks[0] = 0;
|
||
for (uint32_t i = 1; i != count; ++i) {
|
||
int rank = m_ranks[i] = i;
|
||
uint32_t j = i;
|
||
while (j != 0 && input[rank] < input[m_ranks[j - 1]]) {
|
||
m_ranks[j] = m_ranks[j - 1];
|
||
--j;
|
||
}
|
||
if (i != j) {
|
||
m_ranks[j] = rank;
|
||
}
|
||
}
|
||
m_validRanks = true;
|
||
} else {
|
||
for (uint32_t i = 1; i != count; ++i) {
|
||
int rank = m_ranks[i];
|
||
uint32_t j = i;
|
||
while (j != 0 && input[rank] < input[m_ranks[j - 1]]) {
|
||
m_ranks[j] = m_ranks[j - 1];
|
||
--j;
|
||
}
|
||
if (i != j) {
|
||
m_ranks[j] = rank;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
template <typename T>
|
||
void radixSort(const T *input, uint32_t count) {
|
||
const uint32_t P = sizeof(T); // pass count
|
||
// Allocate histograms & offsets on the stack
|
||
uint32_t histogram[256 * P];
|
||
uint32_t *link[256];
|
||
createHistograms(input, count, histogram);
|
||
// Radix sort, j is the pass number (0=LSB, P=MSB)
|
||
for (uint32_t j = 0; j < P; j++) {
|
||
// Pointer to this bucket.
|
||
const uint32_t *h = &histogram[j * 256];
|
||
const uint8_t *inputBytes = (const uint8_t *)input; // @@ Is this aliasing legal?
|
||
inputBytes += j;
|
||
if (h[inputBytes[0]] == count) {
|
||
// Skip this pass, all values are the same.
|
||
continue;
|
||
}
|
||
// Create offsets
|
||
link[0] = m_ranks2;
|
||
for (uint32_t i = 1; i < 256; i++)
|
||
link[i] = link[i - 1] + h[i - 1];
|
||
// Perform Radix Sort
|
||
if (!m_validRanks) {
|
||
for (uint32_t i = 0; i < count; i++) {
|
||
*link[inputBytes[i * P]]++ = i;
|
||
}
|
||
m_validRanks = true;
|
||
} else {
|
||
for (uint32_t i = 0; i < count; i++) {
|
||
const uint32_t idx = m_ranks[i];
|
||
*link[inputBytes[idx * P]]++ = idx;
|
||
}
|
||
}
|
||
// Swap pointers for next pass. Valid indices - the most recent ones - are in m_ranks after the swap.
|
||
std::swap(m_ranks, m_ranks2);
|
||
}
|
||
// All values were equal, generate linear ranks.
|
||
if (!m_validRanks) {
|
||
for (uint32_t i = 0; i < count; i++) {
|
||
m_ranks[i] = i;
|
||
}
|
||
m_validRanks = true;
|
||
}
|
||
}
|
||
};
|
||
|
||
namespace raster {
|
||
class ClippedTriangle {
|
||
public:
|
||
ClippedTriangle(Vector2::Arg a, Vector2::Arg b, Vector2::Arg c) {
|
||
m_numVertices = 3;
|
||
m_activeVertexBuffer = 0;
|
||
m_verticesA[0] = a;
|
||
m_verticesA[1] = b;
|
||
m_verticesA[2] = c;
|
||
m_vertexBuffers[0] = m_verticesA;
|
||
m_vertexBuffers[1] = m_verticesB;
|
||
}
|
||
|
||
uint32_t vertexCount() {
|
||
return m_numVertices;
|
||
}
|
||
|
||
const Vector2 *vertices() {
|
||
return m_vertexBuffers[m_activeVertexBuffer];
|
||
}
|
||
|
||
void clipHorizontalPlane(float offset, float clipdirection) {
|
||
Vector2 *v = m_vertexBuffers[m_activeVertexBuffer];
|
||
m_activeVertexBuffer ^= 1;
|
||
Vector2 *v2 = m_vertexBuffers[m_activeVertexBuffer];
|
||
v[m_numVertices] = v[0];
|
||
float dy2, dy1 = offset - v[0].y;
|
||
int dy2in, dy1in = clipdirection * dy1 >= 0;
|
||
uint32_t p = 0;
|
||
for (uint32_t k = 0; k < m_numVertices; k++) {
|
||
dy2 = offset - v[k + 1].y;
|
||
dy2in = clipdirection * dy2 >= 0;
|
||
if (dy1in) v2[p++] = v[k];
|
||
if (dy1in + dy2in == 1) { // not both in/out
|
||
float dx = v[k + 1].x - v[k].x;
|
||
float dy = v[k + 1].y - v[k].y;
|
||
v2[p++] = Vector2(v[k].x + dy1 * (dx / dy), offset);
|
||
}
|
||
dy1 = dy2;
|
||
dy1in = dy2in;
|
||
}
|
||
m_numVertices = p;
|
||
//for (uint32_t k=0; k<m_numVertices; k++) printf("(%f, %f)\n", v2[k].x, v2[k].y); printf("\n");
|
||
}
|
||
|
||
void clipVerticalPlane(float offset, float clipdirection) {
|
||
Vector2 *v = m_vertexBuffers[m_activeVertexBuffer];
|
||
m_activeVertexBuffer ^= 1;
|
||
Vector2 *v2 = m_vertexBuffers[m_activeVertexBuffer];
|
||
v[m_numVertices] = v[0];
|
||
float dx2, dx1 = offset - v[0].x;
|
||
int dx2in, dx1in = clipdirection * dx1 >= 0;
|
||
uint32_t p = 0;
|
||
for (uint32_t k = 0; k < m_numVertices; k++) {
|
||
dx2 = offset - v[k + 1].x;
|
||
dx2in = clipdirection * dx2 >= 0;
|
||
if (dx1in) v2[p++] = v[k];
|
||
if (dx1in + dx2in == 1) { // not both in/out
|
||
float dx = v[k + 1].x - v[k].x;
|
||
float dy = v[k + 1].y - v[k].y;
|
||
v2[p++] = Vector2(offset, v[k].y + dx1 * (dy / dx));
|
||
}
|
||
dx1 = dx2;
|
||
dx1in = dx2in;
|
||
}
|
||
m_numVertices = p;
|
||
}
|
||
|
||
void computeAreaCentroid() {
|
||
Vector2 *v = m_vertexBuffers[m_activeVertexBuffer];
|
||
v[m_numVertices] = v[0];
|
||
m_area = 0;
|
||
float centroidx = 0, centroidy = 0;
|
||
for (uint32_t k = 0; k < m_numVertices; k++) {
|
||
// http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/
|
||
float f = v[k].x * v[k + 1].y - v[k + 1].x * v[k].y;
|
||
m_area += f;
|
||
centroidx += f * (v[k].x + v[k + 1].x);
|
||
centroidy += f * (v[k].y + v[k + 1].y);
|
||
}
|
||
m_area = 0.5f * fabsf(m_area);
|
||
if (m_area == 0) {
|
||
m_centroid = Vector2(0.0f);
|
||
} else {
|
||
m_centroid = Vector2(centroidx / (6 * m_area), centroidy / (6 * m_area));
|
||
}
|
||
}
|
||
|
||
void clipAABox(float x0, float y0, float x1, float y1) {
|
||
clipVerticalPlane(x0, -1);
|
||
clipHorizontalPlane(y0, -1);
|
||
clipVerticalPlane(x1, 1);
|
||
clipHorizontalPlane(y1, 1);
|
||
computeAreaCentroid();
|
||
}
|
||
|
||
Vector2 centroid() {
|
||
return m_centroid;
|
||
}
|
||
|
||
float area() {
|
||
return m_area;
|
||
}
|
||
|
||
private:
|
||
Vector2 m_verticesA[7 + 1];
|
||
Vector2 m_verticesB[7 + 1];
|
||
Vector2 *m_vertexBuffers[2];
|
||
uint32_t m_numVertices;
|
||
uint32_t m_activeVertexBuffer;
|
||
float m_area;
|
||
Vector2 m_centroid;
|
||
};
|
||
|
||
/// A callback to sample the environment. Return false to terminate rasterization.
|
||
typedef bool (*SamplingCallback)(void *param, int x, int y, Vector3::Arg bar, Vector3::Arg dx, Vector3::Arg dy, float coverage);
|
||
|
||
/// A triangle for rasterization.
|
||
struct Triangle {
|
||
Triangle(Vector2::Arg v0, Vector2::Arg v1, Vector2::Arg v2, Vector3::Arg t0, Vector3::Arg t1, Vector3::Arg t2) {
|
||
// Init vertices.
|
||
this->v1 = v0;
|
||
this->v2 = v2;
|
||
this->v3 = v1;
|
||
// Set barycentric coordinates.
|
||
this->t1 = t0;
|
||
this->t2 = t2;
|
||
this->t3 = t1;
|
||
// make sure every triangle is front facing.
|
||
flipBackface();
|
||
// Compute deltas.
|
||
valid = computeDeltas();
|
||
computeUnitInwardNormals();
|
||
}
|
||
|
||
/// Compute texture space deltas.
|
||
/// This method takes two edge vectors that form a basis, determines the
|
||
/// coordinates of the canonic vectors in that basis, and computes the
|
||
/// texture gradient that corresponds to those vectors.
|
||
bool computeDeltas() {
|
||
Vector2 e0 = v3 - v1;
|
||
Vector2 e1 = v2 - v1;
|
||
Vector3 de0 = t3 - t1;
|
||
Vector3 de1 = t2 - t1;
|
||
float denom = 1.0f / (e0.y * e1.x - e1.y * e0.x);
|
||
if (!std::isfinite(denom)) {
|
||
return false;
|
||
}
|
||
float lambda1 = -e1.y * denom;
|
||
float lambda2 = e0.y * denom;
|
||
float lambda3 = e1.x * denom;
|
||
float lambda4 = -e0.x * denom;
|
||
dx = de0 * lambda1 + de1 * lambda2;
|
||
dy = de0 * lambda3 + de1 * lambda4;
|
||
return true;
|
||
}
|
||
|
||
bool draw(const Vector2 &extents, bool enableScissors, SamplingCallback cb, void *param) {
|
||
// 28.4 fixed-point coordinates
|
||
const int Y1 = ftoi_round(16.0f * v1.y);
|
||
const int Y2 = ftoi_round(16.0f * v2.y);
|
||
const int Y3 = ftoi_round(16.0f * v3.y);
|
||
const int X1 = ftoi_round(16.0f * v1.x);
|
||
const int X2 = ftoi_round(16.0f * v2.x);
|
||
const int X3 = ftoi_round(16.0f * v3.x);
|
||
// Deltas
|
||
const int DX12 = X1 - X2;
|
||
const int DX23 = X2 - X3;
|
||
const int DX31 = X3 - X1;
|
||
const int DY12 = Y1 - Y2;
|
||
const int DY23 = Y2 - Y3;
|
||
const int DY31 = Y3 - Y1;
|
||
// Fixed-point deltas
|
||
const int FDX12 = DX12 << 4;
|
||
const int FDX23 = DX23 << 4;
|
||
const int FDX31 = DX31 << 4;
|
||
const int FDY12 = DY12 << 4;
|
||
const int FDY23 = DY23 << 4;
|
||
const int FDY31 = DY31 << 4;
|
||
int minx, miny, maxx, maxy;
|
||
if (enableScissors) {
|
||
int frustumX0 = 0 << 4;
|
||
int frustumY0 = 0 << 4;
|
||
int frustumX1 = (int)extents.x << 4;
|
||
int frustumY1 = (int)extents.y << 4;
|
||
// Bounding rectangle
|
||
minx = (std::max(min3(X1, X2, X3), frustumX0) + 0xF) >> 4;
|
||
miny = (std::max(min3(Y1, Y2, Y3), frustumY0) + 0xF) >> 4;
|
||
maxx = (std::min(max3(X1, X2, X3), frustumX1) + 0xF) >> 4;
|
||
maxy = (std::min(max3(Y1, Y2, Y3), frustumY1) + 0xF) >> 4;
|
||
} else {
|
||
// Bounding rectangle
|
||
minx = (min3(X1, X2, X3) + 0xF) >> 4;
|
||
miny = (min3(Y1, Y2, Y3) + 0xF) >> 4;
|
||
maxx = (max3(X1, X2, X3) + 0xF) >> 4;
|
||
maxy = (max3(Y1, Y2, Y3) + 0xF) >> 4;
|
||
}
|
||
// Block size, standard 8x8 (must be power of two)
|
||
const int q = 8;
|
||
// @@ This won't work when minx,miny are negative. This code path is not used. Leaving as is for now.
|
||
xaAssert(minx >= 0);
|
||
xaAssert(miny >= 0);
|
||
// Start in corner of 8x8 block
|
||
minx &= ~(q - 1);
|
||
miny &= ~(q - 1);
|
||
// Half-edge constants
|
||
int C1 = DY12 * X1 - DX12 * Y1;
|
||
int C2 = DY23 * X2 - DX23 * Y2;
|
||
int C3 = DY31 * X3 - DX31 * Y3;
|
||
// Correct for fill convention
|
||
if (DY12 < 0 || (DY12 == 0 && DX12 > 0)) C1++;
|
||
if (DY23 < 0 || (DY23 == 0 && DX23 > 0)) C2++;
|
||
if (DY31 < 0 || (DY31 == 0 && DX31 > 0)) C3++;
|
||
// Loop through blocks
|
||
for (int y = miny; y < maxy; y += q) {
|
||
for (int x = minx; x < maxx; x += q) {
|
||
// Corners of block
|
||
int x0 = x << 4;
|
||
int x1 = (x + q - 1) << 4;
|
||
int y0 = y << 4;
|
||
int y1 = (y + q - 1) << 4;
|
||
// Evaluate half-space functions
|
||
bool a00 = C1 + DX12 * y0 - DY12 * x0 > 0;
|
||
bool a10 = C1 + DX12 * y0 - DY12 * x1 > 0;
|
||
bool a01 = C1 + DX12 * y1 - DY12 * x0 > 0;
|
||
bool a11 = C1 + DX12 * y1 - DY12 * x1 > 0;
|
||
int a = (a00 << 0) | (a10 << 1) | (a01 << 2) | (a11 << 3);
|
||
bool b00 = C2 + DX23 * y0 - DY23 * x0 > 0;
|
||
bool b10 = C2 + DX23 * y0 - DY23 * x1 > 0;
|
||
bool b01 = C2 + DX23 * y1 - DY23 * x0 > 0;
|
||
bool b11 = C2 + DX23 * y1 - DY23 * x1 > 0;
|
||
int b = (b00 << 0) | (b10 << 1) | (b01 << 2) | (b11 << 3);
|
||
bool c00 = C3 + DX31 * y0 - DY31 * x0 > 0;
|
||
bool c10 = C3 + DX31 * y0 - DY31 * x1 > 0;
|
||
bool c01 = C3 + DX31 * y1 - DY31 * x0 > 0;
|
||
bool c11 = C3 + DX31 * y1 - DY31 * x1 > 0;
|
||
int c = (c00 << 0) | (c10 << 1) | (c01 << 2) | (c11 << 3);
|
||
// Skip block when outside an edge
|
||
if (a == 0x0 || b == 0x0 || c == 0x0) continue;
|
||
// Accept whole block when totally covered
|
||
if (a == 0xF && b == 0xF && c == 0xF) {
|
||
Vector3 texRow = t1 + dy * (y0 - v1.y) + dx * (x0 - v1.x);
|
||
for (int iy = y; iy < y + q; iy++) {
|
||
Vector3 tex = texRow;
|
||
for (int ix = x; ix < x + q; ix++) {
|
||
//Vector3 tex = t1 + dx * (ix - v1.x) + dy * (iy - v1.y);
|
||
if (!cb(param, ix, iy, tex, dx, dy, 1.0)) {
|
||
// early out.
|
||
return false;
|
||
}
|
||
tex += dx;
|
||
}
|
||
texRow += dy;
|
||
}
|
||
} else { // Partially covered block
|
||
int CY1 = C1 + DX12 * y0 - DY12 * x0;
|
||
int CY2 = C2 + DX23 * y0 - DY23 * x0;
|
||
int CY3 = C3 + DX31 * y0 - DY31 * x0;
|
||
Vector3 texRow = t1 + dy * (y0 - v1.y) + dx * (x0 - v1.x);
|
||
for (int iy = y; iy < y + q; iy++) {
|
||
int CX1 = CY1;
|
||
int CX2 = CY2;
|
||
int CX3 = CY3;
|
||
Vector3 tex = texRow;
|
||
for (int ix = x; ix < x + q; ix++) {
|
||
if (CX1 > 0 && CX2 > 0 && CX3 > 0) {
|
||
if (!cb(param, ix, iy, tex, dx, dy, 1.0)) {
|
||
// early out.
|
||
return false;
|
||
}
|
||
}
|
||
CX1 -= FDY12;
|
||
CX2 -= FDY23;
|
||
CX3 -= FDY31;
|
||
tex += dx;
|
||
}
|
||
CY1 += FDX12;
|
||
CY2 += FDX23;
|
||
CY3 += FDX31;
|
||
texRow += dy;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
return true;
|
||
}
|
||
|
||
// extents has to be multiple of BK_SIZE!!
|
||
bool drawAA(const Vector2 &extents, bool enableScissors, SamplingCallback cb, void *param) {
|
||
const float PX_INSIDE = 1.0f / sqrt(2.0f);
|
||
const float PX_OUTSIDE = -1.0f / sqrt(2.0f);
|
||
const float BK_SIZE = 8;
|
||
const float BK_INSIDE = sqrt(BK_SIZE * BK_SIZE / 2.0f);
|
||
const float BK_OUTSIDE = -sqrt(BK_SIZE * BK_SIZE / 2.0f);
|
||
|
||
float minx, miny, maxx, maxy;
|
||
if (enableScissors) {
|
||
// Bounding rectangle
|
||
minx = floorf(std::max(min3(v1.x, v2.x, v3.x), 0.0f));
|
||
miny = floorf(std::max(min3(v1.y, v2.y, v3.y), 0.0f));
|
||
maxx = ceilf(std::min(max3(v1.x, v2.x, v3.x), extents.x - 1.0f));
|
||
maxy = ceilf(std::min(max3(v1.y, v2.y, v3.y), extents.y - 1.0f));
|
||
} else {
|
||
// Bounding rectangle
|
||
minx = floorf(min3(v1.x, v2.x, v3.x));
|
||
miny = floorf(min3(v1.y, v2.y, v3.y));
|
||
maxx = ceilf(max3(v1.x, v2.x, v3.x));
|
||
maxy = ceilf(max3(v1.y, v2.y, v3.y));
|
||
}
|
||
// There's no reason to align the blocks to the viewport, instead we align them to the origin of the triangle bounds.
|
||
minx = floorf(minx);
|
||
miny = floorf(miny);
|
||
//minx = (float)(((int)minx) & (~((int)BK_SIZE - 1))); // align to blocksize (we don't need to worry about blocks partially out of viewport)
|
||
//miny = (float)(((int)miny) & (~((int)BK_SIZE - 1)));
|
||
minx += 0.5;
|
||
miny += 0.5; // sampling at texel centers!
|
||
maxx += 0.5;
|
||
maxy += 0.5;
|
||
// Half-edge constants
|
||
float C1 = n1.x * (-v1.x) + n1.y * (-v1.y);
|
||
float C2 = n2.x * (-v2.x) + n2.y * (-v2.y);
|
||
float C3 = n3.x * (-v3.x) + n3.y * (-v3.y);
|
||
// Loop through blocks
|
||
for (float y0 = miny; y0 <= maxy; y0 += BK_SIZE) {
|
||
for (float x0 = minx; x0 <= maxx; x0 += BK_SIZE) {
|
||
// Corners of block
|
||
float xc = (x0 + (BK_SIZE - 1) / 2.0f);
|
||
float yc = (y0 + (BK_SIZE - 1) / 2.0f);
|
||
// Evaluate half-space functions
|
||
float aC = C1 + n1.x * xc + n1.y * yc;
|
||
float bC = C2 + n2.x * xc + n2.y * yc;
|
||
float cC = C3 + n3.x * xc + n3.y * yc;
|
||
// Skip block when outside an edge
|
||
if ((aC <= BK_OUTSIDE) || (bC <= BK_OUTSIDE) || (cC <= BK_OUTSIDE)) continue;
|
||
// Accept whole block when totally covered
|
||
if ((aC >= BK_INSIDE) && (bC >= BK_INSIDE) && (cC >= BK_INSIDE)) {
|
||
Vector3 texRow = t1 + dy * (y0 - v1.y) + dx * (x0 - v1.x);
|
||
for (float y = y0; y < y0 + BK_SIZE; y++) {
|
||
Vector3 tex = texRow;
|
||
for (float x = x0; x < x0 + BK_SIZE; x++) {
|
||
if (!cb(param, (int)x, (int)y, tex, dx, dy, 1.0f)) {
|
||
return false;
|
||
}
|
||
tex += dx;
|
||
}
|
||
texRow += dy;
|
||
}
|
||
} else { // Partially covered block
|
||
float CY1 = C1 + n1.x * x0 + n1.y * y0;
|
||
float CY2 = C2 + n2.x * x0 + n2.y * y0;
|
||
float CY3 = C3 + n3.x * x0 + n3.y * y0;
|
||
Vector3 texRow = t1 + dy * (y0 - v1.y) + dx * (x0 - v1.x);
|
||
for (float y = y0; y < y0 + BK_SIZE; y++) { // @@ This is not clipping to scissor rectangle correctly.
|
||
float CX1 = CY1;
|
||
float CX2 = CY2;
|
||
float CX3 = CY3;
|
||
Vector3 tex = texRow;
|
||
for (float x = x0; x < x0 + BK_SIZE; x++) { // @@ This is not clipping to scissor rectangle correctly.
|
||
if (CX1 >= PX_INSIDE && CX2 >= PX_INSIDE && CX3 >= PX_INSIDE) {
|
||
// pixel completely covered
|
||
Vector3 tex2 = t1 + dx * (x - v1.x) + dy * (y - v1.y);
|
||
if (!cb(param, (int)x, (int)y, tex2, dx, dy, 1.0f)) {
|
||
return false;
|
||
}
|
||
} else if ((CX1 >= PX_OUTSIDE) && (CX2 >= PX_OUTSIDE) && (CX3 >= PX_OUTSIDE)) {
|
||
// triangle partially covers pixel. do clipping.
|
||
ClippedTriangle ct(v1 - Vector2(x, y), v2 - Vector2(x, y), v3 - Vector2(x, y));
|
||
ct.clipAABox(-0.5, -0.5, 0.5, 0.5);
|
||
Vector2 centroid = ct.centroid();
|
||
float area = ct.area();
|
||
if (area > 0.0f) {
|
||
Vector3 texCent = tex - dx * centroid.x - dy * centroid.y;
|
||
//xaAssert(texCent.x >= -0.1f && texCent.x <= 1.1f); // @@ Centroid is not very exact...
|
||
//xaAssert(texCent.y >= -0.1f && texCent.y <= 1.1f);
|
||
//xaAssert(texCent.z >= -0.1f && texCent.z <= 1.1f);
|
||
//Vector3 texCent2 = t1 + dx * (x - v1.x) + dy * (y - v1.y);
|
||
if (!cb(param, (int)x, (int)y, texCent, dx, dy, area)) {
|
||
return false;
|
||
}
|
||
}
|
||
}
|
||
CX1 += n1.x;
|
||
CX2 += n2.x;
|
||
CX3 += n3.x;
|
||
tex += dx;
|
||
}
|
||
CY1 += n1.y;
|
||
CY2 += n2.y;
|
||
CY3 += n3.y;
|
||
texRow += dy;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
return true;
|
||
}
|
||
|
||
void flipBackface() {
|
||
// check if triangle is backfacing, if so, swap two vertices
|
||
if (((v3.x - v1.x) * (v2.y - v1.y) - (v3.y - v1.y) * (v2.x - v1.x)) < 0) {
|
||
Vector2 hv = v1;
|
||
v1 = v2;
|
||
v2 = hv; // swap pos
|
||
Vector3 ht = t1;
|
||
t1 = t2;
|
||
t2 = ht; // swap tex
|
||
}
|
||
}
|
||
|
||
// compute unit inward normals for each edge.
|
||
void computeUnitInwardNormals() {
|
||
n1 = v1 - v2;
|
||
n1 = Vector2(-n1.y, n1.x);
|
||
n1 = n1 * (1.0f / sqrtf(n1.x * n1.x + n1.y * n1.y));
|
||
n2 = v2 - v3;
|
||
n2 = Vector2(-n2.y, n2.x);
|
||
n2 = n2 * (1.0f / sqrtf(n2.x * n2.x + n2.y * n2.y));
|
||
n3 = v3 - v1;
|
||
n3 = Vector2(-n3.y, n3.x);
|
||
n3 = n3 * (1.0f / sqrtf(n3.x * n3.x + n3.y * n3.y));
|
||
}
|
||
|
||
// Vertices.
