394 lines
14 KiB
C++
394 lines
14 KiB
C++
/**************************************************************************/
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/* delaunay_3d.h */
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/**************************************************************************/
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/* This file is part of: */
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/* GODOT ENGINE */
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/* https://godotengine.org */
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/**************************************************************************/
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/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
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/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
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/* */
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/* Permission is hereby granted, free of charge, to any person obtaining */
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/* a copy of this software and associated documentation files (the */
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/* "Software"), to deal in the Software without restriction, including */
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/* without limitation the rights to use, copy, modify, merge, publish, */
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/* distribute, sublicense, and/or sell copies of the Software, and to */
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/* permit persons to whom the Software is furnished to do so, subject to */
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/* the following conditions: */
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/* */
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/* The above copyright notice and this permission notice shall be */
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/* included in all copies or substantial portions of the Software. */
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/* */
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/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
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/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
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/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. */
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/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
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/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
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/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
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/**************************************************************************/
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#ifndef DELAUNAY_3D_H
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#define DELAUNAY_3D_H
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#include "core/io/file_access.h"
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#include "core/math/aabb.h"
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#include "core/math/projection.h"
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#include "core/math/vector3.h"
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#include "core/templates/local_vector.h"
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#include "core/templates/oa_hash_map.h"
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#include "core/templates/vector.h"
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#include "core/variant/variant.h"
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#include "thirdparty/misc/r128.h"
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class Delaunay3D {
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struct Simplex;
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enum {
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ACCEL_GRID_SIZE = 16,
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QUANTIZATION_MAX = 1 << 16 // A power of two smaller than the 23 bit significand of a float.
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};
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struct GridPos {
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Vector3i pos;
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List<Simplex *>::Element *E = nullptr;
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};
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struct Simplex {
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uint32_t points[4];
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R128 circum_center_x;
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R128 circum_center_y;
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R128 circum_center_z;
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R128 circum_r2;
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LocalVector<GridPos> grid_positions;
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List<Simplex *>::Element *SE = nullptr;
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_FORCE_INLINE_ Simplex() {}
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_FORCE_INLINE_ Simplex(uint32_t p_a, uint32_t p_b, uint32_t p_c, uint32_t p_d) {
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points[0] = p_a;
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points[1] = p_b;
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points[2] = p_c;
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points[3] = p_d;
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}
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};
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struct Triangle {
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uint32_t triangle[3];
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bool bad = false;
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_FORCE_INLINE_ bool operator==(const Triangle &p_triangle) const {
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return triangle[0] == p_triangle.triangle[0] && triangle[1] == p_triangle.triangle[1] && triangle[2] == p_triangle.triangle[2];
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}
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_FORCE_INLINE_ Triangle() {}
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_FORCE_INLINE_ Triangle(uint32_t p_a, uint32_t p_b, uint32_t p_c) {
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if (p_a > p_b) {
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SWAP(p_a, p_b);
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}
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if (p_b > p_c) {
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SWAP(p_b, p_c);
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}
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if (p_a > p_b) {
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SWAP(p_a, p_b);
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}
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triangle[0] = p_a;
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triangle[1] = p_b;
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triangle[2] = p_c;
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}
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};
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struct TriangleHasher {
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_FORCE_INLINE_ static uint32_t hash(const Triangle &p_triangle) {
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uint32_t h = hash_djb2_one_32(p_triangle.triangle[0]);
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h = hash_djb2_one_32(p_triangle.triangle[1], h);
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return hash_fmix32(hash_djb2_one_32(p_triangle.triangle[2], h));
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}
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};
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_FORCE_INLINE_ static void circum_sphere_compute(const Vector3 *p_points, Simplex *p_simplex) {
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// The only part in the algorithm where there may be precision errors is this one,
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// so ensure that we do it with the maximum precision possible.