|
||
Vector2 v1, v2, v3;
|
||
Vector2 n1, n2, n3; // unit inward normals
|
||
Vector3 t1, t2, t3;
|
||
|
||
// Deltas.
|
||
Vector3 dx, dy;
|
||
|
||
float sign;
|
||
bool valid;
|
||
};
|
||
|
||
enum Mode {
|
||
Mode_Nearest,
|
||
Mode_Antialiased
|
||
};
|
||
|
||
// Process the given triangle. Returns false if rasterization was interrupted by the callback.
|
||
static bool drawTriangle(Mode mode, Vector2::Arg extents, bool enableScissors, const Vector2 v[3], SamplingCallback cb, void *param) {
|
||
Triangle tri(v[0], v[1], v[2], Vector3(1, 0, 0), Vector3(0, 1, 0), Vector3(0, 0, 1));
|
||
// @@ It would be nice to have a conservative drawing mode that enlarges the triangle extents by one texel and is able to handle degenerate triangles.
|
||
// @@ Maybe the simplest thing to do would be raster triangle edges.
|
||
if (tri.valid) {
|
||
if (mode == Mode_Antialiased) {
|
||
return tri.drawAA(extents, enableScissors, cb, param);
|
||
}
|
||
if (mode == Mode_Nearest) {
|
||
return tri.draw(extents, enableScissors, cb, param);
|
||
}
|
||
}
|
||
return true;
|
||
}
|
||
|
||
// Process the given quad. Returns false if rasterization was interrupted by the callback.
|
||
static bool drawQuad(Mode mode, Vector2::Arg extents, bool enableScissors, const Vector2 v[4], SamplingCallback cb, void *param) {
|
||
bool sign0 = triangleArea2(v[0], v[1], v[2]) > 0.0f;
|
||
bool sign1 = triangleArea2(v[0], v[2], v[3]) > 0.0f;
|
||
// Divide the quad into two non overlapping triangles.
|
||
if (sign0 == sign1) {
|
||
Triangle tri0(v[0], v[1], v[2], Vector3(0, 0, 0), Vector3(1, 0, 0), Vector3(1, 1, 0));
|
||
Triangle tri1(v[0], v[2], v[3], Vector3(0, 0, 0), Vector3(1, 1, 0), Vector3(0, 1, 0));
|
||
if (tri0.valid && tri1.valid) {
|
||
if (mode == Mode_Antialiased) {
|
||
return tri0.drawAA(extents, enableScissors, cb, param) && tri1.drawAA(extents, enableScissors, cb, param);
|
||
} else {
|
||
return tri0.draw(extents, enableScissors, cb, param) && tri1.draw(extents, enableScissors, cb, param);
|
||
}
|
||
}
|
||
} else {
|
||
Triangle tri0(v[0], v[1], v[3], Vector3(0, 0, 0), Vector3(1, 0, 0), Vector3(0, 1, 0));
|
||
Triangle tri1(v[1], v[2], v[3], Vector3(1, 0, 0), Vector3(1, 1, 0), Vector3(0, 1, 0));
|
||
if (tri0.valid && tri1.valid) {
|
||
if (mode == Mode_Antialiased) {
|
||
return tri0.drawAA(extents, enableScissors, cb, param) && tri1.drawAA(extents, enableScissors, cb, param);
|
||
} else {
|
||
return tri0.draw(extents, enableScissors, cb, param) && tri1.draw(extents, enableScissors, cb, param);
|
||
}
|
||
}
|
||
}
|
||
return true;
|
||
}
|
||
} // namespace raster
|
||
|
||
// Full and sparse vector and matrix classes. BLAS subset.
|
||
// Pseudo-BLAS interface.
|
||
namespace sparse {
|
||
enum Transpose {
|
||
NoTransposed = 0,
|
||
Transposed = 1
|
||
};
|
||
|
||
/**
|
||
* Sparse matrix class. The matrix is assumed to be sparse and to have
|
||
* very few non-zero elements, for this reason it's stored in indexed
|
||
* format. To multiply column vectors efficiently, the matrix stores
|
||
* the elements in indexed-column order, there is a list of indexed
|
||
* elements for each row of the matrix. As with the FullVector the
|
||
* dimension of the matrix is constant.
|
||
**/
|
||
class Matrix {
|
||
public:
|
||
// An element of the sparse array.
|
||
struct Coefficient {
|
||
uint32_t x; // column
|
||
float v; // value
|
||
};
|
||
|
||
Matrix(uint32_t d) :
|
||
m_width(d) { m_array.resize(d); }
|
||
Matrix(uint32_t w, uint32_t h) :
|
||
m_width(w) { m_array.resize(h); }
|
||
Matrix(const Matrix &m) :
|
||
m_width(m.m_width) { m_array = m.m_array; }
|
||
|
||
const Matrix &operator=(const Matrix &m) {
|
||
xaAssert(width() == m.width());
|
||
xaAssert(height() == m.height());
|
||
m_array = m.m_array;
|
||
return *this;
|
||
}
|
||
|
||
uint32_t width() const { return m_width; }
|
||
uint32_t height() const { return m_array.size(); }
|
||
bool isSquare() const { return width() == height(); }
|
||
|
||
// x is column, y is row
|
||
float getCoefficient(uint32_t x, uint32_t y) const {
|
||
xaDebugAssert(x < width());
|
||
xaDebugAssert(y < height());
|
||
const uint32_t count = m_array[y].size();
|
||
for (uint32_t i = 0; i < count; i++) {
|
||
if (m_array[y][i].x == x) return m_array[y][i].v;
|
||
}
|
||
return 0.0f;
|
||
}
|
||
|
||
void setCoefficient(uint32_t x, uint32_t y, float f) {
|
||
xaDebugAssert(x < width());
|
||
xaDebugAssert(y < height());
|
||
const uint32_t count = m_array[y].size();
|
||
for (uint32_t i = 0; i < count; i++) {
|
||
if (m_array[y][i].x == x) {
|
||
m_array[y][i].v = f;
|
||
return;
|
||
}
|
||
}
|
||
if (f != 0.0f) {
|
||
Coefficient c = { x, f };
|
||
m_array[y].push_back(c);
|
||
}
|
||
}
|
||
|
||
float dotRow(uint32_t y, const FullVector &v) const {
|
||
xaDebugAssert(y < height());
|
||
const uint32_t count = m_array[y].size();
|
||
float sum = 0;
|
||
for (uint32_t i = 0; i < count; i++) {
|
||
sum += m_array[y][i].v * v[m_array[y][i].x];
|
||
}
|
||
return sum;
|
||
}
|
||
|
||
void madRow(uint32_t y, float alpha, FullVector &v) const {
|
||
xaDebugAssert(y < height());
|
||
const uint32_t count = m_array[y].size();
|
||
for (uint32_t i = 0; i < count; i++) {
|
||
v[m_array[y][i].x] += alpha * m_array[y][i].v;
|
||
}
|
||
}
|
||
|
||
void clearRow(uint32_t y) {
|
||
xaDebugAssert(y < height());
|
||
m_array[y].clear();
|
||
}
|
||
|
||
void scaleRow(uint32_t y, float f) {
|
||
xaDebugAssert(y < height());
|
||
const uint32_t count = m_array[y].size();
|
||
for (uint32_t i = 0; i < count; i++) {
|
||
m_array[y][i].v *= f;
|
||
}
|
||
}
|
||
|
||
const std::vector<Coefficient> &getRow(uint32_t y) const { return m_array[y]; }
|
||
|
||
private:
|
||
/// Number of columns.
|
||
const uint32_t m_width;
|
||
|
||
/// Array of matrix elements.
|
||
std::vector<std::vector<Coefficient> > m_array;
|
||
};
|
||
|
||
// y = a * x + y
|
||
static void saxpy(float a, const FullVector &x, FullVector &y) {
|
||
xaDebugAssert(x.dimension() == y.dimension());
|
||
const uint32_t dim = x.dimension();
|
||
for (uint32_t i = 0; i < dim; i++) {
|
||
y[i] += a * x[i];
|
||
}
|
||
}
|
||
|
||
static void copy(const FullVector &x, FullVector &y) {
|
||
xaDebugAssert(x.dimension() == y.dimension());
|
||
const uint32_t dim = x.dimension();
|
||
for (uint32_t i = 0; i < dim; i++) {
|
||
y[i] = x[i];
|
||
}
|
||
}
|
||
|
||
static void scal(float a, FullVector &x) {
|
||
const uint32_t dim = x.dimension();
|
||
for (uint32_t i = 0; i < dim; i++) {
|
||
x[i] *= a;
|
||
}
|
||
}
|
||
|
||
static float dot(const FullVector &x, const FullVector &y) {
|
||
xaDebugAssert(x.dimension() == y.dimension());
|
||
const uint32_t dim = x.dimension();
|
||
float sum = 0;
|
||
for (uint32_t i = 0; i < dim; i++) {
|
||
sum += x[i] * y[i];
|
||
}
|
||
return sum;
|
||
}
|
||
|
||
static void mult(Transpose TM, const Matrix &M, const FullVector &x, FullVector &y) {
|
||
const uint32_t w = M.width();
|
||
const uint32_t h = M.height();
|
||
if (TM == Transposed) {
|
||
xaDebugAssert(h == x.dimension());
|
||
xaDebugAssert(w == y.dimension());
|
||
y.fill(0.0f);
|
||
for (uint32_t i = 0; i < h; i++) {
|
||
M.madRow(i, x[i], y);
|
||
}
|
||
} else {
|
||
xaDebugAssert(w == x.dimension());
|
||
xaDebugAssert(h == y.dimension());
|
||
for (uint32_t i = 0; i < h; i++) {
|
||
y[i] = M.dotRow(i, x);
|
||
}
|
||
}
|
||
}
|
||
|
||
// y = M * x
|
||
static void mult(const Matrix &M, const FullVector &x, FullVector &y) {
|
||
mult(NoTransposed, M, x, y);
|
||
}
|
||
|
||
static void sgemv(float alpha, Transpose TA, const Matrix &A, const FullVector &x, float beta, FullVector &y) {
|
||
const uint32_t w = A.width();
|
||
const uint32_t h = A.height();
|
||
if (TA == Transposed) {
|
||
xaDebugAssert(h == x.dimension());
|
||
xaDebugAssert(w == y.dimension());
|
||
for (uint32_t i = 0; i < h; i++) {
|
||
A.madRow(i, alpha * x[i], y);
|
||
}
|
||
} else {
|
||
xaDebugAssert(w == x.dimension());
|
||
xaDebugAssert(h == y.dimension());
|
||
for (uint32_t i = 0; i < h; i++) {
|
||
y[i] = alpha * A.dotRow(i, x) + beta * y[i];
|
||
}
|
||
}
|
||
}
|
||
|
||
// y = alpha*A*x + beta*y
|
||
static void sgemv(float alpha, const Matrix &A, const FullVector &x, float beta, FullVector &y) {
|
||
sgemv(alpha, NoTransposed, A, x, beta, y);
|
||
}
|
||
|
||
// dot y-row of A by x-column of B
|
||
static float dotRowColumn(int y, const Matrix &A, int x, const Matrix &B) {
|
||
const std::vector<Matrix::Coefficient> &row = A.getRow(y);
|
||
const uint32_t count = row.size();
|
||
float sum = 0.0f;
|
||
for (uint32_t i = 0; i < count; i++) {
|
||
const Matrix::Coefficient &c = row[i];
|
||
sum += c.v * B.getCoefficient(x, c.x);
|
||
}
|
||
return sum;
|
||
}
|
||
|
||
// dot y-row of A by x-row of B
|
||
static float dotRowRow(int y, const Matrix &A, int x, const Matrix &B) {
|
||
const std::vector<Matrix::Coefficient> &row = A.getRow(y);
|
||
const uint32_t count = row.size();
|
||
float sum = 0.0f;
|
||
for (uint32_t i = 0; i < count; i++) {
|
||
const Matrix::Coefficient &c = row[i];
|
||
sum += c.v * B.getCoefficient(c.x, x);
|
||
}
|
||
return sum;
|
||
}
|
||
|
||
// dot y-column of A by x-column of B
|
||
static float dotColumnColumn(int y, const Matrix &A, int x, const Matrix &B) {
|
||
xaDebugAssert(A.height() == B.height());
|
||
const uint32_t h = A.height();
|
||
float sum = 0.0f;
|
||
for (uint32_t i = 0; i < h; i++) {
|
||
sum += A.getCoefficient(y, i) * B.getCoefficient(x, i);
|
||
}
|
||
return sum;
|
||
}
|
||
|
||
static void transpose(const Matrix &A, Matrix &B) {
|
||
xaDebugAssert(A.width() == B.height());
|
||
xaDebugAssert(B.width() == A.height());
|
||
const uint32_t w = A.width();
|
||
for (uint32_t x = 0; x < w; x++) {
|
||
B.clearRow(x);
|
||
}
|
||
const uint32_t h = A.height();
|
||
for (uint32_t y = 0; y < h; y++) {
|
||
const std::vector<Matrix::Coefficient> &row = A.getRow(y);
|
||
const uint32_t count = row.size();
|
||
for (uint32_t i = 0; i < count; i++) {
|
||
const Matrix::Coefficient &c = row[i];
|
||
xaDebugAssert(c.x < w);
|
||
B.setCoefficient(y, c.x, c.v);
|
||
}
|
||
}
|
||
}
|
||
|
||
static void sgemm(float alpha, Transpose TA, const Matrix &A, Transpose TB, const Matrix &B, float beta, Matrix &C) {
|
||
const uint32_t w = C.width();
|
||
const uint32_t h = C.height();
|
||
uint32_t aw = (TA == NoTransposed) ? A.width() : A.height();
|
||
uint32_t ah = (TA == NoTransposed) ? A.height() : A.width();
|
||
uint32_t bw = (TB == NoTransposed) ? B.width() : B.height();
|
||
uint32_t bh = (TB == NoTransposed) ? B.height() : B.width();
|
||
xaDebugAssert(aw == bh);
|
||
xaDebugAssert(bw == ah);
|
||
xaDebugAssert(w == bw);
|
||
xaDebugAssert(h == ah);
|
||
#ifdef NDEBUG
|
||
aw = ah = bw = bh = 0; // silence unused parameter warning
|
||
#endif
|
||
for (uint32_t y = 0; y < h; y++) {
|
||
for (uint32_t x = 0; x < w; x++) {
|
||
float c = beta * C.getCoefficient(x, y);
|
||
if (TA == NoTransposed && TB == NoTransposed) {
|
||
// dot y-row of A by x-column of B.
|
||
c += alpha * dotRowColumn(y, A, x, B);
|
||
} else if (TA == Transposed && TB == Transposed) {
|
||
// dot y-column of A by x-row of B.
|
||
c += alpha * dotRowColumn(x, B, y, A);
|
||
} else if (TA == Transposed && TB == NoTransposed) {
|
||
// dot y-column of A by x-column of B.
|
||
c += alpha * dotColumnColumn(y, A, x, B);
|
||
} else if (TA == NoTransposed && TB == Transposed) {
|
||
// dot y-row of A by x-row of B.
|
||
c += alpha * dotRowRow(y, A, x, B);
|
||
}
|
||
C.setCoefficient(x, y, c);
|
||
}
|
||
}
|
||
}
|
||
|
||
static void mult(Transpose TA, const Matrix &A, Transpose TB, const Matrix &B, Matrix &C) {
|
||
sgemm(1.0f, TA, A, TB, B, 0.0f, C);
|
||
}
|
||
|
||
// C = A * B
|
||
static void mult(const Matrix &A, const Matrix &B, Matrix &C) {
|
||
mult(NoTransposed, A, NoTransposed, B, C);
|
||
}
|
||
|
||
} // namespace sparse
|
||
|
||
class JacobiPreconditioner {
|
||
public:
|
||
JacobiPreconditioner(const sparse::Matrix &M, bool symmetric) :
|
||
m_inverseDiagonal(M.width()) {
|
||
xaAssert(M.isSquare());
|
||
for (uint32_t x = 0; x < M.width(); x++) {
|
||
float elem = M.getCoefficient(x, x);
|
||
//xaDebugAssert( elem != 0.0f ); // This can be zero in the presence of zero area triangles.
|
||
if (symmetric) {
|
||
m_inverseDiagonal[x] = (elem != 0) ? 1.0f / sqrtf(fabsf(elem)) : 1.0f;
|
||
} else {
|
||
m_inverseDiagonal[x] = (elem != 0) ? 1.0f / elem : 1.0f;
|
||
}
|
||
}
|
||
}
|
||
|
||
void apply(const FullVector &x, FullVector &y) const {
|
||
xaDebugAssert(x.dimension() == m_inverseDiagonal.dimension());
|
||
xaDebugAssert(y.dimension() == m_inverseDiagonal.dimension());
|
||
// @@ Wrap vector component-wise product into a separate function.
|
||
const uint32_t D = x.dimension();
|
||
for (uint32_t i = 0; i < D; i++) {
|
||
y[i] = m_inverseDiagonal[i] * x[i];
|
||
}
|
||
}
|
||
|
||
private:
|
||
FullVector m_inverseDiagonal;
|
||
};
|
||
|
||
// Linear solvers.
|
||
class Solver {
|
||
public:
|
||
// Solve the symmetric system: At<41>A<EFBFBD>x = At<41>b
|
||
static bool LeastSquaresSolver(const sparse::Matrix &A, const FullVector &b, FullVector &x, float epsilon = 1e-5f) {
|
||
xaDebugAssert(A.width() == x.dimension());
|
||
xaDebugAssert(A.height() == b.dimension());
|
||
xaDebugAssert(A.height() >= A.width()); // @@ If height == width we could solve it directly...
|
||
const uint32_t D = A.width();
|
||
sparse::Matrix At(A.height(), A.width());
|
||
sparse::transpose(A, At);
|
||
FullVector Atb(D);
|
||
sparse::mult(At, b, Atb);
|
||
sparse::Matrix AtA(D);
|
||
sparse::mult(At, A, AtA);
|
||
return SymmetricSolver(AtA, Atb, x, epsilon);
|
||
}
|
||
|
||
// See section 10.4.3 in: Mesh Parameterization: Theory and Practice, Siggraph Course Notes, August 2007
|
||
static bool LeastSquaresSolver(const sparse::Matrix &A, const FullVector &b, FullVector &x, const uint32_t *lockedParameters, uint32_t lockedCount, float epsilon = 1e-5f) {
|
||
xaDebugAssert(A.width() == x.dimension());
|
||
xaDebugAssert(A.height() == b.dimension());
|
||
xaDebugAssert(A.height() >= A.width() - lockedCount);
|
||
// @@ This is not the most efficient way of building a system with reduced degrees of freedom. It would be faster to do it on the fly.
|
||
const uint32_t D = A.width() - lockedCount;
|
||
xaDebugAssert(D > 0);
|
||
// Compute: b - Al * xl
|
||
FullVector b_Alxl(b);
|
||
for (uint32_t y = 0; y < A.height(); y++) {
|
||
const uint32_t count = A.getRow(y).size();
|
||
for (uint32_t e = 0; e < count; e++) {
|
||
uint32_t column = A.getRow(y)[e].x;
|
||
bool isFree = true;
|
||
for (uint32_t i = 0; i < lockedCount; i++) {
|
||
isFree &= (lockedParameters[i] != column);
|
||
}
|
||
if (!isFree) {
|
||
b_Alxl[y] -= x[column] * A.getRow(y)[e].v;
|
||
}
|
||
}
|
||
}
|
||
// Remove locked columns from A.
|
||
sparse::Matrix Af(D, A.height());
|
||
for (uint32_t y = 0; y < A.height(); y++) {
|
||
const uint32_t count = A.getRow(y).size();
|
||
for (uint32_t e = 0; e < count; e++) {
|
||
uint32_t column = A.getRow(y)[e].x;
|
||
uint32_t ix = column;
|
||
bool isFree = true;
|
||
for (uint32_t i = 0; i < lockedCount; i++) {
|
||
isFree &= (lockedParameters[i] != column);
|
||
if (column > lockedParameters[i]) ix--; // shift columns
|
||
}
|
||
if (isFree) {
|
||
Af.setCoefficient(ix, y, A.getRow(y)[e].v);
|
||
}
|
||
}
|
||
}
|
||
// Remove elements from x
|
||
FullVector xf(D);
|
||
for (uint32_t i = 0, j = 0; i < A.width(); i++) {
|
||
bool isFree = true;
|
||
for (uint32_t l = 0; l < lockedCount; l++) {
|
||
isFree &= (lockedParameters[l] != i);
|
||
}
|
||
if (isFree) {
|
||
xf[j++] = x[i];
|
||
}
|
||
}
|
||
// Solve reduced system.
|
||
bool result = LeastSquaresSolver(Af, b_Alxl, xf, epsilon);
|
||
// Copy results back to x.
|
||
for (uint32_t i = 0, j = 0; i < A.width(); i++) {
|
||
bool isFree = true;
|
||
for (uint32_t l = 0; l < lockedCount; l++) {
|
||
isFree &= (lockedParameters[l] != i);
|
||
}
|
||
if (isFree) {
|
||
x[i] = xf[j++];
|
||
}
|
||
}
|
||
return result;
|
||
}
|
||
|
||
private:
|
||
/**
|
||
* Compute the solution of the sparse linear system Ab=x using the Conjugate
|
||
* Gradient method.
|
||
*
|
||
* Solving sparse linear systems:
|
||
* (1) A<>x = b
|
||
*
|
||
* The conjugate gradient algorithm solves (1) only in the case that A is
|
||
* symmetric and positive definite. It is based on the idea of minimizing the
|
||
* function
|
||
*
|
||
* (2) f(x) = 1/2<>x<EFBFBD>A<EFBFBD>x - b<>x
|
||
*
|
||
* This function is minimized when its gradient
|
||
*
|
||
* (3) df = A<>x - b
|
||
*
|
||
* is zero, which is equivalent to (1). The minimization is carried out by
|
||
* generating a succession of search directions p.k and improved minimizers x.k.
|
||
* At each stage a quantity alfa.k is found that minimizes f(x.k + alfa.k<>p.k),
|
||
* and x.k+1 is set equal to the new point x.k + alfa.k<>p.k. The p.k and x.k are
|
||
* built up in such a way that x.k+1 is also the minimizer of f over the whole
|
||
* vector space of directions already taken, {p.1, p.2, . . . , p.k}. After N
|
||
* iterations you arrive at the minimizer over the entire vector space, i.e., the
|
||
* solution to (1).
|
||
*
|
||
* For a really good explanation of the method see:
|
||
*
|
||
* "An Introduction to the Conjugate Gradient Method Without the Agonizing Pain",
|
||
* Jonhathan Richard Shewchuk.
|
||
*
|
||
**/
|
||
static bool ConjugateGradientSolver(const sparse::Matrix &A, const FullVector &b, FullVector &x, float epsilon) {
|
||
xaDebugAssert(A.isSquare());
|
||
xaDebugAssert(A.width() == b.dimension());
|
||
xaDebugAssert(A.width() == x.dimension());
|
||
int i = 0;
|
||
const int D = A.width();
|
||
const int i_max = 4 * D; // Convergence should be linear, but in some cases, it's not.
|
||
FullVector r(D); // residual
|
||
FullVector p(D); // search direction
|
||
FullVector q(D); //
|
||
float delta_0;
|
||
float delta_old;
|
||
float delta_new;
|
||
float alpha;
|
||
float beta;
|
||
// r = b - A<>x;
|
||
sparse::copy(b, r);
|
||
sparse::sgemv(-1, A, x, 1, r);
|
||
// p = r;
|
||
sparse::copy(r, p);
|
||
delta_new = sparse::dot(r, r);
|
||
delta_0 = delta_new;
|
||
while (i < i_max && delta_new > epsilon * epsilon * delta_0) {
|
||
i++;
|
||
// q = A<>p
|
||
mult(A, p, q);
|
||
// alpha = delta_new / p<>q
|
||
alpha = delta_new / sparse::dot(p, q);
|
||
// x = alfa<66>p + x
|
||
sparse::saxpy(alpha, p, x);
|
||
if ((i & 31) == 0) { // recompute r after 32 steps
|
||
// r = b - A<>x
|
||
sparse::copy(b, r);
|
||
sparse::sgemv(-1, A, x, 1, r);
|
||
} else {
|
||
// r = r - alpha<68>q
|
||
sparse::saxpy(-alpha, q, r);
|
||
}
|
||
delta_old = delta_new;
|
||
delta_new = sparse::dot(r, r);
|
||
beta = delta_new / delta_old;
|
||
// p = beta<74>p + r
|
||
sparse::scal(beta, p);
|
||
sparse::saxpy(1, r, p);
|
||
}
|
||
return delta_new <= epsilon * epsilon * delta_0;
|
||
}
|
||
|
||
// Conjugate gradient with preconditioner.
|
||
static bool ConjugateGradientSolver(const JacobiPreconditioner &preconditioner, const sparse::Matrix &A, const FullVector &b, FullVector &x, float epsilon) {
|
||
xaDebugAssert(A.isSquare());
|
||
xaDebugAssert(A.width() == b.dimension());
|
||
xaDebugAssert(A.width() == x.dimension());
|
||
int i = 0;
|
||
const int D = A.width();
|
||
const int i_max = 4 * D; // Convergence should be linear, but in some cases, it's not.
|
||
FullVector r(D); // residual
|
||
FullVector p(D); // search direction
|
||
FullVector q(D); //
|
||
FullVector s(D); // preconditioned
|
||
float delta_0;
|
||
float delta_old;
|
||
float delta_new;
|
||
float alpha;
|
||
float beta;
|
||
// r = b - A<>x
|
||
sparse::copy(b, r);
|
||
sparse::sgemv(-1, A, x, 1, r);
|
||
// p = M^-1 <20> r
|
||
preconditioner.apply(r, p);
|
||
delta_new = sparse::dot(r, p);
|
||
delta_0 = delta_new;
|
||
while (i < i_max && delta_new > epsilon * epsilon * delta_0) {
|
||
i++;
|
||
// q = A<>p
|
||
mult(A, p, q);
|
||
// alpha = delta_new / p<>q
|
||
alpha = delta_new / sparse::dot(p, q);
|
||
// x = alfa<66>p + x
|
||
sparse::saxpy(alpha, p, x);
|
||
if ((i & 31) == 0) { // recompute r after 32 steps
|
||
// r = b - A<>x
|
||
sparse::copy(b, r);
|
||
sparse::sgemv(-1, A, x, 1, r);
|
||
} else {
|
||
// r = r - alfa<66>q
|
||
sparse::saxpy(-alpha, q, r);
|
||
}
|
||
// s = M^-1 <20> r
|
||
preconditioner.apply(r, s);
|
||
delta_old = delta_new;
|
||
delta_new = sparse::dot(r, s);
|
||
beta = delta_new / delta_old;
|
||
// p = s + beta<74>p
|
||
sparse::scal(beta, p);
|
||
sparse::saxpy(1, s, p);
|
||
}
|
||
return delta_new <= epsilon * epsilon * delta_0;
|
||
}
|
||
|
||
static bool SymmetricSolver(const sparse::Matrix &A, const FullVector &b, FullVector &x, float epsilon = 1e-5f) {
|
||
xaDebugAssert(A.height() == A.width());
|
||
xaDebugAssert(A.height() == b.dimension());
|
||
xaDebugAssert(b.dimension() == x.dimension());
|
||
JacobiPreconditioner jacobi(A, true);
|
||
return ConjugateGradientSolver(jacobi, A, b, x, epsilon);
|
||
}
|
||
};
|
||
|
||
namespace param {
|
||
class Atlas;
|
||
class Chart;
|
||
|
||
// Fast sweep in 3 directions
|
||
static bool findApproximateDiameterVertices(halfedge::Mesh *mesh, halfedge::Vertex **a, halfedge::Vertex **b) {
|
||
xaDebugAssert(mesh != NULL);
|
||
xaDebugAssert(a != NULL);
|
||
xaDebugAssert(b != NULL);
|
||
const uint32_t vertexCount = mesh->vertexCount();
|
||
halfedge::Vertex *minVertex[3];
|
||
halfedge::Vertex *maxVertex[3];
|
||
minVertex[0] = minVertex[1] = minVertex[2] = NULL;
|
||
maxVertex[0] = maxVertex[1] = maxVertex[2] = NULL;
|
||
for (uint32_t v = 1; v < vertexCount; v++) {
|
||
halfedge::Vertex *vertex = mesh->vertexAt(v);
|
||
xaDebugAssert(vertex != NULL);
|
||
if (vertex->isBoundary()) {
|
||
minVertex[0] = minVertex[1] = minVertex[2] = vertex;
|
||
maxVertex[0] = maxVertex[1] = maxVertex[2] = vertex;
|
||
break;
|
||
}
|
||
}
|
||
if (minVertex[0] == NULL) {
|
||
// Input mesh has not boundaries.
|
||
return false;
|
||
}
|
||
for (uint32_t v = 1; v < vertexCount; v++) {
|
||
halfedge::Vertex *vertex = mesh->vertexAt(v);
|
||
xaDebugAssert(vertex != NULL);
|
||
if (!vertex->isBoundary()) {
|
||
// Skip interior vertices.
|
||
continue;
|
||
}
|
||
if (vertex->pos.x < minVertex[0]->pos.x)
|
||
minVertex[0] = vertex;
|
||
else if (vertex->pos.x > maxVertex[0]->pos.x)
|
||
maxVertex[0] = vertex;
|
||
if (vertex->pos.y < minVertex[1]->pos.y)
|
||
minVertex[1] = vertex;
|
||
else if (vertex->pos.y > maxVertex[1]->pos.y)
|
||
maxVertex[1] = vertex;
|
||
if (vertex->pos.z < minVertex[2]->pos.z)
|
||
minVertex[2] = vertex;
|
||
else if (vertex->pos.z > maxVertex[2]->pos.z)
|
||
maxVertex[2] = vertex;
|
||
}
|
||
float lengths[3];
|
||
for (int i = 0; i < 3; i++) {
|
||
lengths[i] = length(minVertex[i]->pos - maxVertex[i]->pos);
|
||
}
|
||
if (lengths[0] > lengths[1] && lengths[0] > lengths[2]) {
|
||
*a = minVertex[0];
|
||
*b = maxVertex[0];
|
||
} else if (lengths[1] > lengths[2]) {
|
||
*a = minVertex[1];
|
||
*b = maxVertex[1];
|
||
} else {
|
||
*a = minVertex[2];
|
||
*b = maxVertex[2];
|
||
}
|
||
return true;
|
||
}
|
||
|
||
// Conformal relations from Brecht Van Lommel (based on ABF):
|
||
|
||
static float vec_angle_cos(Vector3::Arg v1, Vector3::Arg v2, Vector3::Arg v3) {
|
||
Vector3 d1 = v1 - v2;
|
||
Vector3 d2 = v3 - v2;
|
||
return clamp(dot(d1, d2) / (length(d1) * length(d2)), -1.0f, 1.0f);
|
||
}
|
||
|
||
static float vec_angle(Vector3::Arg v1, Vector3::Arg v2, Vector3::Arg v3) {
|
||
float dot = vec_angle_cos(v1, v2, v3);
|
||
return acosf(dot);
|
||
}
|
||
|
||
static void triangle_angles(Vector3::Arg v1, Vector3::Arg v2, Vector3::Arg v3, float *a1, float *a2, float *a3) {
|
||
*a1 = vec_angle(v3, v1, v2);
|
||
*a2 = vec_angle(v1, v2, v3);
|
||
*a3 = PI - *a2 - *a1;
|
||
}
|
||
|
||
static void setup_abf_relations(sparse::Matrix &A, int row, const halfedge::Vertex *v0, const halfedge::Vertex *v1, const halfedge::Vertex *v2) {
|
||
int id0 = v0->id;
|
||
int id1 = v1->id;
|
||
int id2 = v2->id;
|
||
Vector3 p0 = v0->pos;
|
||
Vector3 p1 = v1->pos;
|
||
Vector3 p2 = v2->pos;
|
||
// @@ IC: Wouldn't it be more accurate to return cos and compute 1-cos^2?
|
||
// It does indeed seem to be a little bit more robust.
|
||
// @@ Need to revisit this more carefully!
|
||
float a0, a1, a2;
|
||
triangle_angles(p0, p1, p2, &a0, &a1, &a2);
|
||
float s0 = sinf(a0);
|
||
float s1 = sinf(a1);
|
||
float s2 = sinf(a2);
|
||
if (s1 > s0 && s1 > s2) {
|
||
std::swap(s1, s2);
|
||
std::swap(s0, s1);
|
||
std::swap(a1, a2);
|
||
std::swap(a0, a1);
|
||
std::swap(id1, id2);
|
||
std::swap(id0, id1);
|
||
} else if (s0 > s1 && s0 > s2) {
|
||
std::swap(s0, s2);
|
||
std::swap(s0, s1);
|
||
std::swap(a0, a2);
|
||
std::swap(a0, a1);
|
||
std::swap(id0, id2);
|
||
std::swap(id0, id1);
|
||
}
|
||
float c0 = cosf(a0);
|
||
float ratio = (s2 == 0.0f) ? 1.0f : s1 / s2;
|
||
float cosine = c0 * ratio;
|
||
float sine = s0 * ratio;
|
||
// Note : 2*id + 0 --> u
|
||
// 2*id + 1 --> v
|
||
int u0_id = 2 * id0 + 0;
|
||
int v0_id = 2 * id0 + 1;
|
||
int u1_id = 2 * id1 + 0;
|
||
int v1_id = 2 * id1 + 1;
|
||
int u2_id = 2 * id2 + 0;
|
||
int v2_id = 2 * id2 + 1;
|
||
// Real part
|
||
A.setCoefficient(u0_id, 2 * row + 0, cosine - 1.0f);
|
||
A.setCoefficient(v0_id, 2 * row + 0, -sine);
|
||
A.setCoefficient(u1_id, 2 * row + 0, -cosine);
|
||
A.setCoefficient(v1_id, 2 * row + 0, sine);
|
||
A.setCoefficient(u2_id, 2 * row + 0, 1);
|
||
// Imaginary part
|
||
A.setCoefficient(u0_id, 2 * row + 1, sine);
|
||
A.setCoefficient(v0_id, 2 * row + 1, cosine - 1.0f);
|
||
A.setCoefficient(u1_id, 2 * row + 1, -sine);
|
||
A.setCoefficient(v1_id, 2 * row + 1, -cosine);
|
||
A.setCoefficient(v2_id, 2 * row + 1, 1);
|
||
}
|
||
|
||
bool computeLeastSquaresConformalMap(halfedge::Mesh *mesh) {
|
||
xaDebugAssert(mesh != NULL);
|
||
// For this to work properly, mesh should not have colocals that have the same
|
||
// attributes, unless you want the vertices to actually have different texcoords.
|
||
const uint32_t vertexCount = mesh->vertexCount();
|
||
const uint32_t D = 2 * vertexCount;
|
||
const uint32_t N = 2 * halfedge::countMeshTriangles(mesh);
|
||
// N is the number of equations (one per triangle)
|
||
// D is the number of variables (one per vertex; there are 2 pinned vertices).
|
||
if (N < D - 4) {
|
||
return false;
|
||
}
|
||
sparse::Matrix A(D, N);
|
||
FullVector b(N);
|
||
FullVector x(D);
|
||
// Fill b:
|
||
b.fill(0.0f);
|
||
// Fill x:
|
||
halfedge::Vertex *v0;
|
||
halfedge::Vertex *v1;
|
||
if (!findApproximateDiameterVertices(mesh, &v0, &v1)) {
|
||
// Mesh has no boundaries.
|
||
return false;
|
||
}
|
||
if (v0->tex == v1->tex) {
|
||
// LSCM expects an existing parameterization.
|
||
return false;
|
||
}
|
||
for (uint32_t v = 0; v < vertexCount; v++) {
|
||
halfedge::Vertex *vertex = mesh->vertexAt(v);
|
||
xaDebugAssert(vertex != NULL);
|
||
// Initial solution.
|
||
x[2 * v + 0] = vertex->tex.x;
|
||
x[2 * v + 1] = vertex->tex.y;
|
||
}
|
||
// Fill A:
|
||
const uint32_t faceCount = mesh->faceCount();
|
||
for (uint32_t f = 0, t = 0; f < faceCount; f++) {
|
||
const halfedge::Face *face = mesh->faceAt(f);
|
||
xaDebugAssert(face != NULL);
|
||
xaDebugAssert(face->edgeCount() == 3);
|
||
const halfedge::Vertex *vertex0 = NULL;
|
||
for (halfedge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const halfedge::Edge *edge = it.current();
|
||
xaAssert(edge != NULL);
|
||
if (vertex0 == NULL) {
|
||
vertex0 = edge->vertex;
|
||
} else if (edge->next->vertex != vertex0) {
|
||
const halfedge::Vertex *vertex1 = edge->from();
|
||
const halfedge::Vertex *vertex2 = edge->to();
|
||
setup_abf_relations(A, t, vertex0, vertex1, vertex2);
|
||
//setup_conformal_map_relations(A, t, vertex0, vertex1, vertex2);
|
||
t++;
|
||
}
|
||
}
|
||
}
|
||
const uint32_t lockedParameters[] = {
|
||
2 * v0->id + 0,
|
||
2 * v0->id + 1,
|
||
2 * v1->id + 0,
|
||
2 * v1->id + 1
|
||
};
|
||
// Solve
|
||
Solver::LeastSquaresSolver(A, b, x, lockedParameters, 4, 0.000001f);
|
||
// Map x back to texcoords:
|
||
for (uint32_t v = 0; v < vertexCount; v++) {
|
||
halfedge::Vertex *vertex = mesh->vertexAt(v);
|
||
xaDebugAssert(vertex != NULL);
|
||
vertex->tex = Vector2(x[2 * v + 0], x[2 * v + 1]);
|
||
}
|
||
return true;
|
||
}
|
||
|
||
bool computeOrthogonalProjectionMap(halfedge::Mesh *mesh) {
|
||
Vector3 axis[2];
|
||
uint32_t vertexCount = mesh->vertexCount();
|
||
std::vector<Vector3> points(vertexCount);
|
||
points.resize(vertexCount);
|
||
for (uint32_t i = 0; i < vertexCount; i++) {
|
||
points[i] = mesh->vertexAt(i)->pos;
|
||
}
|
||
// Avoid redundant computations.
|
||
float matrix[6];
|
||
Fit::computeCovariance(vertexCount, points.data(), matrix);
|
||
if (matrix[0] == 0 && matrix[3] == 0 && matrix[5] == 0) {
|
||
return false;
|
||
}
|
||
float eigenValues[3];
|
||
Vector3 eigenVectors[3];
|
||
if (!Fit::eigenSolveSymmetric3(matrix, eigenValues, eigenVectors)) {
|
||
return false;
|
||
}
|
||
axis[0] = normalize(eigenVectors[0]);
|
||
axis[1] = normalize(eigenVectors[1]);
|
||
// Project vertices to plane.
|
||
for (halfedge::Mesh::VertexIterator it(mesh->vertices()); !it.isDone(); it.advance()) {
|
||
halfedge::Vertex *vertex = it.current();
|
||
vertex->tex.x = dot(axis[0], vertex->pos);
|
||
vertex->tex.y = dot(axis[1], vertex->pos);
|
||
}
|
||
return true;
|
||
}
|
||
|
||
void computeSingleFaceMap(halfedge::Mesh *mesh) {
|
||
xaDebugAssert(mesh != NULL);
|
||
xaDebugAssert(mesh->faceCount() == 1);
|
||
halfedge::Face *face = mesh->faceAt(0);
|
||
xaAssert(face != NULL);
|
||
Vector3 p0 = face->edge->from()->pos;
|
||
Vector3 p1 = face->edge->to()->pos;
|
||
Vector3 X = normalizeSafe(p1 - p0, Vector3(0.0f), 0.0f);
|
||
Vector3 Z = face->normal();
|
||
Vector3 Y = normalizeSafe(cross(Z, X), Vector3(0.0f), 0.0f);
|
||
uint32_t i = 0;
|
||
for (halfedge::Face::EdgeIterator it(face->edges()); !it.isDone(); it.advance(), i++) {
|
||
halfedge::Vertex *vertex = it.vertex();
|
||
xaAssert(vertex != NULL);
|
||
if (i == 0) {
|
||
vertex->tex = Vector2(0);
|
||
} else {
|
||
Vector3 pn = vertex->pos;
|
||
float xn = dot((pn - p0), X);
|
||
float yn = dot((pn - p0), Y);
|
||
vertex->tex = Vector2(xn, yn);
|
||
}
|
||
}
|
||
}
|
||
|
||
// Dummy implementation of a priority queue using sort at insertion.
|
||
// - Insertion is o(n)
|
||
// - Smallest element goes at the end, so that popping it is o(1).
|
||
// - Resorting is n*log(n)
|
||
// @@ Number of elements in the queue is usually small, and we'd have to rebalance often. I'm not sure it's worth implementing a heap.
|
||
// @@ Searcing at removal would remove the need for sorting when priorities change.
|
||
struct PriorityQueue {
|
||
PriorityQueue(uint32_t size = UINT_MAX) :
|
||
maxSize(size) {}
|
||
|
||
void push(float priority, uint32_t face) {
|
||
uint32_t i = 0;
|
||
const uint32_t count = pairs.size();
|
||
for (; i < count; i++) {
|
||
if (pairs[i].priority > priority) break;
|
||
}
|
||
Pair p = { priority, face };
|
||
pairs.insert(pairs.begin() + i, p);
|
||
if (pairs.size() > maxSize) {
|
||
pairs.erase(pairs.begin());
|
||
}
|
||
}
|
||
|
||
// push face out of order, to be sorted later.
|
||
void push(uint32_t face) {
|
||
Pair p = { 0.0f, face };
|
||
pairs.push_back(p);
|
||
}
|
||
|
||
uint32_t pop() {
|
||
uint32_t f = pairs.back().face;
|
||
pairs.pop_back();
|
||
return f;
|
||
}
|
||
|
||
void sort() {
|
||
//sort(pairs); // @@ My intro sort appears to be much slower than it should!
|
||
std::sort(pairs.begin(), pairs.end());
|
||
}
|
||
|
||
void clear() {
|
||
pairs.clear();
|
||
}
|
||
|
||
uint32_t count() const {
|
||
return pairs.size();
|
||
}
|
||
|
||
float firstPriority() const {
|
||
return pairs.back().priority;
|
||
}
|
||
|
||
const uint32_t maxSize;
|
||
|
||
struct Pair {
|
||
bool operator<(const Pair &p) const {
|
||
return priority > p.priority; // !! Sort in inverse priority order!
|
||
}
|
||
|
||
float priority;
|
||
uint32_t face;
|
||
};
|
||
|
||
std::vector<Pair> pairs;
|
||
};
|
||
|
||
struct ChartBuildData {
|
||
ChartBuildData(int p_id) :
|
||
id(p_id) {
|
||
planeNormal = Vector3(0);
|
||
centroid = Vector3(0);
|
||
coneAxis = Vector3(0);
|
||
coneAngle = 0;
|
||
area = 0;
|
||
boundaryLength = 0;
|
||
normalSum = Vector3(0);
|
||
centroidSum = Vector3(0);
|
||
}
|
||
|
||
int id;
|
||
|
||
// Proxy info:
|
||
Vector3 planeNormal;
|
||
Vector3 centroid;
|
||
Vector3 coneAxis;
|
||
float coneAngle;
|
||
|
||
float area;
|
||
float boundaryLength;
|
||
Vector3 normalSum;
|
||
Vector3 centroidSum;
|
||
|
||
std::vector<uint32_t> seeds; // @@ These could be a pointers to the halfedge faces directly.
|
||
std::vector<uint32_t> faces;
|
||
PriorityQueue candidates;
|
||
};
|
||
|
||
struct AtlasBuilder {
|
||
AtlasBuilder(const halfedge::Mesh *m) :
|
||
mesh(m),
|
||
facesLeft(m->faceCount()) {
|
||
const uint32_t faceCount = m->faceCount();
|
||
faceChartArray.resize(faceCount, -1);
|
||
faceCandidateArray.resize(faceCount, (uint32_t)-1);
|
||
// @@ Floyd for the whole mesh is too slow. We could compute floyd progressively per patch as the patch grows. We need a better solution to compute most central faces.
|
||
//computeShortestPaths();
|
||
// Precompute edge lengths and face areas.
|
||
uint32_t edgeCount = m->edgeCount();
|
||
edgeLengths.resize(edgeCount);
|
||
for (uint32_t i = 0; i < edgeCount; i++) {
|
||
uint32_t id = m->edgeAt(i)->id;
|
||
xaDebugAssert(id / 2 == i);
|
||
#ifdef NDEBUG
|
||
id = 0; // silence unused parameter warning
|
||
#endif
|
||
edgeLengths[i] = m->edgeAt(i)->length();
|
||
}
|
||
faceAreas.resize(faceCount);
|
||
for (uint32_t i = 0; i < faceCount; i++) {
|
||
faceAreas[i] = m->faceAt(i)->area();
|
||
}
|
||
}
|
||
|
||
~AtlasBuilder() {
|
||
const uint32_t chartCount = chartArray.size();
|
||
for (uint32_t i = 0; i < chartCount; i++) {
|
||
delete chartArray[i];
|
||
}
|
||
}
|
||
|
||
void markUnchartedFaces(const std::vector<uint32_t> &unchartedFaces) {
|
||
const uint32_t unchartedFaceCount = unchartedFaces.size();
|
||
for (uint32_t i = 0; i < unchartedFaceCount; i++) {
|
||
uint32_t f = unchartedFaces[i];
|
||
faceChartArray[f] = -2;
|
||
//faceCandidateArray[f] = -2; // @@ ?
|
||
removeCandidate(f);
|
||
}
|
||
xaDebugAssert(facesLeft >= unchartedFaceCount);
|
||
facesLeft -= unchartedFaceCount;
|
||
}
|
||
|
||
void computeShortestPaths() {
|
||
const uint32_t faceCount = mesh->faceCount();
|
||
shortestPaths.resize(faceCount * faceCount, FLT_MAX);
|
||
// Fill edges:
|
||
for (uint32_t i = 0; i < faceCount; i++) {
|
||
shortestPaths[i * faceCount + i] = 0.0f;
|
||
const halfedge::Face *face_i = mesh->faceAt(i);
|
||
Vector3 centroid_i = face_i->centroid();
|
||
for (halfedge::Face::ConstEdgeIterator it(face_i->edges()); !it.isDone(); it.advance()) {
|
||
const halfedge::Edge *edge = it.current();
|
||
if (!edge->isBoundary()) {
|
||
const halfedge::Face *face_j = edge->pair->face;
|
||
uint32_t j = face_j->id;
|
||
Vector3 centroid_j = face_j->centroid();
|
||
shortestPaths[i * faceCount + j] = shortestPaths[j * faceCount + i] = length(centroid_i - centroid_j);
|
||
}
|
||
}
|
||
}
|
||
// Use Floyd-Warshall algorithm to compute all paths:
|
||
for (uint32_t k = 0; k < faceCount; k++) {
|
||
for (uint32_t i = 0; i < faceCount; i++) {
|
||
for (uint32_t j = 0; j < faceCount; j++) {
|
||
shortestPaths[i * faceCount + j] = std::min(shortestPaths[i * faceCount + j], shortestPaths[i * faceCount + k] + shortestPaths[k * faceCount + j]);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
void placeSeeds(float threshold, uint32_t maxSeedCount) {
|
||
// Instead of using a predefiened number of seeds:
|
||
// - Add seeds one by one, growing chart until a certain treshold.
|
||
// - Undo charts and restart growing process.
|
||
// @@ How can we give preference to faces far from sharp features as in the LSCM paper?
|
||
// - those points can be found using a simple flood filling algorithm.
|
||
// - how do we weight the probabilities?
|
||
for (uint32_t i = 0; i < maxSeedCount; i++) {
|
||
if (facesLeft == 0) {
|
||
// No faces left, stop creating seeds.
|
||
break;
|
||
}
|
||
createRandomChart(threshold);
|
||
}
|
||
}
|
||
|
||
void createRandomChart(float threshold) {
|
||
ChartBuildData *chart = new ChartBuildData(chartArray.size());
|
||
chartArray.push_back(chart);
|
||
// Pick random face that is not used by any chart yet.
|
||
uint32_t randomFaceIdx = rand.getRange(facesLeft - 1);
|
||
uint32_t i = 0;
|
||
for (uint32_t f = 0; f != randomFaceIdx; f++, i++) {
|
||
while (faceChartArray[i] != -1)
|
||
i++;
|
||
}
|
||
while (faceChartArray[i] != -1)
|
||
i++;
|
||
chart->seeds.push_back(i);
|
||
addFaceToChart(chart, i, true);
|
||
// Grow the chart as much as possible within the given threshold.
|
||
growChart(chart, threshold * 0.5f, facesLeft);
|
||
//growCharts(threshold - threshold * 0.75f / chartCount(), facesLeft);
|
||
}
|
||
|
||
void addFaceToChart(ChartBuildData *chart, uint32_t f, bool recomputeProxy = false) {
|
||
// Add face to chart.
|
||
chart->faces.push_back(f);
|
||
xaDebugAssert(faceChartArray[f] == -1);
|
||
faceChartArray[f] = chart->id;
|
||
facesLeft--;
|
||
// Update area and boundary length.
|
||
chart->area = evaluateChartArea(chart, f);
|
||
chart->boundaryLength = evaluateBoundaryLength(chart, f);
|
||
chart->normalSum = evaluateChartNormalSum(chart, f);
|
||
chart->centroidSum = evaluateChartCentroidSum(chart, f);
|
||
if (recomputeProxy) {
|
||
// Update proxy and candidate's priorities.
|
||
updateProxy(chart);
|
||
}
|
||
// Update candidates.
|
||
removeCandidate(f);
|
||
updateCandidates(chart, f);
|
||
updatePriorities(chart);
|
||
}
|
||
|
||
// Returns true if any of the charts can grow more.
|
||
bool growCharts(float threshold, uint32_t faceCount) {
|
||
// Using one global list.
|
||
faceCount = std::min(faceCount, facesLeft);
|
||
for (uint32_t i = 0; i < faceCount; i++) {
|
||
const Candidate &candidate = getBestCandidate();
|
||
if (candidate.metric > threshold) {
|
||
return false; // Can't grow more.
|
||
}
|
||
addFaceToChart(candidate.chart, candidate.face);
|
||
}
|
||
return facesLeft != 0; // Can continue growing.
|
||
}
|
||
|
||
bool growChart(ChartBuildData *chart, float threshold, uint32_t faceCount) {
|
||
// Try to add faceCount faces within threshold to chart.
|
||
for (uint32_t i = 0; i < faceCount;) {
|
||
if (chart->candidates.count() == 0 || chart->candidates.firstPriority() > threshold) {
|
||
return false;
|
||
}
|
||
uint32_t f = chart->candidates.pop();
|
||
if (faceChartArray[f] == -1) {
|
||
addFaceToChart(chart, f);
|
||
i++;
|
||
}
|
||
}
|
||
if (chart->candidates.count() == 0 || chart->candidates.firstPriority() > threshold) {
|
||
return false;
|
||
}
|
||
return true;
|
||
}
|
||
|
||
void resetCharts() {
|
||
const uint32_t faceCount = mesh->faceCount();
|
||
for (uint32_t i = 0; i < faceCount; i++) {
|
||
faceChartArray[i] = -1;
|
||
faceCandidateArray[i] = (uint32_t)-1;
|
||
}
|
||
facesLeft = faceCount;
|
||
candidateArray.clear();
|
||
const uint32_t chartCount = chartArray.size();
|
||
for (uint32_t i = 0; i < chartCount; i++) {
|
||
ChartBuildData *chart = chartArray[i];
|
||
const uint32_t seed = chart->seeds.back();
|
||
chart->area = 0.0f;
|
||
chart->boundaryLength = 0.0f;
|
||
chart->normalSum = Vector3(0);
|
||
chart->centroidSum = Vector3(0);
|
||
chart->faces.clear();
|
||
chart->candidates.clear();
|
||
addFaceToChart(chart, seed);
|
||
}
|
||
}
|
||
|
||
void updateCandidates(ChartBuildData *chart, uint32_t f) {
|
||
const halfedge::Face *face = mesh->faceAt(f);
|
||
// Traverse neighboring faces, add the ones that do not belong to any chart yet.
|
||
for (halfedge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const halfedge::Edge *edge = it.current()->pair;
|
||
if (!edge->isBoundary()) {
|
||
uint32_t faceId = edge->face->id;
|
||
if (faceChartArray[faceId] == -1) {
|
||
chart->candidates.push(faceId);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
void updateProxies() {
|
||
const uint32_t chartCount = chartArray.size();
|
||
for (uint32_t i = 0; i < chartCount; i++) {
|
||
updateProxy(chartArray[i]);
|
||
}
|
||
}
|
||
|
||
void updateProxy(ChartBuildData *chart) {
|
||
//#pragma message(NV_FILE_LINE "TODO: Use best fit plane instead of average normal.")
|
||
chart->planeNormal = normalizeSafe(chart->normalSum, Vector3(0), 0.0f);
|
||
chart->centroid = chart->centroidSum / float(chart->faces.size());
|
||
}
|
||
|
||
bool relocateSeeds() {
|
||
bool anySeedChanged = false;
|
||
const uint32_t chartCount = chartArray.size();
|
||
for (uint32_t i = 0; i < chartCount; i++) {
|
||
if (relocateSeed(chartArray[i])) {
|
||
anySeedChanged = true;
|
||
}
|
||
}
|
||
return anySeedChanged;
|
||
}
|
||
|
||
bool relocateSeed(ChartBuildData *chart) {
|
||
Vector3 centroid = computeChartCentroid(chart);
|
||
const uint32_t N = 10; // @@ Hardcoded to 10?
|
||
PriorityQueue bestTriangles(N);
|
||
// Find the first N triangles that fit the proxy best.
|
||
const uint32_t faceCount = chart->faces.size();
|
||
for (uint32_t i = 0; i < faceCount; i++) {
|
||
float priority = evaluateProxyFitMetric(chart, chart->faces[i]);
|
||
bestTriangles.push(priority, chart->faces[i]);
|
||
}
|
||
// Of those, choose the most central triangle.
|
||
uint32_t mostCentral;
|
||
float maxDistance = -1;
|
||
const uint32_t bestCount = bestTriangles.count();
|
||
for (uint32_t i = 0; i < bestCount; i++) {
|
||
const halfedge::Face *face = mesh->faceAt(bestTriangles.pairs[i].face);
|
||
Vector3 faceCentroid = face->triangleCenter();
|
||
float distance = length(centroid - faceCentroid);
|
||
if (distance > maxDistance) {
|
||
maxDistance = distance;
|
||
mostCentral = bestTriangles.pairs[i].face;
|
||
}
|
||
}
|
||
xaDebugAssert(maxDistance >= 0);
|
||
// In order to prevent k-means cyles we record all the previously chosen seeds.
|
||
uint32_t index = std::find(chart->seeds.begin(), chart->seeds.end(), mostCentral) - chart->seeds.begin();
|
||
if (index < chart->seeds.size()) {
|
||
// Move new seed to the end of the seed array.
|
||
uint32_t last = chart->seeds.size() - 1;
|
||
std::swap(chart->seeds[index], chart->seeds[last]);
|
||
return false;
|
||
} else {
|
||
// Append new seed.
|
||
chart->seeds.push_back(mostCentral);
|
||
return true;
|
||
}
|
||
}
|
||
|
||
void updatePriorities(ChartBuildData *chart) {
|
||
// Re-evaluate candidate priorities.
|
||
uint32_t candidateCount = chart->candidates.count();
|
||
for (uint32_t i = 0; i < candidateCount; i++) {
|
||
chart->candidates.pairs[i].priority = evaluatePriority(chart, chart->candidates.pairs[i].face);
|
||
if (faceChartArray[chart->candidates.pairs[i].face] == -1) {
|
||
updateCandidate(chart, chart->candidates.pairs[i].face, chart->candidates.pairs[i].priority);
|
||
}
|
||
}
|
||
// Sort candidates.
|
||
chart->candidates.sort();
|
||
}
|
||
|
||
// Evaluate combined metric.
|
||
float evaluatePriority(ChartBuildData *chart, uint32_t face) {
|
||
// Estimate boundary length and area:
|
||
float newBoundaryLength = evaluateBoundaryLength(chart, face);
|
||
float newChartArea = evaluateChartArea(chart, face);
|
||
float F = evaluateProxyFitMetric(chart, face);
|
||
float C = evaluateRoundnessMetric(chart, face, newBoundaryLength, newChartArea);
|
||
float P = evaluateStraightnessMetric(chart, face);
|
||
// Penalize faces that cross seams, reward faces that close seams or reach boundaries.
|
||
float N = evaluateNormalSeamMetric(chart, face);
|
||
float T = evaluateTextureSeamMetric(chart, face);
|
||
//float R = evaluateCompletenessMetric(chart, face);
|
||
//float D = evaluateDihedralAngleMetric(chart, face);
|
||
// @@ Add a metric based on local dihedral angle.
|
||
// @@ Tweaking the normal and texture seam metrics.
|
||
// - Cause more impedance. Never cross 90 degree edges.
|
||
// -
|
||
float cost = float(
|
||
options.proxyFitMetricWeight * F +
|
||
options.roundnessMetricWeight * C +
|
||
options.straightnessMetricWeight * P +
|
||
options.normalSeamMetricWeight * N +
|
||
options.textureSeamMetricWeight * T);
|
||
// Enforce limits strictly:
|
||
if (newChartArea > options.maxChartArea) cost = FLT_MAX;
|
||
if (newBoundaryLength > options.maxBoundaryLength) cost = FLT_MAX;
|
||
// Make sure normal seams are fully respected:
|
||
if (options.normalSeamMetricWeight >= 1000 && N != 0) cost = FLT_MAX;
|
||
xaAssert(std::isfinite(cost));
|
||
return cost;
|
||
}
|
||
|
||
// Returns a value in [0-1].
|
||
float evaluateProxyFitMetric(ChartBuildData *chart, uint32_t f) {
|
||
const halfedge::Face *face = mesh->faceAt(f);
|
||
Vector3 faceNormal = face->triangleNormal();
|
||
// Use plane fitting metric for now:
|
||
return 1 - dot(faceNormal, chart->planeNormal); // @@ normal deviations should be weighted by face area
|
||
}
|
||
|
||
float evaluateRoundnessMetric(ChartBuildData *chart, uint32_t /*face*/, float newBoundaryLength, float newChartArea) {
|
||
float roundness = square(chart->boundaryLength) / chart->area;
|
||
float newRoundness = square(newBoundaryLength) / newChartArea;
|
||
if (newRoundness > roundness) {
|
||
return square(newBoundaryLength) / (newChartArea * 4 * PI);
|
||
} else {
|
||
// Offer no impedance to faces that improve roundness.
|
||
return 0;
|
||
}
|
||
}
|
||
|
||
float evaluateStraightnessMetric(ChartBuildData *chart, uint32_t f) {
|
||
float l_out = 0.0f;
|
||
float l_in = 0.0f;
|
||
const halfedge::Face *face = mesh->faceAt(f);
|
||
for (halfedge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const halfedge::Edge *edge = it.current();
|
||
float l = edgeLengths[edge->id / 2];
|
||
if (edge->isBoundary()) {
|
||
l_out += l;
|
||
} else {
|
||
uint32_t neighborFaceId = edge->pair->face->id;
|
||
if (faceChartArray[neighborFaceId] != chart->id) {
|
||
l_out += l;
|
||
} else {
|
||
l_in += l;
|
||
}
|
||
}
|
||
}
|
||
xaDebugAssert(l_in != 0.0f); // Candidate face must be adjacent to chart. @@ This is not true if the input mesh has zero-length edges.
|
||
float ratio = (l_out - l_in) / (l_out + l_in);
|
||
return std::min(ratio, 0.0f); // Only use the straightness metric to close gaps.
|
||
}
|
||
|
||
float evaluateNormalSeamMetric(ChartBuildData *chart, uint32_t f) {
|
||
float seamFactor = 0.0f;
|
||
float totalLength = 0.0f;
|
||
const halfedge::Face *face = mesh->faceAt(f);
|
||
for (halfedge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const halfedge::Edge *edge = it.current();
|
||
if (edge->isBoundary()) {
|
||
continue;
|
||
}
|
||
const uint32_t neighborFaceId = edge->pair->face->id;
|
||
if (faceChartArray[neighborFaceId] != chart->id) {
|
||
continue;
|
||
}
|
||
//float l = edge->length();
|
||
float l = edgeLengths[edge->id / 2];
|
||
totalLength += l;
|
||
if (!edge->isSeam()) {
|
||
continue;
|
||
}
|
||
// Make sure it's a normal seam.
|
||
if (edge->isNormalSeam()) {
|
||
float d0 = clamp(dot(edge->vertex->nor, edge->pair->next->vertex->nor), 0.0f, 1.0f);
|
||
float d1 = clamp(dot(edge->next->vertex->nor, edge->pair->vertex->nor), 0.0f, 1.0f);
|
||
l *= 1 - (d0 + d1) * 0.5f;
|
||
seamFactor += l;
|
||
}
|
||
}
|
||
if (seamFactor == 0) return 0.0f;
|
||
return seamFactor / totalLength;
|
||
}
|
||
|
||
float evaluateTextureSeamMetric(ChartBuildData *chart, uint32_t f) {
|
||
float seamLength = 0.0f;
|
||
float totalLength = 0.0f;
|
||
const halfedge::Face *face = mesh->faceAt(f);
|
||
for (halfedge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const halfedge::Edge *edge = it.current();
|
||
if (edge->isBoundary()) {
|
||
continue;
|
||
}
|
||
const uint32_t neighborFaceId = edge->pair->face->id;
|
||
if (faceChartArray[neighborFaceId] != chart->id) {
|
||
continue;
|
||
}
|
||
//float l = edge->length();
|
||
float l = edgeLengths[edge->id / 2];
|
||
totalLength += l;
|
||
if (!edge->isSeam()) {
|
||
continue;
|
||
}
|
||
// Make sure it's a texture seam.
|
||
if (edge->isTextureSeam()) {
|
||
seamLength += l;
|
||
}
|
||
}
|
||
if (seamLength == 0.0f) {
|
||
return 0.0f; // Avoid division by zero.
|
||
}
|
||
return seamLength / totalLength;
|
||
}
|
||
|
||
float evaluateChartArea(ChartBuildData *chart, uint32_t f) {
|
||
const halfedge::Face *face = mesh->faceAt(f);
|
||
return chart->area + faceAreas[face->id];
|
||
}
|
||
|
||
float evaluateBoundaryLength(ChartBuildData *chart, uint32_t f) {
|
||
float boundaryLength = chart->boundaryLength;
|
||
// Add new edges, subtract edges shared with the chart.
|
||
const halfedge::Face *face = mesh->faceAt(f);
|
||
for (halfedge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const halfedge::Edge *edge = it.current();
|
||
//float edgeLength = edge->length();
|
||
float edgeLength = edgeLengths[edge->id / 2];
|
||
if (edge->isBoundary()) {
|
||
boundaryLength += edgeLength;
|
||
} else {
|
||
uint32_t neighborFaceId = edge->pair->face->id;
|
||
if (faceChartArray[neighborFaceId] != chart->id) {
|
||
boundaryLength += edgeLength;
|
||
} else {
|
||
boundaryLength -= edgeLength;
|
||
}
|
||
}
|
||
}
|
||
return std::max(0.0f, boundaryLength); // @@ Hack!
|
||
}
|
||
|
||
Vector3 evaluateChartNormalSum(ChartBuildData *chart, uint32_t f) {
|
||
const halfedge::Face *face = mesh->faceAt(f);
|
||
return chart->normalSum + face->triangleNormalAreaScaled();
|
||
}
|
||
|
||
Vector3 evaluateChartCentroidSum(ChartBuildData *chart, uint32_t f) {
|
||
const halfedge::Face *face = mesh->faceAt(f);
|
||
return chart->centroidSum + face->centroid();
|
||
}
|
||
|
||
Vector3 computeChartCentroid(const ChartBuildData *chart) {
|
||
Vector3 centroid(0);
|
||
const uint32_t faceCount = chart->faces.size();
|
||
for (uint32_t i = 0; i < faceCount; i++) {
|
||
const halfedge::Face *face = mesh->faceAt(chart->faces[i]);
|
||
centroid += face->triangleCenter();
|
||
}
|
||
return centroid / float(faceCount);
|
||
}
|
||
|
||
void fillHoles(float threshold) {
|
||
while (facesLeft > 0)
|
||
createRandomChart(threshold);
|
||
}
|
||
|
||
void mergeCharts() {
|
||
std::vector<float> sharedBoundaryLengths;
|
||
const uint32_t chartCount = chartArray.size();
|
||
for (int c = chartCount - 1; c >= 0; c--) {
|
||
sharedBoundaryLengths.clear();
|
||
sharedBoundaryLengths.resize(chartCount, 0.0f);
|
||
ChartBuildData *chart = chartArray[c];
|
||
float externalBoundary = 0.0f;
|
||
const uint32_t faceCount = chart->faces.size();
|
||
for (uint32_t i = 0; i < faceCount; i++) {
|
||
uint32_t f = chart->faces[i];
|
||
const halfedge::Face *face = mesh->faceAt(f);
|
||
for (halfedge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const halfedge::Edge *edge = it.current();
|
||
//float l = edge->length();
|
||
float l = edgeLengths[edge->id / 2];
|
||
if (edge->isBoundary()) {
|
||
externalBoundary += l;
|
||
} else {
|
||
uint32_t neighborFace = edge->pair->face->id;
|
||
uint32_t neighborChart = faceChartArray[neighborFace];
|
||
if (neighborChart != (uint32_t)c) {
|
||
if ((edge->isSeam() && (edge->isNormalSeam() || edge->isTextureSeam())) || neighborChart == -2) {
|
||
externalBoundary += l;
|
||
} else {
|
||
sharedBoundaryLengths[neighborChart] += l;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
for (int cc = chartCount - 1; cc >= 0; cc--) {
|
||
if (cc == c)
|
||
continue;
|
||
ChartBuildData *chart2 = chartArray[cc];
|
||
if (chart2 == NULL)
|
||
continue;
|
||
if (sharedBoundaryLengths[cc] > 0.8 * std::max(0.0f, chart->boundaryLength - externalBoundary)) {
|
||
// Try to avoid degenerate configurations.
|
||
if (chart2->boundaryLength > sharedBoundaryLengths[cc]) {
|
||
if (dot(chart2->planeNormal, chart->planeNormal) > -0.25) {
|
||
mergeChart(chart2, chart, sharedBoundaryLengths[cc]);
|
||
delete chart;
|
||
chartArray[c] = NULL;
|
||
break;
|
||
}
|
||
}
|
||
}
|
||
if (sharedBoundaryLengths[cc] > 0.20 * std::max(0.0f, chart->boundaryLength - externalBoundary)) {
|
||
// Compare proxies.
|
||
if (dot(chart2->planeNormal, chart->planeNormal) > 0) {
|
||
mergeChart(chart2, chart, sharedBoundaryLengths[cc]);
|
||
delete chart;
|
||
chartArray[c] = NULL;
|
||
break;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
// Remove deleted charts.
|
||
for (int c = 0; c < int32_t(chartArray.size()); /*do not increment if removed*/) {
|
||
if (chartArray[c] == NULL) {
|
||
chartArray.erase(chartArray.begin() + c);
|
||
// Update faceChartArray.
|
||
const uint32_t faceCount = faceChartArray.size();
|
||
for (uint32_t i = 0; i < faceCount; i++) {
|
||
xaDebugAssert(faceChartArray[i] != -1);
|
||
xaDebugAssert(faceChartArray[i] != c);
|
||
xaDebugAssert(faceChartArray[i] <= int32_t(chartArray.size()));
|
||
if (faceChartArray[i] > c) {
|
||
faceChartArray[i]--;
|
||
}
|
||
}
|
||
} else {
|
||
chartArray[c]->id = c;
|
||
c++;
|
||
}
|
||
}
|
||
}
|
||
|
||
// @@ Cleanup.
|
||
struct Candidate {
|
||
uint32_t face;
|
||
ChartBuildData *chart;
|
||
float metric;
|
||
};
|
||
|
||
// @@ Get N best candidates in one pass.
|
||
const Candidate &getBestCandidate() const {
|
||
uint32_t best = 0;
|
||
float bestCandidateMetric = FLT_MAX;
|
||
const uint32_t candidateCount = candidateArray.size();
|
||
xaAssert(candidateCount > 0);
|
||
for (uint32_t i = 0; i < candidateCount; i++) {
|
||
const Candidate &candidate = candidateArray[i];
|
||
if (candidate.metric < bestCandidateMetric) {
|
||
bestCandidateMetric = candidate.metric;
|
||
best = i;
|
||
}
|
||
}
|
||
return candidateArray[best];
|
||
}
|
||
|
||
void removeCandidate(uint32_t f) {
|
||
int c = faceCandidateArray[f];
|
||
if (c != -1) {
|
||
faceCandidateArray[f] = (uint32_t)-1;
|
||
if (c == int(candidateArray.size() - 1)) {
|
||
candidateArray.pop_back();
|
||
} else {
|
||
// Replace with last.
|
||
candidateArray[c] = candidateArray[candidateArray.size() - 1];
|
||
candidateArray.pop_back();
|
||
faceCandidateArray[candidateArray[c].face] = c;
|
||
}
|
||
}
|
||
}
|
||
|
||
void updateCandidate(ChartBuildData *chart, uint32_t f, float metric) {
|
||
if (faceCandidateArray[f] == -1) {
|
||
const uint32_t index = candidateArray.size();
|
||
faceCandidateArray[f] = index;
|
||
candidateArray.resize(index + 1);
|
||
candidateArray[index].face = f;
|
||
candidateArray[index].chart = chart;
|
||
candidateArray[index].metric = metric;
|
||
} else {
|
||
int c = faceCandidateArray[f];
|
||
xaDebugAssert(c != -1);
|
||
Candidate &candidate = candidateArray[c];
|
||
xaDebugAssert(candidate.face == f);
|
||
if (metric < candidate.metric || chart == candidate.chart) {
|
||
candidate.metric = metric;
|
||
candidate.chart = chart;
|
||
}
|
||
}
|
||
}
|
||
|
||
void mergeChart(ChartBuildData *owner, ChartBuildData *chart, float sharedBoundaryLength) {
|
||
const uint32_t faceCount = chart->faces.size();
|
||
for (uint32_t i = 0; i < faceCount; i++) {
|
||
uint32_t f = chart->faces[i];
|
||
xaDebugAssert(faceChartArray[f] == chart->id);
|
||
faceChartArray[f] = owner->id;
|
||
owner->faces.push_back(f);
|
||
}
|
||
// Update adjacencies?
|
||
owner->area += chart->area;
|
||
owner->boundaryLength += chart->boundaryLength - sharedBoundaryLength;
|
||
owner->normalSum += chart->normalSum;
|
||
owner->centroidSum += chart->centroidSum;
|
||
updateProxy(owner);
|
||
}
|
||
|
||
uint32_t chartCount() const { return chartArray.size(); }
|
||
const std::vector<uint32_t> &chartFaces(uint32_t i) const { return chartArray[i]->faces; }
|
||
|
||
const halfedge::Mesh *mesh;
|
||
uint32_t facesLeft;
|
||
std::vector<int> faceChartArray;
|
||
std::vector<ChartBuildData *> chartArray;
|
||
std::vector<float> shortestPaths;
|
||
std::vector<float> edgeLengths;
|
||
std::vector<float> faceAreas;
|
||
std::vector<Candidate> candidateArray; //
|
||
std::vector<uint32_t> faceCandidateArray; // Map face index to candidate index.
|
||
MTRand rand;
|
||
CharterOptions options;
|
||
};
|
||
|
||
/// A chart is a connected set of faces with a certain topology (usually a disk).
|
||
class Chart {
|
||
public:
|
||
Chart() :
|
||
m_isDisk(false),
|
||
m_isVertexMapped(false) {}
|
||
|
||
void build(const halfedge::Mesh *originalMesh, const std::vector<uint32_t> &faceArray) {
|
||
// Copy face indices.
|
||
m_faceArray = faceArray;
|
||
const uint32_t meshVertexCount = originalMesh->vertexCount();
|
||
m_chartMesh.reset(new halfedge::Mesh());
|
||
m_unifiedMesh.reset(new halfedge::Mesh());
|
||
std::vector<uint32_t> chartMeshIndices(meshVertexCount, (uint32_t)~0);
|
||
std::vector<uint32_t> unifiedMeshIndices(meshVertexCount, (uint32_t)~0);
|
||
// Add vertices.
|
||
const uint32_t faceCount = faceArray.size();
|
||
for (uint32_t f = 0; f < faceCount; f++) {
|
||
const halfedge::Face *face = originalMesh->faceAt(faceArray[f]);
|
||
xaDebugAssert(face != NULL);
|
||
for (halfedge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const halfedge::Vertex *vertex = it.current()->vertex;
|
||
const halfedge::Vertex *unifiedVertex = vertex->firstColocal();
|
||
if (unifiedMeshIndices[unifiedVertex->id] == ~0) {
|
||
unifiedMeshIndices[unifiedVertex->id] = m_unifiedMesh->vertexCount();
|
||
xaDebugAssert(vertex->pos == unifiedVertex->pos);
|
||
m_unifiedMesh->addVertex(vertex->pos);
|
||
}
|
||
if (chartMeshIndices[vertex->id] == ~0) {
|
||
chartMeshIndices[vertex->id] = m_chartMesh->vertexCount();
|
||
m_chartToOriginalMap.push_back(vertex->original_id);
|
||
m_chartToUnifiedMap.push_back(unifiedMeshIndices[unifiedVertex->id]);
|
||
halfedge::Vertex *v = m_chartMesh->addVertex(vertex->pos);
|
||
v->nor = vertex->nor;
|
||
v->tex = vertex->tex;
|
||
}
|
||
}
|
||
}
|
||
// This is ignoring the canonical map:
|
||
// - Is it really necessary to link colocals?
|
||
m_chartMesh->linkColocals();
|
||
//m_unifiedMesh->linkColocals(); // Not strictly necessary, no colocals in the unified mesh. # Wrong.
|
||
// This check is not valid anymore, if the original mesh vertices were linked with a canonical map, then it might have
|
||
// some colocal vertices that were unlinked. So, the unified mesh might have some duplicate vertices, because firstColocal()
|
||
// is not guaranteed to return the same vertex for two colocal vertices.
|
||
//xaAssert(m_chartMesh->colocalVertexCount() == m_unifiedMesh->vertexCount());
|
||
// Is that OK? What happens in meshes were that happens? Does anything break? Apparently not...
|
||
std::vector<uint32_t> faceIndices;
|
||
faceIndices.reserve(7);
|
||
// Add faces.
|
||
for (uint32_t f = 0; f < faceCount; f++) {
|
||
const halfedge::Face *face = originalMesh->faceAt(faceArray[f]);
|
||
xaDebugAssert(face != NULL);
|
||
faceIndices.clear();
|
||
for (halfedge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const halfedge::Vertex *vertex = it.current()->vertex;
|
||
xaDebugAssert(vertex != NULL);
|
||
faceIndices.push_back(chartMeshIndices[vertex->id]);
|
||
}
|
||
m_chartMesh->addFace(faceIndices);
|
||
faceIndices.clear();
|
||
for (halfedge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const halfedge::Vertex *vertex = it.current()->vertex;
|
||
xaDebugAssert(vertex != NULL);
|
||
vertex = vertex->firstColocal();
|
||
faceIndices.push_back(unifiedMeshIndices[vertex->id]);
|
||
}
|
||
m_unifiedMesh->addFace(faceIndices);
|
||
}
|
||
m_chartMesh->linkBoundary();
|
||
m_unifiedMesh->linkBoundary();
|
||
//exportMesh(m_unifiedMesh.ptr(), "debug_input.obj");
|
||
if (m_unifiedMesh->splitBoundaryEdges()) {
|
||
m_unifiedMesh.reset(halfedge::unifyVertices(m_unifiedMesh.get()));
|
||
}
|
||
//exportMesh(m_unifiedMesh.ptr(), "debug_split.obj");
|
||
// Closing the holes is not always the best solution and does not fix all the problems.
|
||
// We need to do some analysis of the holes and the genus to:
|
||
// - Find cuts that reduce genus.
|
||
// - Find cuts to connect holes.
|
||
// - Use minimal spanning trees or seamster.
|
||
if (!closeHoles()) {
|
||
/*static int pieceCount = 0;
|
||
StringBuilder fileName;
|
||
fileName.format("debug_hole_%d.obj", pieceCount++);
|
||
exportMesh(m_unifiedMesh.ptr(), fileName.str());*/
|
||
}
|
||
m_unifiedMesh.reset(halfedge::triangulate(m_unifiedMesh.get()));
|
||
//exportMesh(m_unifiedMesh.ptr(), "debug_triangulated.obj");
|
||
// Analyze chart topology.
|
||
halfedge::MeshTopology topology(m_unifiedMesh.get());
|
||
m_isDisk = topology.isDisk();
|
||
}
|
||
|
||
void buildVertexMap(const halfedge::Mesh *originalMesh, const std::vector<uint32_t> &unchartedMaterialArray) {
|
||
xaAssert(m_chartMesh.get() == NULL && m_unifiedMesh.get() == NULL);
|
||
m_isVertexMapped = true;
|
||
// Build face indices.
|
||
m_faceArray.clear();
|
||
const uint32_t meshFaceCount = originalMesh->faceCount();
|
||
for (uint32_t f = 0; f < meshFaceCount; f++) {
|
||
const halfedge::Face *face = originalMesh->faceAt(f);
|
||
if (std::find(unchartedMaterialArray.begin(), unchartedMaterialArray.end(), face->material) != unchartedMaterialArray.end()) {
|
||
m_faceArray.push_back(f);
|
||
}
|
||
}
|
||
const uint32_t faceCount = m_faceArray.size();
|
||
if (faceCount == 0) {
|
||
return;
|
||
}
|
||
// @@ The chartMesh construction is basically the same as with regular charts, don't duplicate!
|
||
const uint32_t meshVertexCount = originalMesh->vertexCount();
|
||
m_chartMesh.reset(new halfedge::Mesh());
|
||
std::vector<uint32_t> chartMeshIndices(meshVertexCount, (uint32_t)~0);
|
||
// Vertex map mesh only has disconnected vertices.
|
||
for (uint32_t f = 0; f < faceCount; f++) {
|
||
const halfedge::Face *face = originalMesh->faceAt(m_faceArray[f]);
|
||
xaDebugAssert(face != NULL);
|
||
for (halfedge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const halfedge::Vertex *vertex = it.current()->vertex;
|
||
if (chartMeshIndices[vertex->id] == ~0) {
|
||
chartMeshIndices[vertex->id] = m_chartMesh->vertexCount();
|
||
m_chartToOriginalMap.push_back(vertex->original_id);
|
||
halfedge::Vertex *v = m_chartMesh->addVertex(vertex->pos);
|
||
v->nor = vertex->nor;
|
||
v->tex = vertex->tex; // @@ Not necessary.
|
||
}
|
||
}
|
||
}
|
||
// @@ Link colocals using the original mesh canonical map? Build canonical map on the fly? Do we need to link colocals at all for this?
|
||
//m_chartMesh->linkColocals();
|
||
std::vector<uint32_t> faceIndices;
|
||
faceIndices.reserve(7);
|
||
// Add faces.
|
||
for (uint32_t f = 0; f < faceCount; f++) {
|
||
const halfedge::Face *face = originalMesh->faceAt(m_faceArray[f]);
|
||
xaDebugAssert(face != NULL);
|
||
faceIndices.clear();
|
||
for (halfedge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const halfedge::Vertex *vertex = it.current()->vertex;
|
||
xaDebugAssert(vertex != NULL);
|
||
xaDebugAssert(chartMeshIndices[vertex->id] != ~0);
|
||
faceIndices.push_back(chartMeshIndices[vertex->id]);
|
||
}
|
||
halfedge::Face *new_face = m_chartMesh->addFace(faceIndices);
|
||
xaDebugAssert(new_face != NULL);
|
||
#ifdef NDEBUG
|
||
new_face = NULL; // silence unused parameter warning
|
||
#endif
|
||
}
|
||
m_chartMesh->linkBoundary();
|
||
const uint32_t chartVertexCount = m_chartMesh->vertexCount();
|
||
Box bounds;
|
||
bounds.clearBounds();
|
||
for (uint32_t i = 0; i < chartVertexCount; i++) {
|
||
halfedge::Vertex *vertex = m_chartMesh->vertexAt(i);
|
||
bounds.addPointToBounds(vertex->pos);
|
||
}
|
||
ProximityGrid grid;
|
||
grid.init(bounds, chartVertexCount);
|
||
for (uint32_t i = 0; i < chartVertexCount; i++) {
|
||
halfedge::Vertex *vertex = m_chartMesh->vertexAt(i);
|
||
grid.add(vertex->pos, i);
|
||
}
|
||
uint32_t texelCount = 0;
|
||
const float positionThreshold = 0.01f;
|
||
const float normalThreshold = 0.01f;
|
||
uint32_t verticesVisited = 0;
|
||
uint32_t cellsVisited = 0;
|
||
std::vector<int> vertexIndexArray(chartVertexCount, -1); // Init all indices to -1.
|
||
// Traverse vertices in morton order. @@ It may be more interesting to sort them based on orientation.
|
||
const uint32_t cellCodeCount = grid.mortonCount();
|
||
for (uint32_t cellCode = 0; cellCode < cellCodeCount; cellCode++) {
|
||
int cell = grid.mortonIndex(cellCode);
|
||
if (cell < 0) continue;
|
||
cellsVisited++;
|
||
const std::vector<uint32_t> &indexArray = grid.cellArray[cell].indexArray;
|
||
for (uint32_t i = 0; i < indexArray.size(); i++) {
|
||
uint32_t idx = indexArray[i];
|
||
halfedge::Vertex *vertex = m_chartMesh->vertexAt(idx);
|
||
xaDebugAssert(vertexIndexArray[idx] == -1);
|
||
std::vector<uint32_t> neighbors;
|
||
grid.gather(vertex->pos, positionThreshold, /*ref*/ neighbors);
|
||
// Compare against all nearby vertices, cluster greedily.
|
||
for (uint32_t j = 0; j < neighbors.size(); j++) {
|
||
uint32_t otherIdx = neighbors[j];
|
||
if (vertexIndexArray[otherIdx] != -1) {
|
||
halfedge::Vertex *otherVertex = m_chartMesh->vertexAt(otherIdx);
|
||
if (distance(vertex->pos, otherVertex->pos) < positionThreshold &&
|
||
distance(vertex->nor, otherVertex->nor) < normalThreshold) {
|
||
vertexIndexArray[idx] = vertexIndexArray[otherIdx];
|
||
break;
|
||
}
|
||
}
|
||
}
|
||
// If index not assigned, assign new one.
|
||
if (vertexIndexArray[idx] == -1) {
|
||
vertexIndexArray[idx] = texelCount++;
|
||
}
|
||
verticesVisited++;
|
||
}
|
||
}
|
||
xaDebugAssert(cellsVisited == grid.cellArray.size());
|
||
xaDebugAssert(verticesVisited == chartVertexCount);
|
||
vertexMapWidth = ftoi_ceil(sqrtf(float(texelCount)));
|
||
vertexMapWidth = (vertexMapWidth + 3) & ~3; // Width aligned to 4.
|
||
vertexMapHeight = vertexMapWidth == 0 ? 0 : (texelCount + vertexMapWidth - 1) / vertexMapWidth;
|
||
//vertexMapHeight = (vertexMapHeight + 3) & ~3; // Height aligned to 4.
|
||
xaDebugAssert(vertexMapWidth >= vertexMapHeight);
|
||
xaPrint("Reduced vertex count from %d to %d.\n", chartVertexCount, texelCount);
|
||
// Lay down the clustered vertices in morton order.
|
||
std::vector<uint32_t> texelCodes(texelCount);
|
||
// For each texel, assign one morton code.
|
||
uint32_t texelCode = 0;
|
||
for (uint32_t i = 0; i < texelCount; i++) {
|
||
uint32_t x, y;
|
||
do {
|
||
x = morton::decodeMorton2X(texelCode);
|
||
y = morton::decodeMorton2Y(texelCode);
|
||
texelCode++;
|
||
} while (x >= uint32_t(vertexMapWidth) || y >= uint32_t(vertexMapHeight));
|
||
texelCodes[i] = texelCode - 1;
|
||
}
|
||
for (uint32_t i = 0; i < chartVertexCount; i++) {
|
||
halfedge::Vertex *vertex = m_chartMesh->vertexAt(i);
|
||
int idx = vertexIndexArray[i];
|
||
if (idx != -1) {
|
||
uint32_t tc = texelCodes[idx];
|
||
uint32_t x = morton::decodeMorton2X(tc);
|
||
uint32_t y = morton::decodeMorton2Y(tc);
|
||
vertex->tex.x = float(x);
|
||
vertex->tex.y = float(y);
|
||
}
|
||
}
|
||
}
|
||
|
||
bool closeHoles() {
|
||
xaDebugAssert(!m_isVertexMapped);
|
||
std::vector<halfedge::Edge *> boundaryEdges;
|
||
getBoundaryEdges(m_unifiedMesh.get(), boundaryEdges);
|
||
uint32_t boundaryCount = boundaryEdges.size();
|
||
if (boundaryCount <= 1) {
|
||
// Nothing to close.
|
||
return true;
|
||
}
|
||
// Compute lengths and areas.
|
||
std::vector<float> boundaryLengths;
|
||
for (uint32_t i = 0; i < boundaryCount; i++) {
|
||
const halfedge::Edge *startEdge = boundaryEdges[i];
|
||
xaAssert(startEdge->face == NULL);
|
||
//float boundaryEdgeCount = 0;
|
||
float boundaryLength = 0.0f;
|
||
//Vector3 boundaryCentroid(zero);
|
||
const halfedge::Edge *edge = startEdge;
|
||
do {
|
||
Vector3 t0 = edge->from()->pos;
|
||
Vector3 t1 = edge->to()->pos;
|
||
//boundaryEdgeCount++;
|
||
boundaryLength += length(t1 - t0);
|
||
//boundaryCentroid += edge->vertex()->pos;
|
||
edge = edge->next;
|
||
} while (edge != startEdge);
|
||
boundaryLengths.push_back(boundaryLength);
|
||
//boundaryCentroids.append(boundaryCentroid / boundaryEdgeCount);
|
||
}
|
||
// Find disk boundary.
|
||
uint32_t diskBoundary = 0;
|
||
float maxLength = boundaryLengths[0];
|
||
for (uint32_t i = 1; i < boundaryCount; i++) {
|
||
if (boundaryLengths[i] > maxLength) {
|
||
maxLength = boundaryLengths[i];
|
||
diskBoundary = i;
|
||
}
|
||
}
|
||
// Close holes.
|
||
for (uint32_t i = 0; i < boundaryCount; i++) {
|
||
if (diskBoundary == i) {
|
||
// Skip disk boundary.
|
||
continue;
|
||
}
|
||
halfedge::Edge *startEdge = boundaryEdges[i];
|
||
xaDebugAssert(startEdge != NULL);
|
||
xaDebugAssert(startEdge->face == NULL);
|
||
std::vector<halfedge::Vertex *> vertexLoop;
|
||
std::vector<halfedge::Edge *> edgeLoop;
|
||
halfedge::Edge *edge = startEdge;
|
||
do {
|
||
halfedge::Vertex *vertex = edge->next->vertex; // edge->to()
|
||
uint32_t j;
|
||
for (j = 0; j < vertexLoop.size(); j++) {
|
||
if (vertex->isColocal(vertexLoop[j])) {
|
||
break;
|
||
}
|
||
}
|
||
bool isCrossing = (j != vertexLoop.size());
|
||
if (isCrossing) {
|
||
halfedge::Edge *prev = edgeLoop[j]; // Previous edge before the loop.
|
||
halfedge::Edge *next = edge->next; // Next edge after the loop.
|
||
xaDebugAssert(prev->to()->isColocal(next->from()));
|
||
// Close loop.
|
||
edgeLoop.push_back(edge);
|
||
closeLoop(j + 1, edgeLoop);
|
||
// Link boundary loop.
|
||
prev->setNext(next);
|
||
vertex->setEdge(next);
|
||
// Start over again.
|
||
vertexLoop.clear();
|
||
edgeLoop.clear();
|
||
edge = startEdge;
|
||
vertex = edge->to();
|
||
}
|
||
vertexLoop.push_back(vertex);
|
||
edgeLoop.push_back(edge);
|
||
edge = edge->next;
|
||
} while (edge != startEdge);
|
||
closeLoop(0, edgeLoop);
|
||
}
|
||
getBoundaryEdges(m_unifiedMesh.get(), boundaryEdges);
|
||
boundaryCount = boundaryEdges.size();
|
||
xaDebugAssert(boundaryCount == 1);
|
||
return boundaryCount == 1;
|
||
}
|
||
|
||
bool isDisk() const {
|
||
return m_isDisk;
|
||
}
|
||
bool isVertexMapped() const {
|
||
return m_isVertexMapped;
|
||
}
|
||
|
||
uint32_t vertexCount() const {
|
||
return m_chartMesh->vertexCount();
|
||
}
|
||
uint32_t colocalVertexCount() const {
|
||
return m_unifiedMesh->vertexCount();
|
||
}
|
||
|
||
uint32_t faceCount() const {
|
||
return m_faceArray.size();
|
||
}
|
||
uint32_t faceAt(uint32_t i) const {
|
||
return m_faceArray[i];
|
||
}
|
||
|
||
const halfedge::Mesh *chartMesh() const {
|
||
return m_chartMesh.get();
|
||
}
|
||
halfedge::Mesh *chartMesh() {
|
||
return m_chartMesh.get();
|
||
}
|
||
const halfedge::Mesh *unifiedMesh() const {
|
||
return m_unifiedMesh.get();
|
||
}
|
||
halfedge::Mesh *unifiedMesh() {
|
||
return m_unifiedMesh.get();
|
||
}
|
||
|
||
//uint32_t vertexIndex(uint32_t i) const { return m_vertexIndexArray[i]; }
|
||
|
||
uint32_t mapChartVertexToOriginalVertex(uint32_t i) const {
|
||
return m_chartToOriginalMap[i];
|
||
}
|
||
uint32_t mapChartVertexToUnifiedVertex(uint32_t i) const {
|
||
return m_chartToUnifiedMap[i];
|
||
}
|
||
|
||
const std::vector<uint32_t> &faceArray() const {
|
||
return m_faceArray;
|
||
}
|
||
|
||
// Transfer parameterization from unified mesh to chart mesh.
|
||
void transferParameterization() {
|
||
xaDebugAssert(!m_isVertexMapped);
|
||
uint32_t vertexCount = m_chartMesh->vertexCount();
|
||
for (uint32_t v = 0; v < vertexCount; v++) {
|
||
halfedge::Vertex *vertex = m_chartMesh->vertexAt(v);
|
||
halfedge::Vertex *unifiedVertex = m_unifiedMesh->vertexAt(mapChartVertexToUnifiedVertex(v));
|
||
vertex->tex = unifiedVertex->tex;
|
||
}
|
||
}
|
||
|
||
float computeSurfaceArea() const {
|
||
return halfedge::computeSurfaceArea(m_chartMesh.get()) * scale;
|
||
}
|
||
|
||
float computeParametricArea() const {
|
||
// This only makes sense in parameterized meshes.
|
||
xaDebugAssert(m_isDisk);
|
||
xaDebugAssert(!m_isVertexMapped);
|
||
return halfedge::computeParametricArea(m_chartMesh.get());
|
||
}
|
||
|
||
Vector2 computeParametricBounds() const {
|
||
// This only makes sense in parameterized meshes.
|
||
xaDebugAssert(m_isDisk);
|
||
xaDebugAssert(!m_isVertexMapped);
|
||
Box bounds;
|
||
bounds.clearBounds();
|
||
uint32_t vertexCount = m_chartMesh->vertexCount();
|
||
for (uint32_t v = 0; v < vertexCount; v++) {
|
||
halfedge::Vertex *vertex = m_chartMesh->vertexAt(v);
|
||
bounds.addPointToBounds(Vector3(vertex->tex, 0));
|
||
}
|
||
return bounds.extents().xy();
|
||
}
|
||
|
||
float scale = 1.0f;
|
||
uint32_t vertexMapWidth;
|
||
uint32_t vertexMapHeight;
|
||
bool blockAligned = true;
|
||
|
||
private:
|
||
bool closeLoop(uint32_t start, const std::vector<halfedge::Edge *> &loop) {
|
||
const uint32_t vertexCount = loop.size() - start;
|
||
xaDebugAssert(vertexCount >= 3);
|
||
if (vertexCount < 3) return false;
|
||
xaDebugAssert(loop[start]->vertex->isColocal(loop[start + vertexCount - 1]->to()));
|
||
// If the hole is planar, then we add a single face that will be properly triangulated later.
|
||
// If the hole is not planar, we add a triangle fan with a vertex at the hole centroid.
|
||
// This is still a bit of a hack. There surely are better hole filling algorithms out there.
|
||
std::vector<Vector3> points(vertexCount);
|
||
for (uint32_t i = 0; i < vertexCount; i++) {
|
||
points[i] = loop[start + i]->vertex->pos;
|
||
}
|
||
bool isPlanar = Fit::isPlanar(vertexCount, points.data());
|
||
if (isPlanar) {
|
||
// Add face and connect edges.
|
||
halfedge::Face *face = m_unifiedMesh->addFace();
|
||
for (uint32_t i = 0; i < vertexCount; i++) {
|
||
halfedge::Edge *edge = loop[start + i];
|
||
edge->face = face;
|
||
edge->setNext(loop[start + (i + 1) % vertexCount]);
|
||
}
|
||
face->edge = loop[start];
|
||
xaDebugAssert(face->isValid());
|
||
} else {
|
||
// If the polygon is not planar, we just cross our fingers, and hope this will work:
|
||
// Compute boundary centroid:
|
||
Vector3 centroidPos(0);
|
||
for (uint32_t i = 0; i < vertexCount; i++) {
|
||
centroidPos += points[i];
|
||
}
|
||
centroidPos *= (1.0f / vertexCount);
|
||
halfedge::Vertex *centroid = m_unifiedMesh->addVertex(centroidPos);
|
||
// Add one pair of edges for each boundary vertex.
|
||
for (uint32_t j = vertexCount - 1, i = 0; i < vertexCount; j = i++) {
|
||
halfedge::Face *face = m_unifiedMesh->addFace(centroid->id, loop[start + j]->vertex->id, loop[start + i]->vertex->id);
|
||
xaDebugAssert(face != NULL);
|
||
#ifdef NDEBUG
|
||
face = NULL; // silence unused parameter warning
|
||
#endif
|
||
}
|
||
}
|
||
return true;
|
||
}
|
||
|
||
static void getBoundaryEdges(halfedge::Mesh *mesh, std::vector<halfedge::Edge *> &boundaryEdges) {
|
||
xaDebugAssert(mesh != NULL);
|
||
const uint32_t edgeCount = mesh->edgeCount();
|
||
BitArray bitFlags(edgeCount);
|
||
bitFlags.clearAll();
|
||
boundaryEdges.clear();
|
||
// Search for boundary edges. Mark all the edges that belong to the same boundary.
|
||
for (uint32_t e = 0; e < edgeCount; e++) {
|
||
halfedge::Edge *startEdge = mesh->edgeAt(e);
|
||
if (startEdge != NULL && startEdge->isBoundary() && bitFlags.bitAt(e) == false) {
|
||
xaDebugAssert(startEdge->face != NULL);
|
||
xaDebugAssert(startEdge->pair->face == NULL);
|
||
startEdge = startEdge->pair;
|
||
const halfedge::Edge *edge = startEdge;
|
||
do {
|
||
xaDebugAssert(edge->face == NULL);
|
||
xaDebugAssert(bitFlags.bitAt(edge->id / 2) == false);
|
||
bitFlags.setBitAt(edge->id / 2);
|
||
edge = edge->next;
|
||
} while (startEdge != edge);
|
||
boundaryEdges.push_back(startEdge);
|
||
}
|
||
}
|
||
}
|
||
|
||
// Chart mesh.
|
||
std::auto_ptr<halfedge::Mesh> m_chartMesh;
|
||
|
||
std::auto_ptr<halfedge::Mesh> m_unifiedMesh;
|
||
bool m_isDisk;
|
||
bool m_isVertexMapped;
|
||
|
||
// List of faces of the original mesh that belong to this chart.
|
||
std::vector<uint32_t> m_faceArray;
|
||
|
||
// Map vertices of the chart mesh to vertices of the original mesh.
|
||
std::vector<uint32_t> m_chartToOriginalMap;
|
||
|
||
std::vector<uint32_t> m_chartToUnifiedMap;
|
||
};
|
||
|
||
// Estimate quality of existing parameterization.
|
||
class ParameterizationQuality {
|
||
public:
|
||
ParameterizationQuality() {
|
||
m_totalTriangleCount = 0;
|
||
m_flippedTriangleCount = 0;
|
||
m_zeroAreaTriangleCount = 0;
|
||
m_parametricArea = 0.0f;
|
||
m_geometricArea = 0.0f;
|
||
m_stretchMetric = 0.0f;
|
||
m_maxStretchMetric = 0.0f;
|
||
m_conformalMetric = 0.0f;
|
||
m_authalicMetric = 0.0f;
|
||
}
|
||
|
||
ParameterizationQuality(const halfedge::Mesh *mesh) {
|
||
xaDebugAssert(mesh != NULL);
|
||
m_totalTriangleCount = 0;
|
||
m_flippedTriangleCount = 0;
|
||
m_zeroAreaTriangleCount = 0;
|
||
m_parametricArea = 0.0f;
|
||
m_geometricArea = 0.0f;
|
||
m_stretchMetric = 0.0f;
|
||
m_maxStretchMetric = 0.0f;
|
||
m_conformalMetric = 0.0f;
|
||
m_authalicMetric = 0.0f;
|
||
const uint32_t faceCount = mesh->faceCount();
|
||
for (uint32_t f = 0; f < faceCount; f++) {
|
||
const halfedge::Face *face = mesh->faceAt(f);
|
||
const halfedge::Vertex *vertex0 = NULL;
|
||
Vector3 p[3];
|
||
Vector2 t[3];
|
||
for (halfedge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const halfedge::Edge *edge = it.current();
|
||
if (vertex0 == NULL) {
|
||
vertex0 = edge->vertex;
|
||
p[0] = vertex0->pos;
|
||
t[0] = vertex0->tex;
|
||
} else if (edge->to() != vertex0) {
|
||
p[1] = edge->from()->pos;
|
||
p[2] = edge->to()->pos;
|
||
t[1] = edge->from()->tex;
|
||
t[2] = edge->to()->tex;
|
||
processTriangle(p, t);
|
||
}
|
||
}
|
||
}
|
||
if (m_flippedTriangleCount + m_zeroAreaTriangleCount == faceCount) {
|
||
// If all triangles are flipped, then none is.
|
||
m_flippedTriangleCount = 0;
|
||
}
|
||
xaDebugAssert(std::isfinite(m_parametricArea) && m_parametricArea >= 0);
|
||
xaDebugAssert(std::isfinite(m_geometricArea) && m_geometricArea >= 0);
|
||
xaDebugAssert(std::isfinite(m_stretchMetric));
|
||
xaDebugAssert(std::isfinite(m_maxStretchMetric));
|
||
xaDebugAssert(std::isfinite(m_conformalMetric));
|
||
xaDebugAssert(std::isfinite(m_authalicMetric));
|
||
}
|
||
|
||
bool isValid() const {
|
||
return m_flippedTriangleCount == 0; // @@ Does not test for self-overlaps.
|
||
}
|
||
|
||
float rmsStretchMetric() const {
|
||
if (m_geometricArea == 0) return 0.0f;
|
||
float normFactor = sqrtf(m_parametricArea / m_geometricArea);
|
||
return sqrtf(m_stretchMetric / m_geometricArea) * normFactor;
|
||
}
|
||
|
||
float maxStretchMetric() const {
|
||
if (m_geometricArea == 0) return 0.0f;
|
||
float normFactor = sqrtf(m_parametricArea / m_geometricArea);
|
||
return m_maxStretchMetric * normFactor;
|
||
}
|
||
|
||
float rmsConformalMetric() const {
|
||
if (m_geometricArea == 0) return 0.0f;
|
||
return sqrtf(m_conformalMetric / m_geometricArea);
|
||
}
|
||
|
||
float maxAuthalicMetric() const {
|
||
if (m_geometricArea == 0) return 0.0f;
|
||
return sqrtf(m_authalicMetric / m_geometricArea);
|
||
}
|
||
|
||
void operator+=(const ParameterizationQuality &pq) {
|
||
m_totalTriangleCount += pq.m_totalTriangleCount;
|
||
m_flippedTriangleCount += pq.m_flippedTriangleCount;
|
||
m_zeroAreaTriangleCount += pq.m_zeroAreaTriangleCount;
|
||
m_parametricArea += pq.m_parametricArea;
|
||
m_geometricArea += pq.m_geometricArea;
|
||
m_stretchMetric += pq.m_stretchMetric;
|
||
m_maxStretchMetric = std::max(m_maxStretchMetric, pq.m_maxStretchMetric);
|
||
m_conformalMetric += pq.m_conformalMetric;
|
||
m_authalicMetric += pq.m_authalicMetric;
|
||
}
|
||
|
||
private:
|
||
void processTriangle(Vector3 q[3], Vector2 p[3]) {
|
||
m_totalTriangleCount++;
|
||
// Evaluate texture stretch metric. See:
|
||
// - "Texture Mapping Progressive Meshes", Sander, Snyder, Gortler & Hoppe
|
||
// - "Mesh Parameterization: Theory and Practice", Siggraph'07 Course Notes, Hormann, Levy & Sheffer.
|
||
float t1 = p[0].x;
|
||
float s1 = p[0].y;
|
||
float t2 = p[1].x;
|
||
float s2 = p[1].y;
|
||
float t3 = p[2].x;
|
||
float s3 = p[2].y;
|
||
float geometricArea = length(cross(q[1] - q[0], q[2] - q[0])) / 2;
|
||
float parametricArea = ((s2 - s1) * (t3 - t1) - (s3 - s1) * (t2 - t1)) / 2;
|
||
if (isZero(parametricArea)) {
|
||
m_zeroAreaTriangleCount++;
|
||
return;
|
||
}
|
||
Vector3 Ss = (q[0] * (t2 - t3) + q[1] * (t3 - t1) + q[2] * (t1 - t2)) / (2 * parametricArea);
|
||
Vector3 St = (q[0] * (s3 - s2) + q[1] * (s1 - s3) + q[2] * (s2 - s1)) / (2 * parametricArea);
|
||
float a = dot(Ss, Ss); // E
|
||
float b = dot(Ss, St); // F
|
||
float c = dot(St, St); // G
|
||
// Compute eigen-values of the first fundamental form:
|
||
float sigma1 = sqrtf(0.5f * std::max(0.0f, a + c - sqrtf(square(a - c) + 4 * square(b)))); // gamma uppercase, min eigenvalue.
|
||
float sigma2 = sqrtf(0.5f * std::max(0.0f, a + c + sqrtf(square(a - c) + 4 * square(b)))); // gamma lowercase, max eigenvalue.
|
||
xaAssert(sigma2 >= sigma1);
|
||
// isometric: sigma1 = sigma2 = 1
|
||
// conformal: sigma1 / sigma2 = 1
|
||
// authalic: sigma1 * sigma2 = 1
|
||
float rmsStretch = sqrtf((a + c) * 0.5f);
|
||
float rmsStretch2 = sqrtf((square(sigma1) + square(sigma2)) * 0.5f);
|
||
xaDebugAssert(equal(rmsStretch, rmsStretch2, 0.01f));
|
||
#ifdef NDEBUG
|
||
rmsStretch2 = 0; // silence unused parameter warning
|
||
#endif
|
||
if (parametricArea < 0.0f) {
|
||
// Count flipped triangles.
|
||
m_flippedTriangleCount++;
|
||
parametricArea = fabsf(parametricArea);
|
||
}
|
||
m_stretchMetric += square(rmsStretch) * geometricArea;
|
||
m_maxStretchMetric = std::max(m_maxStretchMetric, sigma2);
|
||
if (!isZero(sigma1, 0.000001f)) {
|
||
// sigma1 is zero when geometricArea is zero.
|
||
m_conformalMetric += (sigma2 / sigma1) * geometricArea;
|
||
}
|
||
m_authalicMetric += (sigma1 * sigma2) * geometricArea;
|
||
// Accumulate total areas.
|
||
m_geometricArea += geometricArea;
|
||
m_parametricArea += parametricArea;
|
||
//triangleConformalEnergy(q, p);
|
||
}
|
||
|
||
uint32_t m_totalTriangleCount;
|
||
uint32_t m_flippedTriangleCount;
|
||
uint32_t m_zeroAreaTriangleCount;
|
||
float m_parametricArea;
|
||
float m_geometricArea;
|
||
float m_stretchMetric;
|
||
float m_maxStretchMetric;
|
||
float m_conformalMetric;
|
||
float m_authalicMetric;
|
||
};
|
||
|
||
// Set of charts corresponding to a single mesh.
|
||
class MeshCharts {
|
||
public:
|
||
MeshCharts(const halfedge::Mesh *mesh) :
|
||
m_mesh(mesh) {}
|
||
|
||
~MeshCharts() {
|
||
for (size_t i = 0; i < m_chartArray.size(); i++)
|
||
delete m_chartArray[i];
|
||
}
|
||
|
||
uint32_t chartCount() const {
|
||
return m_chartArray.size();
|
||
}
|
||
uint32_t vertexCount() const {
|
||
return m_totalVertexCount;
|
||
}
|
||
|
||
const Chart *chartAt(uint32_t i) const {
|
||
return m_chartArray[i];
|
||
}
|
||
Chart *chartAt(uint32_t i) {
|
||
return m_chartArray[i];
|
||
}
|
||
|
||
// Extract the charts of the input mesh.
|
||
void extractCharts() {
|
||
const uint32_t faceCount = m_mesh->faceCount();
|
||
int first = 0;
|
||
std::vector<uint32_t> queue;
|
||
queue.reserve(faceCount);
|
||
BitArray bitFlags(faceCount);
|
||
bitFlags.clearAll();
|
||
for (uint32_t f = 0; f < faceCount; f++) {
|
||
if (bitFlags.bitAt(f) == false) {
|
||
// Start new patch. Reset queue.
|
||
first = 0;
|
||
queue.clear();
|
||
queue.push_back(f);
|
||
bitFlags.setBitAt(f);
|
||
while (first != (int)queue.size()) {
|
||
const halfedge::Face *face = m_mesh->faceAt(queue[first]);
|
||
// Visit face neighbors of queue[first]
|
||
for (halfedge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
const halfedge::Edge *edge = it.current();
|
||
xaDebugAssert(edge->pair != NULL);
|
||
if (!edge->isBoundary() && /*!edge->isSeam()*/
|
||
//!(edge->from()->tex() != edge->pair()->to()->tex() || edge->to()->tex() != edge->pair()->from()->tex()))
|
||
!(edge->from() != edge->pair->to() || edge->to() != edge->pair->from())) { // Preserve existing seams (not just texture seams).
|
||
const halfedge::Face *neighborFace = edge->pair->face;
|
||
xaDebugAssert(neighborFace != NULL);
|
||
if (bitFlags.bitAt(neighborFace->id) == false) {
|
||
queue.push_back(neighborFace->id);
|
||
bitFlags.setBitAt(neighborFace->id);
|
||
}
|
||
}
|
||
}
|
||
first++;
|
||
}
|
||
Chart *chart = new Chart();
|
||
chart->build(m_mesh, queue);
|
||
m_chartArray.push_back(chart);
|
||
}
|
||
}
|
||
}
|
||
|
||
/*
|
||
Compute charts using a simple segmentation algorithm.
|
||
|
||
LSCM:
|
||
- identify sharp features using local dihedral angles.
|
||
- identify seed faces farthest from sharp features.
|
||
- grow charts from these seeds.
|
||
|
||
MCGIM:
|
||
- phase 1: chart growth
|
||
- grow all charts simultaneously using dijkstra search on the dual graph of the mesh.
|
||
- graph edges are weighted based on planarity metric.
|
||
- metric uses distance to global chart normal.
|
||
- terminate when all faces have been assigned.
|
||
- phase 2: seed computation:
|
||
- place new seed of the chart at the most interior face.
|
||
- most interior is evaluated using distance metric only.
|
||
|
||
- method repeates the two phases, until the location of the seeds does not change.
|
||
- cycles are detected by recording all the previous seeds and chartification terminates.
|
||
|
||
D-Charts:
|
||
|
||
- Uniaxial conic metric:
|
||
- N_c = axis of the generalized cone that best fits the chart. (cone can a be cylinder or a plane).
|
||
- omega_c = angle between the face normals and the axis.
|
||
- Fitting error between chart C and tringle t: F(c,t) = (N_c*n_t - cos(omega_c))^2
|
||
|
||
- Compactness metrics:
|
||
- Roundness:
|
||
- C(c,t) = pi * D(S_c,t)^2 / A_c
|
||
- S_c = chart seed.
|
||
- D(S_c,t) = length of the shortest path inside the chart betwen S_c and t.
|
||
- A_c = chart area.
|
||
- Straightness:
|
||
- P(c,t) = l_out(c,t) / l_in(c,t)
|
||
- l_out(c,t) = lenght of the edges not shared between C and t.
|
||
- l_in(c,t) = lenght of the edges shared between C and t.
|
||
|
||
- Combined metric:
|
||
- Cost(c,t) = F(c,t)^alpha + C(c,t)^beta + P(c,t)^gamma
|
||
- alpha = 1, beta = 0.7, gamma = 0.5
|
||
|
||
Our basic approach:
|
||
- Just one iteration of k-means?
|
||
- Avoid dijkstra by greedily growing charts until a threshold is met. Increase threshold and repeat until no faces left.
|
||
- If distortion metric is too high, split chart, add two seeds.
|
||
- If chart size is low, try removing chart.
|
||
|
||
Postprocess:
|
||
- If topology is not disk:
|
||
- Fill holes, if new faces fit proxy.
|
||
- Find best cut, otherwise.
|
||
- After parameterization:
|
||
- If boundary self-intersects:
|
||
- cut chart along the closest two diametral boundary vertices, repeat parametrization.
|
||
- what if the overlap is on an appendix? How do we find that out and cut appropiately?
|
||
- emphasize roundness metrics to prevent those cases.
|
||
- If interior self-overlaps: preserve boundary parameterization and use mean-value map.
|
||
*/
|
||
void computeCharts(const CharterOptions &options, const std::vector<uint32_t> &unchartedMaterialArray) {
|
||
Chart *vertexMap = NULL;
|
||
if (unchartedMaterialArray.size() != 0) {
|
||
vertexMap = new Chart();
|
||
vertexMap->buildVertexMap(m_mesh, unchartedMaterialArray);
|
||
if (vertexMap->faceCount() == 0) {
|
||
delete vertexMap;
|
||
vertexMap = NULL;
|
||
}
|
||
}
|
||
AtlasBuilder builder(m_mesh);
|
||
if (vertexMap != NULL) {
|
||
// Mark faces that do not need to be charted.
|
||
builder.markUnchartedFaces(vertexMap->faceArray());
|
||
m_chartArray.push_back(vertexMap);
|
||
}
|
||
if (builder.facesLeft != 0) {
|
||
// Tweak these values:
|
||
const float maxThreshold = 2;
|
||
const uint32_t growFaceCount = 32;
|
||
const uint32_t maxIterations = 4;
|
||
builder.options = options;
|
||
//builder.options.proxyFitMetricWeight *= 0.75; // relax proxy fit weight during initial seed placement.
|
||
//builder.options.roundnessMetricWeight = 0;
|
||
//builder.options.straightnessMetricWeight = 0;
|
||
// This seems a reasonable estimate.
|
||
uint32_t maxSeedCount = std::max(6U, builder.facesLeft);
|
||
// Create initial charts greedely.
|
||
xaPrint("### Placing seeds\n");
|
||
builder.placeSeeds(maxThreshold, maxSeedCount);
|
||
xaPrint("### Placed %d seeds (max = %d)\n", builder.chartCount(), maxSeedCount);
|
||
builder.updateProxies();
|
||
builder.mergeCharts();
|
||
#if 1
|
||
xaPrint("### Relocating seeds\n");
|
||
builder.relocateSeeds();
|
||
xaPrint("### Reset charts\n");
|
||
builder.resetCharts();
|
||
if (vertexMap != NULL) {
|
||
builder.markUnchartedFaces(vertexMap->faceArray());
|
||
}
|
||
builder.options = options;
|
||
xaPrint("### Growing charts\n");
|
||
// Restart process growing charts in parallel.
|
||
uint32_t iteration = 0;
|
||
while (true) {
|
||
if (!builder.growCharts(maxThreshold, growFaceCount)) {
|
||
xaPrint("### Can't grow anymore\n");
|
||
// If charts cannot grow more: fill holes, merge charts, relocate seeds and start new iteration.
|
||
xaPrint("### Filling holes\n");
|
||
builder.fillHoles(maxThreshold);
|
||
xaPrint("### Using %d charts now\n", builder.chartCount());
|
||
builder.updateProxies();
|
||
xaPrint("### Merging charts\n");
|
||
builder.mergeCharts();
|
||
xaPrint("### Using %d charts now\n", builder.chartCount());
|
||
xaPrint("### Reseeding\n");
|
||
if (!builder.relocateSeeds()) {
|
||
xaPrint("### Cannot relocate seeds anymore\n");
|
||
// Done!
|
||
break;
|
||
}
|
||
if (iteration == maxIterations) {
|
||
xaPrint("### Reached iteration limit\n");
|
||
break;
|
||
}
|
||
iteration++;
|
||
xaPrint("### Reset charts\n");
|
||
builder.resetCharts();
|
||
if (vertexMap != NULL) {
|
||
builder.markUnchartedFaces(vertexMap->faceArray());
|
||
}
|
||
xaPrint("### Growing charts\n");
|
||
}
|
||
};
|
||
#endif
|
||
// Make sure no holes are left!
|
||
xaDebugAssert(builder.facesLeft == 0);
|
||
const uint32_t chartCount = builder.chartArray.size();
|
||
for (uint32_t i = 0; i < chartCount; i++) {
|
||
Chart *chart = new Chart();
|
||
m_chartArray.push_back(chart);
|
||
chart->build(m_mesh, builder.chartFaces(i));
|
||
}
|
||
}
|
||
const uint32_t chartCount = m_chartArray.size();
|
||
// Build face indices.
|
||
m_faceChart.resize(m_mesh->faceCount());
|
||
m_faceIndex.resize(m_mesh->faceCount());
|
||
for (uint32_t i = 0; i < chartCount; i++) {
|
||
const Chart *chart = m_chartArray[i];
|
||
const uint32_t faceCount = chart->faceCount();
|
||
for (uint32_t f = 0; f < faceCount; f++) {
|
||
uint32_t idx = chart->faceAt(f);
|
||
m_faceChart[idx] = i;
|
||
m_faceIndex[idx] = f;
|
||
}
|
||
}
|
||
// Build an exclusive prefix sum of the chart vertex counts.
|
||
m_chartVertexCountPrefixSum.resize(chartCount);
|
||
if (chartCount > 0) {
|
||
m_chartVertexCountPrefixSum[0] = 0;
|
||
for (uint32_t i = 1; i < chartCount; i++) {
|
||
const Chart *chart = m_chartArray[i - 1];
|
||
m_chartVertexCountPrefixSum[i] = m_chartVertexCountPrefixSum[i - 1] + chart->vertexCount();
|
||
}
|
||
m_totalVertexCount = m_chartVertexCountPrefixSum[chartCount - 1] + m_chartArray[chartCount - 1]->vertexCount();
|
||
} else {
|
||
m_totalVertexCount = 0;
|
||
}
|
||
}
|
||
|
||
void parameterizeCharts() {
|
||
ParameterizationQuality globalParameterizationQuality;
|
||
// Parameterize the charts.
|
||
uint32_t diskCount = 0;
|
||
const uint32_t chartCount = m_chartArray.size();
|
||
for (uint32_t i = 0; i < chartCount; i++) {
|
||
Chart *chart = m_chartArray[i];
|
||
|
||
bool isValid = false;
|
||
|
||
if (chart->isVertexMapped()) {
|
||
continue;
|
||
}
|
||
|
||
if (chart->isDisk()) {
|
||
diskCount++;
|
||
ParameterizationQuality chartParameterizationQuality;
|
||
if (chart->faceCount() == 1) {
|
||
computeSingleFaceMap(chart->unifiedMesh());
|
||
chartParameterizationQuality = ParameterizationQuality(chart->unifiedMesh());
|
||
} else {
|
||
computeOrthogonalProjectionMap(chart->unifiedMesh());
|
||
ParameterizationQuality orthogonalQuality(chart->unifiedMesh());
|
||
computeLeastSquaresConformalMap(chart->unifiedMesh());
|
||
ParameterizationQuality lscmQuality(chart->unifiedMesh());
|
||
chartParameterizationQuality = lscmQuality;
|
||
}
|
||
isValid = chartParameterizationQuality.isValid();
|
||
if (!isValid) {
|
||
xaPrint("*** Invalid parameterization.\n");
|
||
}
|
||
// @@ Check that parameterization quality is above a certain threshold.
|
||
// @@ Detect boundary self-intersections.
|
||
globalParameterizationQuality += chartParameterizationQuality;
|
||
}
|
||
|
||
// Transfer parameterization from unified mesh to chart mesh.
|
||
chart->transferParameterization();
|
||
}
|
||
xaPrint(" Parameterized %d/%d charts.\n", diskCount, chartCount);
|
||
xaPrint(" RMS stretch metric: %f\n", globalParameterizationQuality.rmsStretchMetric());
|
||
xaPrint(" MAX stretch metric: %f\n", globalParameterizationQuality.maxStretchMetric());
|
||
xaPrint(" RMS conformal metric: %f\n", globalParameterizationQuality.rmsConformalMetric());
|
||
xaPrint(" RMS authalic metric: %f\n", globalParameterizationQuality.maxAuthalicMetric());
|
||
}
|
||
|
||
uint32_t faceChartAt(uint32_t i) const {
|
||
return m_faceChart[i];
|
||
}
|
||
uint32_t faceIndexWithinChartAt(uint32_t i) const {
|
||
return m_faceIndex[i];
|
||
}
|
||
|
||
uint32_t vertexCountBeforeChartAt(uint32_t i) const {
|
||
return m_chartVertexCountPrefixSum[i];
|
||
}
|
||
|
||
private:
|
||
const halfedge::Mesh *m_mesh;
|
||
|
||
std::vector<Chart *> m_chartArray;
|
||
|
||
std::vector<uint32_t> m_chartVertexCountPrefixSum;
|
||
uint32_t m_totalVertexCount;
|
||
|
||
std::vector<uint32_t> m_faceChart; // the chart of every face of the input mesh.
|
||
std::vector<uint32_t> m_faceIndex; // the index within the chart for every face of the input mesh.
|
||
};
|
||
|
||
/// An atlas is a set of charts.
|
||
class Atlas {
|
||
public:
|
||
~Atlas() {
|
||
for (size_t i = 0; i < m_meshChartsArray.size(); i++)
|
||
delete m_meshChartsArray[i];
|
||
}
|
||
|
||
uint32_t meshCount() const {
|
||
return m_meshChartsArray.size();
|
||
}
|
||
|
||
const MeshCharts *meshAt(uint32_t i) const {
|
||
return m_meshChartsArray[i];
|
||
}
|
||
|
||
MeshCharts *meshAt(uint32_t i) {
|
||
return m_meshChartsArray[i];
|
||
}
|
||
|
||
uint32_t chartCount() const {
|
||
uint32_t count = 0;
|
||
for (uint32_t c = 0; c < m_meshChartsArray.size(); c++) {
|
||
count += m_meshChartsArray[c]->chartCount();
|
||
}
|
||
return count;
|
||
}
|
||
|
||
const Chart *chartAt(uint32_t i) const {
|
||
for (uint32_t c = 0; c < m_meshChartsArray.size(); c++) {
|
||
uint32_t count = m_meshChartsArray[c]->chartCount();
|
||
if (i < count) {
|
||
return m_meshChartsArray[c]->chartAt(i);
|
||
}
|
||
i -= count;
|
||
}
|
||
return NULL;
|
||
}
|
||
|
||
Chart *chartAt(uint32_t i) {
|
||
for (uint32_t c = 0; c < m_meshChartsArray.size(); c++) {
|
||
uint32_t count = m_meshChartsArray[c]->chartCount();
|
||
if (i < count) {
|
||
return m_meshChartsArray[c]->chartAt(i);
|
||
}
|
||
i -= count;
|
||
}
|
||
return NULL;
|
||
}
|
||
|
||
// Add mesh charts and takes ownership.
|
||
// Extract the charts and add to this atlas.
|
||
void addMeshCharts(MeshCharts *meshCharts) {
|
||
m_meshChartsArray.push_back(meshCharts);
|
||
}
|
||
|
||
void extractCharts(const halfedge::Mesh *mesh) {
|
||
MeshCharts *meshCharts = new MeshCharts(mesh);
|
||
meshCharts->extractCharts();
|
||
addMeshCharts(meshCharts);
|
||
}
|
||
|
||
void computeCharts(const halfedge::Mesh *mesh, const CharterOptions &options, const std::vector<uint32_t> &unchartedMaterialArray) {
|
||
MeshCharts *meshCharts = new MeshCharts(mesh);
|
||
meshCharts->computeCharts(options, unchartedMaterialArray);
|
||
addMeshCharts(meshCharts);
|
||
}
|
||
|
||
void parameterizeCharts() {
|
||
for (uint32_t i = 0; i < m_meshChartsArray.size(); i++) {
|
||
m_meshChartsArray[i]->parameterizeCharts();
|
||
}
|
||
}
|
||
|
||
private:
|
||
std::vector<MeshCharts *> m_meshChartsArray;
|
||
};
|
||
|
||
struct AtlasPacker {
|
||
AtlasPacker(Atlas *atlas) :
|
||
m_atlas(atlas),
|
||
m_width(0),
|
||
m_height(0) {
|
||
// Save the original uvs.
|
||
m_originalChartUvs.resize(m_atlas->chartCount());
|
||
for (uint32_t i = 0; i < m_atlas->chartCount(); i++) {
|
||
const halfedge::Mesh *mesh = atlas->chartAt(i)->chartMesh();
|
||
m_originalChartUvs[i].resize(mesh->vertexCount());
|
||
for (uint32_t j = 0; j < mesh->vertexCount(); j++)
|
||
m_originalChartUvs[i][j] = mesh->vertexAt(j)->tex;
|
||
}
|
||
}
|
||
|
||
uint32_t getWidth() const { return m_width; }
|
||
uint32_t getHeight() const { return m_height; }
|
||
|
||
// Pack charts in the smallest possible rectangle.
|
||
void packCharts(const PackerOptions &options) {
|
||
const uint32_t chartCount = m_atlas->chartCount();
|
||
if (chartCount == 0) return;
|
||
float texelsPerUnit = 1;
|
||
if (options.method == PackMethod::TexelArea)
|
||
texelsPerUnit = options.texelArea;
|
||
for (int iteration = 0;; iteration++) {
|
||
m_rand = MTRand();
|
||
std::vector<float> chartOrderArray(chartCount);
|
||
std::vector<Vector2> chartExtents(chartCount);
|
||
float meshArea = 0;
|
||
for (uint32_t c = 0; c < chartCount; c++) {
|
||
Chart *chart = m_atlas->chartAt(c);
|
||
if (!chart->isVertexMapped() && !chart->isDisk()) {
|
||
chartOrderArray[c] = 0;
|
||
// Skip non-disks.
|
||
continue;
|
||
}
|
||
Vector2 extents(0.0f);
|
||
if (chart->isVertexMapped()) {
|
||
// Arrange vertices in a rectangle.
|
||
extents.x = float(chart->vertexMapWidth);
|
||
extents.y = float(chart->vertexMapHeight);
|
||
} else {
|
||
// Compute surface area to sort charts.
|
||
float chartArea = chart->computeSurfaceArea();
|
||
meshArea += chartArea;
|
||
//chartOrderArray[c] = chartArea;
|
||
// Compute chart scale
|
||
float parametricArea = fabsf(chart->computeParametricArea()); // @@ There doesn't seem to be anything preventing parametric area to be negative.
|
||
if (parametricArea < NV_EPSILON) {
|
||
// When the parametric area is too small we use a rough approximation to prevent divisions by very small numbers.
|
||
Vector2 bounds = chart->computeParametricBounds();
|
||
parametricArea = bounds.x * bounds.y;
|
||
}
|
||
float scale = (chartArea / parametricArea) * texelsPerUnit;
|
||
if (parametricArea == 0) { // < NV_EPSILON)
|
||
scale = 0;
|
||
}
|
||
xaAssert(std::isfinite(scale));
|
||
// Compute bounding box of chart.
|
||
Vector2 majorAxis, minorAxis, origin, end;
|
||
computeBoundingBox(chart, &majorAxis, &minorAxis, &origin, &end);
|
||
xaAssert(isFinite(majorAxis) && isFinite(minorAxis) && isFinite(origin));
|
||
// Sort charts by perimeter. @@ This is sometimes producing somewhat unexpected results. Is this right?
|
||
//chartOrderArray[c] = ((end.x - origin.x) + (end.y - origin.y)) * scale;
|
||
// Translate, rotate and scale vertices. Compute extents.
|
||
halfedge::Mesh *mesh = chart->chartMesh();
|
||
const uint32_t vertexCount = mesh->vertexCount();
|
||
for (uint32_t i = 0; i < vertexCount; i++) {
|
||
halfedge::Vertex *vertex = mesh->vertexAt(i);
|
||
//Vector2 t = vertex->tex - origin;
|
||
Vector2 tmp;
|
||
tmp.x = dot(vertex->tex, majorAxis);
|
||
tmp.y = dot(vertex->tex, minorAxis);
|
||
tmp -= origin;
|
||
tmp *= scale;
|
||
if (tmp.x < 0 || tmp.y < 0) {
|
||
xaPrint("tmp: %f %f\n", tmp.x, tmp.y);
|
||
xaPrint("scale: %f\n", scale);
|
||
xaPrint("origin: %f %f\n", origin.x, origin.y);
|
||
xaPrint("majorAxis: %f %f\n", majorAxis.x, majorAxis.y);
|
||
xaPrint("minorAxis: %f %f\n", minorAxis.x, minorAxis.y);
|
||
xaDebugAssert(false);
|
||
}
|
||
//xaAssert(tmp.x >= 0 && tmp.y >= 0);
|
||
vertex->tex = tmp;
|
||
xaAssert(std::isfinite(vertex->tex.x) && std::isfinite(vertex->tex.y));
|
||
extents = max(extents, tmp);
|
||
}
|
||
xaDebugAssert(extents.x >= 0 && extents.y >= 0);
|
||
// Limit chart size.
|
||
if (extents.x > 1024 || extents.y > 1024) {
|
||
float limit = std::max(extents.x, extents.y);
|
||
scale = 1024 / (limit + 1);
|
||
for (uint32_t i = 0; i < vertexCount; i++) {
|
||
halfedge::Vertex *vertex = mesh->vertexAt(i);
|
||
vertex->tex *= scale;
|
||
}
|
||
extents *= scale;
|
||
xaDebugAssert(extents.x <= 1024 && extents.y <= 1024);
|
||
}
|
||
// Scale the charts to use the entire texel area available. So, if the width is 0.1 we could scale it to 1 without increasing the lightmap usage and making a better
|
||
// use of it. In many cases this also improves the look of the seams, since vertices on the chart boundaries have more chances of being aligned with the texel centers.
|
||
float scale_x = 1.0f;
|
||
float scale_y = 1.0f;
|
||
float divide_x = 1.0f;
|
||
float divide_y = 1.0f;
|
||
if (extents.x > 0) {
|
||
int cw = ftoi_ceil(extents.x);
|
||
if (options.blockAlign && chart->blockAligned) {
|
||
// Align all chart extents to 4x4 blocks, but taking padding into account.
|
||
if (options.conservative) {
|
||
cw = align(cw + 2, 4) - 2;
|
||
} else {
|
||
cw = align(cw + 1, 4) - 1;
|
||
}
|
||
}
|
||
scale_x = (float(cw) - NV_EPSILON);
|
||
divide_x = extents.x;
|
||
extents.x = float(cw);
|
||
}
|
||
if (extents.y > 0) {
|
||
int ch = ftoi_ceil(extents.y);
|
||
if (options.blockAlign && chart->blockAligned) {
|
||
// Align all chart extents to 4x4 blocks, but taking padding into account.
|
||
if (options.conservative) {
|
||
ch = align(ch + 2, 4) - 2;
|
||
} else {
|
||
ch = align(ch + 1, 4) - 1;
|
||
}
|
||
}
|
||
scale_y = (float(ch) - NV_EPSILON);
|
||
divide_y = extents.y;
|
||
extents.y = float(ch);
|
||
}
|
||
for (uint32_t v = 0; v < vertexCount; v++) {
|
||
halfedge::Vertex *vertex = mesh->vertexAt(v);
|
||
vertex->tex.x /= divide_x;
|
||
vertex->tex.y /= divide_y;
|
||
vertex->tex.x *= scale_x;
|
||
vertex->tex.y *= scale_y;
|
||
xaAssert(std::isfinite(vertex->tex.x) && std::isfinite(vertex->tex.y));
|
||
}
|
||
}
|
||
chartExtents[c] = extents;
|
||
// Sort charts by perimeter.
|
||
chartOrderArray[c] = extents.x + extents.y;
|
||
}
|
||
// @@ We can try to improve compression of small charts by sorting them by proximity like we do with vertex samples.
|
||
// @@ How to do that? One idea: compute chart centroid, insert into grid, compute morton index of the cell, sort based on morton index.
|
||
// @@ We would sort by morton index, first, then quantize the chart sizes, so that all small charts have the same size, and sort by size preserving the morton order.
|
||
//xaPrint("Sorting charts.\n");
|
||
// Sort charts by area.
|
||
m_radix = RadixSort();
|
||
m_radix.sort(chartOrderArray);
|
||
const uint32_t *ranks = m_radix.ranks();
|
||
// First iteration - guess texelsPerUnit.
|
||
if (options.method != PackMethod::TexelArea && iteration == 0) {
|
||
// Estimate size of the map based on the mesh surface area and given texel scale.
|
||
const float texelCount = std::max(1.0f, meshArea * square(texelsPerUnit) / 0.75f); // Assume 75% utilization.
|
||
texelsPerUnit = sqrt((options.resolution * options.resolution) / texelCount);
|
||
resetUvs();
|
||
continue;
|
||
}
|
||
// Init bit map.
|
||
m_bitmap.clearAll();
|
||
m_bitmap.resize(options.resolution, options.resolution, false);
|
||
int w = 0;
|
||
int h = 0;
|
||
// Add sorted charts to bitmap.
|
||
for (uint32_t i = 0; i < chartCount; i++) {
|
||
uint32_t c = ranks[chartCount - i - 1]; // largest chart first
|
||
Chart *chart = m_atlas->chartAt(c);
|
||
if (!chart->isVertexMapped() && !chart->isDisk()) continue;
|
||
//float scale_x = 1;
|
||
//float scale_y = 1;
|
||
BitMap chart_bitmap;
|
||
if (chart->isVertexMapped()) {
|
||
chart->blockAligned = false;
|
||
// Init all bits to 1.
|
||
chart_bitmap.resize(ftoi_ceil(chartExtents[c].x), ftoi_ceil(chartExtents[c].y), /*initValue=*/true);
|
||
// @@ Another alternative would be to try to map each vertex to a different texel trying to fill all the available unused texels.
|
||
} else {
|
||
// @@ Add special cases for dot and line charts. @@ Lightmap rasterizer also needs to handle these special cases.
|
||
// @@ We could also have a special case for chart quads. If the quad surface <= 4 texels, align vertices with texel centers and do not add padding. May be very useful for foliage.
|
||
// @@ In general we could reduce the padding of all charts by one texel by using a rasterizer that takes into account the 2-texel footprint of the tent bilinear filter. For example,
|
||
// if we have a chart that is less than 1 texel wide currently we add one texel to the left and one texel to the right creating a 3-texel-wide bitmap. However, if we know that the
|
||
// chart is only 1 texel wide we could align it so that it only touches the footprint of two texels:
|
||
// | | <- Touches texels 0, 1 and 2.
|
||
// | | <- Only touches texels 0 and 1.
|
||
// \ \ / \ / /
|
||
// \ X X /
|
||
// \ / \ / \ /
|
||
// V V V
|
||
// 0 1 2
|
||
if (options.conservative) {
|
||
// Init all bits to 0.
|
||
chart_bitmap.resize(ftoi_ceil(chartExtents[c].x) + 1 + options.padding, ftoi_ceil(chartExtents[c].y) + 1 + options.padding, /*initValue=*/false); // + 2 to add padding on both sides.
|
||
// Rasterize chart and dilate.
|
||
drawChartBitmapDilate(chart, &chart_bitmap, options.padding);
|
||
} else {
|
||
// Init all bits to 0.
|
||
chart_bitmap.resize(ftoi_ceil(chartExtents[c].x) + 1, ftoi_ceil(chartExtents[c].y) + 1, /*initValue=*/false); // Add half a texels on each side.
|
||
// Rasterize chart and dilate.
|
||
drawChartBitmap(chart, &chart_bitmap, Vector2(1), Vector2(0.5));
|
||
}
|
||
}
|
||
int best_x, best_y;
|
||
int best_cw, best_ch; // Includes padding now.
|
||
int best_r;
|
||
findChartLocation(options.quality, &chart_bitmap, chartExtents[c], w, h, &best_x, &best_y, &best_cw, &best_ch, &best_r, chart->blockAligned);
|
||
/*if (w < best_x + best_cw || h < best_y + best_ch)
|
||
{
|
||
xaPrint("Resize extents to (%d, %d).\n", best_x + best_cw, best_y + best_ch);
|
||
}*/
|
||
// Update parametric extents.
|
||
w = std::max(w, best_x + best_cw);
|
||
h = std::max(h, best_y + best_ch);
|
||
w = align(w, 4);
|
||
h = align(h, 4);
|
||
// Resize bitmap if necessary.
|
||
if (uint32_t(w) > m_bitmap.width() || uint32_t(h) > m_bitmap.height()) {
|
||
//xaPrint("Resize bitmap (%d, %d).\n", nextPowerOfTwo(w), nextPowerOfTwo(h));
|
||
m_bitmap.resize(nextPowerOfTwo(uint32_t(w)), nextPowerOfTwo(uint32_t(h)), false);
|
||
}
|
||
//xaPrint("Add chart at (%d, %d).\n", best_x, best_y);
|
||
addChart(&chart_bitmap, w, h, best_x, best_y, best_r);
|
||
//float best_angle = 2 * PI * best_r;
|
||
// Translate and rotate chart texture coordinates.
|
||
halfedge::Mesh *mesh = chart->chartMesh();
|
||
const uint32_t vertexCount = mesh->vertexCount();
|
||
for (uint32_t v = 0; v < vertexCount; v++) {
|
||
halfedge::Vertex *vertex = mesh->vertexAt(v);
|
||
Vector2 t = vertex->tex;
|
||
if (best_r) std::swap(t.x, t.y);
|
||
//vertex->tex.x = best_x + t.x * cosf(best_angle) - t.y * sinf(best_angle);
|
||
//vertex->tex.y = best_y + t.x * sinf(best_angle) + t.y * cosf(best_angle);
|
||
vertex->tex.x = best_x + t.x + 0.5f;
|
||
vertex->tex.y = best_y + t.y + 0.5f;
|
||
xaAssert(vertex->tex.x >= 0 && vertex->tex.y >= 0);
|
||
xaAssert(std::isfinite(vertex->tex.x) && std::isfinite(vertex->tex.y));
|
||
}
|
||
}
|
||
//w -= padding - 1; // Leave one pixel border!
|
||
//h -= padding - 1;
|
||
m_width = std::max(0, w);
|
||
m_height = std::max(0, h);
|
||
xaAssert(isAligned(m_width, 4));
|
||
xaAssert(isAligned(m_height, 4));
|
||
if (options.method == PackMethod::ExactResolution) {
|
||
texelsPerUnit *= sqrt((options.resolution * options.resolution) / (float)(m_width * m_height));
|
||
if (iteration > 1 && m_width <= options.resolution && m_height <= options.resolution) {
|
||
m_width = m_height = options.resolution;
|
||
return;
|
||
}
|
||
resetUvs();
|
||
} else {
|
||
return;
|
||
}
|
||
}
|
||
}
|
||
|
||
float computeAtlasUtilization() const {
|
||
const uint32_t w = m_width;
|
||
const uint32_t h = m_height;
|
||
xaDebugAssert(w <= m_bitmap.width());
|
||
xaDebugAssert(h <= m_bitmap.height());
|
||
uint32_t count = 0;
|
||
for (uint32_t y = 0; y < h; y++) {
|
||
for (uint32_t x = 0; x < w; x++) {
|
||
count += m_bitmap.bitAt(x, y);
|
||
}
|
||
}
|
||
return float(count) / (w * h);
|
||
}
|
||
|
||
private:
|
||
void resetUvs() {
|
||
for (uint32_t i = 0; i < m_atlas->chartCount(); i++) {
|
||
halfedge::Mesh *mesh = m_atlas->chartAt(i)->chartMesh();
|
||
for (uint32_t j = 0; j < mesh->vertexCount(); j++)
|
||
mesh->vertexAt(j)->tex = m_originalChartUvs[i][j];
|
||
}
|
||
}
|
||
|
||
// IC: Brute force is slow, and random may take too much time to converge. We start inserting large charts in a small atlas. Using brute force is lame, because most of the space
|
||
// is occupied at this point. At the end we have many small charts and a large atlas with sparse holes. Finding those holes randomly is slow. A better approach would be to
|
||
// start stacking large charts as if they were tetris pieces. Once charts get small try to place them randomly. It may be interesting to try a intermediate strategy, first try
|
||
// along one axis and then try exhaustively along that axis.
|
||
void findChartLocation(int quality, const BitMap *bitmap, Vector2::Arg extents, int w, int h, int *best_x, int *best_y, int *best_w, int *best_h, int *best_r, bool blockAligned) {
|
||
int attempts = 256;
|
||
if (quality == 1) attempts = 4096;
|
||
if (quality == 2) attempts = 2048;
|
||
if (quality == 3) attempts = 1024;
|
||
if (quality == 4) attempts = 512;
|
||
if (quality == 0 || w * h < attempts) {
|
||
findChartLocation_bruteForce(bitmap, extents, w, h, best_x, best_y, best_w, best_h, best_r, blockAligned);
|
||
} else {
|
||
findChartLocation_random(bitmap, extents, w, h, best_x, best_y, best_w, best_h, best_r, attempts, blockAligned);
|
||
}
|
||
}
|
||
|
||
void findChartLocation_bruteForce(const BitMap *bitmap, Vector2::Arg /*extents*/, int w, int h, int *best_x, int *best_y, int *best_w, int *best_h, int *best_r, bool blockAligned) {
|
||
const int BLOCK_SIZE = 4;
|
||
int best_metric = INT_MAX;
|
||
int step_size = blockAligned ? BLOCK_SIZE : 1;
|
||
// Try two different orientations.
|
||
for (int r = 0; r < 2; r++) {
|
||
int cw = bitmap->width();
|
||
int ch = bitmap->height();
|
||
if (r & 1) std::swap(cw, ch);
|
||
for (int y = 0; y <= h + 1; y += step_size) { // + 1 to extend atlas in case atlas full.
|
||
for (int x = 0; x <= w + 1; x += step_size) { // + 1 not really necessary here.
|
||
// Early out.
|
||
int area = std::max(w, x + cw) * std::max(h, y + ch);
|
||
//int perimeter = max(w, x+cw) + max(h, y+ch);
|
||
int extents = std::max(std::max(w, x + cw), std::max(h, y + ch));
|
||
int metric = extents * extents + area;
|
||
if (metric > best_metric) {
|
||
continue;
|
||
}
|
||
if (metric == best_metric && std::max(x, y) >= std::max(*best_x, *best_y)) {
|
||
// If metric is the same, pick the one closest to the origin.
|
||
continue;
|
||
}
|
||
if (canAddChart(bitmap, w, h, x, y, r)) {
|
||
best_metric = metric;
|
||
*best_x = x;
|
||
*best_y = y;
|
||
*best_w = cw;
|
||
*best_h = ch;
|
||
*best_r = r;
|
||
if (area == w * h) {
|
||
// Chart is completely inside, do not look at any other location.
|
||
goto done;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
done:
|
||
xaDebugAssert(best_metric != INT_MAX);
|
||
}
|
||
|
||
void findChartLocation_random(const BitMap *bitmap, Vector2::Arg /*extents*/, int w, int h, int *best_x, int *best_y, int *best_w, int *best_h, int *best_r, int minTrialCount, bool blockAligned) {
|
||
const int BLOCK_SIZE = 4;
|
||
int best_metric = INT_MAX;
|
||
for (int i = 0; i < minTrialCount || best_metric == INT_MAX; i++) {
|
||
int r = m_rand.getRange(1);
|
||
int x = m_rand.getRange(w + 1); // + 1 to extend atlas in case atlas full. We may want to use a higher number to increase probability of extending atlas.
|
||
int y = m_rand.getRange(h + 1); // + 1 to extend atlas in case atlas full.
|
||
if (blockAligned) {
|
||
x = align(x, BLOCK_SIZE);
|
||
y = align(y, BLOCK_SIZE);
|
||
}
|
||
int cw = bitmap->width();
|
||
int ch = bitmap->height();
|
||
if (r & 1) std::swap(cw, ch);
|
||
// Early out.
|
||
int area = std::max(w, x + cw) * std::max(h, y + ch);
|
||
//int perimeter = max(w, x+cw) + max(h, y+ch);
|
||
int extents = std::max(std::max(w, x + cw), std::max(h, y + ch));
|
||
int metric = extents * extents + area;
|
||
if (metric > best_metric) {
|
||
continue;
|
||
}
|
||
if (metric == best_metric && std::min(x, y) > std::min(*best_x, *best_y)) {
|
||
// If metric is the same, pick the one closest to the origin.
|
||
continue;
|
||
}
|
||
if (canAddChart(bitmap, w, h, x, y, r)) {
|
||
best_metric = metric;
|
||
*best_x = x;
|
||
*best_y = y;
|
||
*best_w = cw;
|
||
*best_h = ch;
|
||
*best_r = r;
|
||
if (area == w * h) {
|
||
// Chart is completely inside, do not look at any other location.
|
||
break;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
void drawChartBitmapDilate(const Chart *chart, BitMap *bitmap, int padding) {
|
||
const int w = bitmap->width();
|
||
const int h = bitmap->height();
|
||
const Vector2 extents = Vector2(float(w), float(h));
|
||
// Rasterize chart faces, check that all bits are not set.
|
||
const uint32_t faceCount = chart->faceCount();
|
||
for (uint32_t f = 0; f < faceCount; f++) {
|
||
const halfedge::Face *face = chart->chartMesh()->faceAt(f);
|
||
Vector2 vertices[4];
|
||
uint32_t edgeCount = 0;
|
||
for (halfedge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
if (edgeCount < 4) {
|
||
vertices[edgeCount] = it.vertex()->tex + Vector2(0.5) + Vector2(float(padding), float(padding));
|
||
}
|
||
edgeCount++;
|
||
}
|
||
if (edgeCount == 3) {
|
||
raster::drawTriangle(raster::Mode_Antialiased, extents, true, vertices, AtlasPacker::setBitsCallback, bitmap);
|
||
} else {
|
||
raster::drawQuad(raster::Mode_Antialiased, extents, true, vertices, AtlasPacker::setBitsCallback, bitmap);
|
||
}
|
||
}
|
||
// Expand chart by padding pixels. (dilation)
|
||
BitMap tmp(w, h);
|
||
for (int i = 0; i < padding; i++) {
|
||
tmp.clearAll();
|
||
for (int y = 0; y < h; y++) {
|
||
for (int x = 0; x < w; x++) {
|
||
bool b = bitmap->bitAt(x, y);
|
||
if (!b) {
|
||
if (x > 0) {
|
||
b |= bitmap->bitAt(x - 1, y);
|
||
if (y > 0) b |= bitmap->bitAt(x - 1, y - 1);
|
||
if (y < h - 1) b |= bitmap->bitAt(x - 1, y + 1);
|
||
}
|
||
if (y > 0) b |= bitmap->bitAt(x, y - 1);
|
||
if (y < h - 1) b |= bitmap->bitAt(x, y + 1);
|
||
if (x < w - 1) {
|
||
b |= bitmap->bitAt(x + 1, y);
|
||
if (y > 0) b |= bitmap->bitAt(x + 1, y - 1);
|
||
if (y < h - 1) b |= bitmap->bitAt(x + 1, y + 1);
|
||
}
|
||
}
|
||
if (b) tmp.setBitAt(x, y);
|
||
}
|
||
}
|
||
std::swap(tmp, *bitmap);
|
||
}
|
||
}
|
||
|
||
void drawChartBitmap(const Chart *chart, BitMap *bitmap, const Vector2 &scale, const Vector2 &offset) {
|
||
const int w = bitmap->width();
|
||
const int h = bitmap->height();
|
||
const Vector2 extents = Vector2(float(w), float(h));
|
||
static const Vector2 pad[4] = {
|
||
Vector2(-0.5, -0.5),
|
||
Vector2(0.5, -0.5),
|
||
Vector2(-0.5, 0.5),
|
||
Vector2(0.5, 0.5)
|
||
};
|
||
// Rasterize 4 times to add proper padding.
|
||
for (int i = 0; i < 4; i++) {
|
||
// Rasterize chart faces, check that all bits are not set.
|
||
const uint32_t faceCount = chart->chartMesh()->faceCount();
|
||
for (uint32_t f = 0; f < faceCount; f++) {
|
||
const halfedge::Face *face = chart->chartMesh()->faceAt(f);
|
||
Vector2 vertices[4];
|
||
uint32_t edgeCount = 0;
|
||
for (halfedge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance()) {
|
||
if (edgeCount < 4) {
|
||
vertices[edgeCount] = it.vertex()->tex * scale + offset + pad[i];
|
||
xaAssert(ftoi_ceil(vertices[edgeCount].x) >= 0);
|
||
xaAssert(ftoi_ceil(vertices[edgeCount].y) >= 0);
|
||
xaAssert(ftoi_ceil(vertices[edgeCount].x) <= w);
|
||
xaAssert(ftoi_ceil(vertices[edgeCount].y) <= h);
|
||
}
|
||
edgeCount++;
|
||
}
|
||
if (edgeCount == 3) {
|
||
raster::drawTriangle(raster::Mode_Antialiased, extents, /*enableScissors=*/true, vertices, AtlasPacker::setBitsCallback, bitmap);
|
||
} else {
|
||
raster::drawQuad(raster::Mode_Antialiased, extents, /*enableScissors=*/true, vertices, AtlasPacker::setBitsCallback, bitmap);
|
||
}
|
||
}
|
||
}
|
||
// Expand chart by padding pixels. (dilation)
|
||
BitMap tmp(w, h);
|
||
tmp.clearAll();
|
||
for (int y = 0; y < h; y++) {
|
||
for (int x = 0; x < w; x++) {
|
||
bool b = bitmap->bitAt(x, y);
|
||
if (!b) {
|
||
if (x > 0) {
|
||
b |= bitmap->bitAt(x - 1, y);
|
||
if (y > 0) b |= bitmap->bitAt(x - 1, y - 1);
|
||
if (y < h - 1) b |= bitmap->bitAt(x - 1, y + 1);
|
||
}
|
||
if (y > 0) b |= bitmap->bitAt(x, y - 1);
|
||
if (y < h - 1) b |= bitmap->bitAt(x, y + 1);
|
||
if (x < w - 1) {
|
||
b |= bitmap->bitAt(x + 1, y);
|
||
if (y > 0) b |= bitmap->bitAt(x + 1, y - 1);
|
||
if (y < h - 1) b |= bitmap->bitAt(x + 1, y + 1);
|
||
}
|
||
}
|
||
if (b) tmp.setBitAt(x, y);
|
||
}
|
||
}
|
||
std::swap(tmp, *bitmap);
|
||
}
|
||
|
||
bool canAddChart(const BitMap *bitmap, int atlas_w, int atlas_h, int offset_x, int offset_y, int r) {
|
||
xaDebugAssert(r == 0 || r == 1);
|
||
// Check whether the two bitmaps overlap.
|
||
const int w = bitmap->width();
|
||
const int h = bitmap->height();
|
||
if (r == 0) {
|
||
for (int y = 0; y < h; y++) {
|
||
int yy = y + offset_y;
|
||
if (yy >= 0) {
|
||
for (int x = 0; x < w; x++) {
|
||
int xx = x + offset_x;
|
||
if (xx >= 0) {
|
||
if (bitmap->bitAt(x, y)) {
|
||
if (xx < atlas_w && yy < atlas_h) {
|
||
if (m_bitmap.bitAt(xx, yy)) return false;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
} else if (r == 1) {
|
||
for (int y = 0; y < h; y++) {
|
||
int xx = y + offset_x;
|
||
if (xx >= 0) {
|
||
for (int x = 0; x < w; x++) {
|
||
int yy = x + offset_y;
|
||
if (yy >= 0) {
|
||
if (bitmap->bitAt(x, y)) {
|
||
if (xx < atlas_w && yy < atlas_h) {
|
||
if (m_bitmap.bitAt(xx, yy)) return false;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
return true;
|
||
}
|
||
|
||
void addChart(const BitMap *bitmap, int atlas_w, int atlas_h, int offset_x, int offset_y, int r) {
|
||
xaDebugAssert(r == 0 || r == 1);
|
||
// Check whether the two bitmaps overlap.
|
||
const int w = bitmap->width();
|
||
const int h = bitmap->height();
|
||
if (r == 0) {
|
||
for (int y = 0; y < h; y++) {
|
||
int yy = y + offset_y;
|
||
if (yy >= 0) {
|
||
for (int x = 0; x < w; x++) {
|
||
int xx = x + offset_x;
|
||
if (xx >= 0) {
|
||
if (bitmap->bitAt(x, y)) {
|
||
if (xx < atlas_w && yy < atlas_h) {
|
||
xaDebugAssert(m_bitmap.bitAt(xx, yy) == false);
|
||
m_bitmap.setBitAt(xx, yy);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
} else if (r == 1) {
|
||
for (int y = 0; y < h; y++) {
|
||
int xx = y + offset_x;
|
||
if (xx >= 0) {
|
||
for (int x = 0; x < w; x++) {
|
||
int yy = x + offset_y;
|
||
if (yy >= 0) {
|
||
if (bitmap->bitAt(x, y)) {
|
||
if (xx < atlas_w && yy < atlas_h) {
|
||
xaDebugAssert(m_bitmap.bitAt(xx, yy) == false);
|
||
m_bitmap.setBitAt(xx, yy);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
static bool setBitsCallback(void *param, int x, int y, Vector3::Arg, Vector3::Arg, Vector3::Arg, float area) {
|
||
BitMap *bitmap = (BitMap *)param;
|
||
if (area > 0.0) {
|
||
bitmap->setBitAt(x, y);
|
||
}
|
||
return true;
|
||
}
|
||
|
||
// Compute the convex hull using Graham Scan.
|
||
static void convexHull(const std::vector<Vector2> &input, std::vector<Vector2> &output, float epsilon) {
|
||
const uint32_t inputCount = input.size();
|
||
std::vector<float> coords(inputCount);
|
||
for (uint32_t i = 0; i < inputCount; i++) {
|
||
coords[i] = input[i].x;
|
||
}
|
||
RadixSort radix;
|
||
radix.sort(coords);
|
||
const uint32_t *ranks = radix.ranks();
|
||
std::vector<Vector2> top;
|
||
top.reserve(inputCount);
|
||
std::vector<Vector2> bottom;
|
||
bottom.reserve(inputCount);
|
||
Vector2 P = input[ranks[0]];
|
||
Vector2 Q = input[ranks[inputCount - 1]];
|
||
float topy = std::max(P.y, Q.y);
|
||
float boty = std::min(P.y, Q.y);
|
||
for (uint32_t i = 0; i < inputCount; i++) {
|
||
Vector2 p = input[ranks[i]];
|
||
if (p.y >= boty) top.push_back(p);
|
||
}
|
||
for (uint32_t i = 0; i < inputCount; i++) {
|
||
Vector2 p = input[ranks[inputCount - 1 - i]];
|
||
if (p.y <= topy) bottom.push_back(p);
|
||
}
|
||
// Filter top list.
|
||
output.clear();
|
||
output.push_back(top[0]);
|
||
output.push_back(top[1]);
|
||
for (uint32_t i = 2; i < top.size();) {
|
||
Vector2 a = output[output.size() - 2];
|
||
Vector2 b = output[output.size() - 1];
|
||
Vector2 c = top[i];
|
||
float area = triangleArea(a, b, c);
|
||
if (area >= -epsilon) {
|
||
output.pop_back();
|
||
}
|
||
if (area < -epsilon || output.size() == 1) {
|
||
output.push_back(c);
|
||
i++;
|
||
}
|
||
}
|
||
uint32_t top_count = output.size();
|
||
output.push_back(bottom[1]);
|
||
// Filter bottom list.
|
||
for (uint32_t i = 2; i < bottom.size();) {
|
||
Vector2 a = output[output.size() - 2];
|
||
Vector2 b = output[output.size() - 1];
|
||
Vector2 c = bottom[i];
|
||
float area = triangleArea(a, b, c);
|
||
if (area >= -epsilon) {
|
||
output.pop_back();
|
||
}
|
||
if (area < -epsilon || output.size() == top_count) {
|
||
output.push_back(c);
|
||
i++;
|
||
}
|
||
}
|
||
// Remove duplicate element.
|
||
xaDebugAssert(output.front() == output.back());
|
||
output.pop_back();
|
||
}
|
||
|
||
// This should compute convex hull and use rotating calipers to find the best box. Currently it uses a brute force method.
|
||
static void computeBoundingBox(Chart *chart, Vector2 *majorAxis, Vector2 *minorAxis, Vector2 *minCorner, Vector2 *maxCorner) {
|
||
// Compute list of boundary points.
|
||
std::vector<Vector2> points;
|
||
points.reserve(16);
|
||
halfedge::Mesh *mesh = chart->chartMesh();
|
||
const uint32_t vertexCount = mesh->vertexCount();
|
||
for (uint32_t i = 0; i < vertexCount; i++) {
|
||
halfedge::Vertex *vertex = mesh->vertexAt(i);
|
||
if (vertex->isBoundary()) {
|
||
points.push_back(vertex->tex);
|
||
}
|
||
}
|
||
xaDebugAssert(points.size() > 0);
|
||
std::vector<Vector2> hull;
|
||
convexHull(points, hull, 0.00001f);
|
||
// @@ Ideally I should use rotating calipers to find the best box. Using brute force for now.
|
||
float best_area = FLT_MAX;
|
||
Vector2 best_min;
|
||
Vector2 best_max;
|
||
Vector2 best_axis;
|
||
const uint32_t hullCount = hull.size();
|
||
for (uint32_t i = 0, j = hullCount - 1; i < hullCount; j = i, i++) {
|
||
if (equal(hull[i], hull[j])) {
|
||
continue;
|
||
}
|
||
Vector2 axis = normalize(hull[i] - hull[j], 0.0f);
|
||
xaDebugAssert(isFinite(axis));
|
||
// Compute bounding box.
|
||
Vector2 box_min(FLT_MAX, FLT_MAX);
|
||
Vector2 box_max(-FLT_MAX, -FLT_MAX);
|
||
for (uint32_t v = 0; v < hullCount; v++) {
|
||
Vector2 point = hull[v];
|
||
float x = dot(axis, point);
|
||
if (x < box_min.x) box_min.x = x;
|
||
if (x > box_max.x) box_max.x = x;
|
||
float y = dot(Vector2(-axis.y, axis.x), point);
|
||
if (y < box_min.y) box_min.y = y;
|
||
if (y > box_max.y) box_max.y = y;
|
||
}
|
||
// Compute box area.
|
||
float area = (box_max.x - box_min.x) * (box_max.y - box_min.y);
|
||
if (area < best_area) {
|
||
best_area = area;
|
||
best_min = box_min;
|
||
best_max = box_max;
|
||
best_axis = axis;
|
||
}
|
||
}
|
||
// Consider all points, not only boundary points, in case the input chart is malformed.
|
||
for (uint32_t i = 0; i < vertexCount; i++) {
|
||
halfedge::Vertex *vertex = mesh->vertexAt(i);
|
||
Vector2 point = vertex->tex;
|
||
float x = dot(best_axis, point);
|
||
if (x < best_min.x) best_min.x = x;
|
||
if (x > best_max.x) best_max.x = x;
|
||
float y = dot(Vector2(-best_axis.y, best_axis.x), point);
|
||
if (y < best_min.y) best_min.y = y;
|
||
if (y > best_max.y) best_max.y = y;
|
||
}
|
||
*majorAxis = best_axis;
|
||
*minorAxis = Vector2(-best_axis.y, best_axis.x);
|
||
*minCorner = best_min;
|
||
*maxCorner = best_max;
|
||
}
|
||
|
||
Atlas *m_atlas;
|
||
BitMap m_bitmap;
|
||
RadixSort m_radix;
|
||
uint32_t m_width;
|
||
uint32_t m_height;
|
||
MTRand m_rand;
|
||
std::vector<std::vector<Vector2> > m_originalChartUvs;
|
||
};
|
||
|
||
} // namespace param
|
||
} // namespace internal
|
||
|
||
struct Atlas {
|
||
internal::param::Atlas atlas;
|
||
std::vector<internal::halfedge::Mesh *> heMeshes;
|
||
uint32_t width = 0;
|
||
uint32_t height = 0;
|
||
OutputMesh **outputMeshes = NULL;
|
||
};
|
||
|
||
void SetPrint(PrintFunc print) {
|
||
internal::s_print = print;
|
||
}
|
||
|
||
Atlas *Create() {
|
||
Atlas *atlas = new Atlas();
|
||
return atlas;
|
||
}
|
||
|
||
void Destroy(Atlas *atlas) {
|
||
xaAssert(atlas);
|
||
for (int i = 0; i < (int)atlas->heMeshes.size(); i++) {
|
||
delete atlas->heMeshes[i];
|
||
if (atlas->outputMeshes) {
|
||
OutputMesh *outputMesh = atlas->outputMeshes[i];
|
||
for (uint32_t j = 0; j < outputMesh->chartCount; j++)
|
||
delete[] outputMesh->chartArray[j].indexArray;
|
||
delete[] outputMesh->chartArray;
|
||
delete[] outputMesh->vertexArray;
|
||
delete[] outputMesh->indexArray;
|
||
delete outputMesh;
|
||
}
|
||
}
|
||
delete[] atlas->outputMeshes;
|
||
delete atlas;
|
||
}
|
||
|
||
static internal::Vector3 DecodePosition(const InputMesh &mesh, uint32_t index) {
|
||
xaAssert(mesh.vertexPositionData);
|
||
return *((const internal::Vector3 *)&((const uint8_t *)mesh.vertexPositionData)[mesh.vertexPositionStride * index]);
|
||
}
|
||
|
||
static internal::Vector3 DecodeNormal(const InputMesh &mesh, uint32_t index) {
|
||
xaAssert(mesh.vertexNormalData);
|
||
return *((const internal::Vector3 *)&((const uint8_t *)mesh.vertexNormalData)[mesh.vertexNormalStride * index]);
|
||
}
|
||
|
||
static internal::Vector2 DecodeUv(const InputMesh &mesh, uint32_t index) {
|
||
xaAssert(mesh.vertexUvData);
|
||
return *((const internal::Vector2 *)&((const uint8_t *)mesh.vertexUvData)[mesh.vertexUvStride * index]);
|
||
}
|
||
|
||
static uint32_t DecodeIndex(IndexFormat::Enum format, const void *indexData, uint32_t i) {
|
||
if (format == IndexFormat::HalfFloat)
|
||
return (uint32_t)((const uint16_t *)indexData)[i];
|
||
return ((const uint32_t *)indexData)[i];
|
||
}
|
||
|
||
static float EdgeLength(internal::Vector3 pos1, internal::Vector3 pos2) {
|
||
return internal::length(pos2 - pos1);
|
||
}
|
||
|
||
AddMeshError AddMesh(Atlas *atlas, const InputMesh &mesh, bool useColocalVertices) {
|
||
xaAssert(atlas);
|
||
AddMeshError error;
|
||
error.code = AddMeshErrorCode::Success;
|
||
error.face = error.index0 = error.index1 = UINT32_MAX;
|
||
// Expecting triangle faces.
|
||
if ((mesh.indexCount % 3) != 0) {
|
||
error.code = AddMeshErrorCode::InvalidIndexCount;
|
||
return error;
|
||
}
|
||
// Check if any index is out of range.
|
||
for (uint32_t j = 0; j < mesh.indexCount; j++) {
|
||
const uint32_t index = DecodeIndex(mesh.indexFormat, mesh.indexData, j);
|
||
if (index < 0 || index >= mesh.vertexCount) {
|
||
error.code = AddMeshErrorCode::IndexOutOfRange;
|
||
error.index0 = index;
|
||
return error;
|
||
}
|
||
}
|
||
// Build half edge mesh.
|
||
internal::halfedge::Mesh *heMesh = new internal::halfedge::Mesh;
|
||
std::vector<uint32_t> canonicalMap;
|
||
canonicalMap.reserve(mesh.vertexCount);
|
||
for (uint32_t i = 0; i < mesh.vertexCount; i++) {
|
||
internal::halfedge::Vertex *vertex = heMesh->addVertex(DecodePosition(mesh, i));
|
||
if (mesh.vertexNormalData)
|
||
vertex->nor = DecodeNormal(mesh, i);
|
||
if (mesh.vertexUvData)
|
||
vertex->tex = DecodeUv(mesh, i);
|
||
// Link colocals. You probably want to do this more efficiently! Sort by one axis or use a hash or grid.
|
||
uint32_t firstColocal = i;
|
||
if (useColocalVertices) {
|
||
for (uint32_t j = 0; j < i; j++) {
|
||
if (vertex->pos != DecodePosition(mesh, j))
|
||
continue;
|
||
#if 0
|
||
if (mesh.vertexNormalData && vertex->nor != DecodeNormal(mesh, j))
|
||
continue;
|
||
#endif
|
||
if (mesh.vertexUvData && vertex->tex != DecodeUv(mesh, j))
|
||
continue;
|
||
firstColocal = j;
|
||
break;
|
||
}
|
||
}
|
||
canonicalMap.push_back(firstColocal);
|
||
}
|
||
heMesh->linkColocalsWithCanonicalMap(canonicalMap);
|
||
for (uint32_t i = 0; i < mesh.indexCount / 3; i++) {
|
||
uint32_t tri[3];
|
||
for (int j = 0; j < 3; j++)
|
||
tri[j] = DecodeIndex(mesh.indexFormat, mesh.indexData, i * 3 + j);
|
||
// Check for zero length edges.
|
||
for (int j = 0; j < 3; j++) {
|
||
const uint32_t edges[6] = { 0, 1, 1, 2, 2, 0 };
|
||
const uint32_t index1 = tri[edges[j * 2 + 0]];
|
||
const uint32_t index2 = tri[edges[j * 2 + 1]];
|
||
const internal::Vector3 pos1 = DecodePosition(mesh, index1);
|
||
const internal::Vector3 pos2 = DecodePosition(mesh, index2);
|
||
if (EdgeLength(pos1, pos2) <= 0.0f) {
|
||
delete heMesh;
|
||
error.code = AddMeshErrorCode::ZeroLengthEdge;
|
||
error.face = i;
|
||
error.index0 = index1;
|
||
error.index1 = index2;
|
||
return error;
|
||
}
|
||
}
|
||
// Check for zero area faces.
|
||
{
|
||
const internal::Vector3 a = DecodePosition(mesh, tri[0]);
|
||
const internal::Vector3 b = DecodePosition(mesh, tri[1]);
|
||
const internal::Vector3 c = DecodePosition(mesh, tri[2]);
|
||
const float area = internal::length(internal::cross(b - a, c - a)) * 0.5f;
|
||
if (area <= 0.0f) {
|
||
delete heMesh;
|
||
error.code = AddMeshErrorCode::ZeroAreaFace;
|
||
error.face = i;
|
||
return error;
|
||
}
|
||
}
|
||
internal::halfedge::Face *face = heMesh->addFace(tri[0], tri[1], tri[2]);
|
||
|
||
if (!face && heMesh->errorCode == internal::halfedge::Mesh::ErrorCode::AlreadyAddedEdge) {
|
||
//there is still hope for this, no reason to not add, at least add as separate
|
||
face = heMesh->addUniqueFace(tri[0], tri[1], tri[2]);
|
||
}
|
||
|
||
if (!face) {
|
||
//continue;
|
||
|
||
if (heMesh->errorCode == internal::halfedge::Mesh::ErrorCode::AlreadyAddedEdge) {
|
||
error.code = AddMeshErrorCode::AlreadyAddedEdge;
|
||
} else if (heMesh->errorCode == internal::halfedge::Mesh::ErrorCode::DegenerateColocalEdge) {
|
||
error.code = AddMeshErrorCode::DegenerateColocalEdge;
|
||
} else if (heMesh->errorCode == internal::halfedge::Mesh::ErrorCode::DegenerateEdge) {
|
||
error.code = AddMeshErrorCode::DegenerateEdge;
|
||
} else if (heMesh->errorCode == internal::halfedge::Mesh::ErrorCode::DuplicateEdge) {
|
||
error.code = AddMeshErrorCode::DuplicateEdge;
|
||
}
|
||
error.face = i;
|
||
error.index0 = heMesh->errorIndex0;
|
||
error.index1 = heMesh->errorIndex1;
|
||
delete heMesh;
|
||
return error;
|
||
}
|
||
if (mesh.faceMaterialData)
|
||
face->material = mesh.faceMaterialData[i];
|
||
}
|
||
heMesh->linkBoundary();
|
||
atlas->heMeshes.push_back(heMesh);
|
||
return error;
|
||
}
|
||
|
||
void Generate(Atlas *atlas, CharterOptions charterOptions, PackerOptions packerOptions) {
|
||
xaAssert(atlas);
|
||
xaAssert(packerOptions.texelArea > 0);
|
||
// Chart meshes.
|
||
for (int i = 0; i < (int)atlas->heMeshes.size(); i++) {
|
||
std::vector<uint32_t> uncharted_materials;
|
||
atlas->atlas.computeCharts(atlas->heMeshes[i], charterOptions, uncharted_materials);
|
||
}
|
||
atlas->atlas.parameterizeCharts();
|
||
internal::param::AtlasPacker packer(&atlas->atlas);
|
||
packer.packCharts(packerOptions);
|
||
//float utilization = return packer.computeAtlasUtilization();
|
||
atlas->width = packer.getWidth();
|
||
atlas->height = packer.getHeight();
|
||
// Build output meshes.
|
||
atlas->outputMeshes = new OutputMesh *[atlas->heMeshes.size()];
|
||
for (int i = 0; i < (int)atlas->heMeshes.size(); i++) {
|
||
const internal::halfedge::Mesh *heMesh = atlas->heMeshes[i];
|
||
OutputMesh *outputMesh = atlas->outputMeshes[i] = new OutputMesh;
|
||
const internal::param::MeshCharts *charts = atlas->atlas.meshAt(i);
|
||
// Vertices.
|
||
outputMesh->vertexCount = charts->vertexCount();
|
||
outputMesh->vertexArray = new OutputVertex[outputMesh->vertexCount];
|
||
for (uint32_t i = 0; i < charts->chartCount(); i++) {
|
||
const internal::param::Chart *chart = charts->chartAt(i);
|
||
const uint32_t vertexOffset = charts->vertexCountBeforeChartAt(i);
|
||
for (uint32_t v = 0; v < chart->vertexCount(); v++) {
|
||
OutputVertex &output_vertex = outputMesh->vertexArray[vertexOffset + v];
|
||
output_vertex.xref = chart->mapChartVertexToOriginalVertex(v);
|
||
internal::Vector2 uv = chart->chartMesh()->vertexAt(v)->tex;
|
||
output_vertex.uv[0] = uv.x;
|
||
output_vertex.uv[1] = uv.y;
|
||
}
|
||
}
|
||
// Indices.
|
||
outputMesh->indexCount = heMesh->faceCount() * 3;
|
||
outputMesh->indexArray = new uint32_t[outputMesh->indexCount];
|
||
for (uint32_t f = 0; f < heMesh->faceCount(); f++) {
|
||
const uint32_t c = charts->faceChartAt(f);
|
||
const uint32_t i = charts->faceIndexWithinChartAt(f);
|
||
const uint32_t vertexOffset = charts->vertexCountBeforeChartAt(c);
|
||
const internal::param::Chart *chart = charts->chartAt(c);
|
||
xaDebugAssert(i < chart->chartMesh()->faceCount());
|
||
xaDebugAssert(chart->faceAt(i) == f);
|
||
const internal::halfedge::Face *face = chart->chartMesh()->faceAt(i);
|
||
const internal::halfedge::Edge *edge = face->edge;
|
||
outputMesh->indexArray[3 * f + 0] = vertexOffset + edge->vertex->id;
|
||
outputMesh->indexArray[3 * f + 1] = vertexOffset + edge->next->vertex->id;
|
||
outputMesh->indexArray[3 * f + 2] = vertexOffset + edge->next->next->vertex->id;
|
||
}
|
||
// Charts.
|
||
outputMesh->chartCount = charts->chartCount();
|
||
outputMesh->chartArray = new OutputChart[outputMesh->chartCount];
|
||
for (uint32_t i = 0; i < charts->chartCount(); i++) {
|
||
OutputChart *outputChart = &outputMesh->chartArray[i];
|
||
const internal::param::Chart *chart = charts->chartAt(i);
|
||
const uint32_t vertexOffset = charts->vertexCountBeforeChartAt(i);
|
||
const internal::halfedge::Mesh *mesh = chart->chartMesh();
|
||
outputChart->indexCount = mesh->faceCount() * 3;
|
||
outputChart->indexArray = new uint32_t[outputChart->indexCount];
|
||
for (uint32_t j = 0; j < mesh->faceCount(); j++) {
|
||
const internal::halfedge::Face *face = mesh->faceAt(j);
|
||
const internal::halfedge::Edge *edge = face->edge;
|
||
outputChart->indexArray[3 * j + 0] = vertexOffset + edge->vertex->id;
|
||
outputChart->indexArray[3 * j + 1] = vertexOffset + edge->next->vertex->id;
|
||
outputChart->indexArray[3 * j + 2] = vertexOffset + edge->next->next->vertex->id;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
uint32_t GetWidth(const Atlas *atlas) {
|
||
xaAssert(atlas);
|
||
return atlas->width;
|
||
}
|
||
|
||
uint32_t GetHeight(const Atlas *atlas) {
|
||
xaAssert(atlas);
|
||
return atlas->height;
|
||
}
|
||
|
||
uint32_t GetNumCharts(const Atlas *atlas) {
|
||
xaAssert(atlas);
|
||
return atlas->atlas.chartCount();
|
||
}
|
||
|
||
const OutputMesh *const *GetOutputMeshes(const Atlas *atlas) {
|
||
xaAssert(atlas);
|
||
return atlas->outputMeshes;
|
||
}
|
||
|
||
const char *StringForEnum(AddMeshErrorCode::Enum error) {
|
||
if (error == AddMeshErrorCode::AlreadyAddedEdge)
|
||
return "already added edge";
|
||
if (error == AddMeshErrorCode::DegenerateColocalEdge)
|
||
return "degenerate colocal edge";
|
||
if (error == AddMeshErrorCode::DegenerateEdge)
|
||
return "degenerate edge";
|
||
if (error == AddMeshErrorCode::DuplicateEdge)
|
||
return "duplicate edge";
|
||
if (error == AddMeshErrorCode::IndexOutOfRange)
|
||
return "index out of range";
|
||
if (error == AddMeshErrorCode::InvalidIndexCount)
|
||
return "invalid index count";
|
||
if (error == AddMeshErrorCode::ZeroAreaFace)
|
||
return "zero area face";
|
||
if (error == AddMeshErrorCode::ZeroLengthEdge)
|
||
return "zero length edge";
|
||
return "success";
|
||
}
|
||
|
||
} // namespace xatlas
|