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R128 v0_x = p_points[p_simplex->points[0]].x;
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R128 v0_y = p_points[p_simplex->points[0]].y;
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R128 v0_z = p_points[p_simplex->points[0]].z;
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R128 v1_x = p_points[p_simplex->points[1]].x;
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R128 v1_y = p_points[p_simplex->points[1]].y;
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R128 v1_z = p_points[p_simplex->points[1]].z;
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R128 v2_x = p_points[p_simplex->points[2]].x;
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R128 v2_y = p_points[p_simplex->points[2]].y;
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R128 v2_z = p_points[p_simplex->points[2]].z;
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R128 v3_x = p_points[p_simplex->points[3]].x;
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R128 v3_y = p_points[p_simplex->points[3]].y;
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R128 v3_z = p_points[p_simplex->points[3]].z;
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// Create the rows of our "unrolled" 3x3 matrix.
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R128 row1_x = v1_x - v0_x;
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R128 row1_y = v1_y - v0_y;
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R128 row1_z = v1_z - v0_z;
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R128 row2_x = v2_x - v0_x;
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R128 row2_y = v2_y - v0_y;
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R128 row2_z = v2_z - v0_z;
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R128 row3_x = v3_x - v0_x;
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R128 row3_y = v3_y - v0_y;
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R128 row3_z = v3_z - v0_z;
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R128 sq_lenght1 = row1_x * row1_x + row1_y * row1_y + row1_z * row1_z;
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R128 sq_lenght2 = row2_x * row2_x + row2_y * row2_y + row2_z * row2_z;
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R128 sq_lenght3 = row3_x * row3_x + row3_y * row3_y + row3_z * row3_z;
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// Compute the determinant of said matrix.
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R128 determinant = row1_x * (row2_y * row3_z - row3_y * row2_z) - row2_x * (row1_y * row3_z - row3_y * row1_z) + row3_x * (row1_y * row2_z - row2_y * row1_z);
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// Compute the volume of the tetrahedron, and precompute a scalar quantity for reuse in the formula.
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R128 volume = determinant / R128(6.f);
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R128 i12volume = R128(1.f) / (volume * R128(12.f));
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R128 center_x = v0_x + i12volume * ((row2_y * row3_z - row3_y * row2_z) * sq_lenght1 - (row1_y * row3_z - row3_y * row1_z) * sq_lenght2 + (row1_y * row2_z - row2_y * row1_z) * sq_lenght3);
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R128 center_y = v0_y + i12volume * (-(row2_x * row3_z - row3_x * row2_z) * sq_lenght1 + (row1_x * row3_z - row3_x * row1_z) * sq_lenght2 - (row1_x * row2_z - row2_x * row1_z) * sq_lenght3);
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R128 center_z = v0_z + i12volume * ((row2_x * row3_y - row3_x * row2_y) * sq_lenght1 - (row1_x * row3_y - row3_x * row1_y) * sq_lenght2 + (row1_x * row2_y - row2_x * row1_y) * sq_lenght3);
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// Once we know the center, the radius is clearly the distance to any vertex.
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R128 rel1_x = center_x - v0_x;
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R128 rel1_y = center_y - v0_y;
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R128 rel1_z = center_z - v0_z;
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R128 radius1 = rel1_x * rel1_x + rel1_y * rel1_y + rel1_z * rel1_z;
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p_simplex->circum_center_x = center_x;
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p_simplex->circum_center_y = center_y;
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p_simplex->circum_center_z = center_z;
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p_simplex->circum_r2 = radius1;
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}
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_FORCE_INLINE_ static bool simplex_contains(const Vector3 *p_points, const Simplex &p_simplex, uint32_t p_vertex) {
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R128 v_x = p_points[p_vertex].x;
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R128 v_y = p_points[p_vertex].y;
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R128 v_z = p_points[p_vertex].z;
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R128 rel2_x = p_simplex.circum_center_x - v_x;
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R128 rel2_y = p_simplex.circum_center_y - v_y;
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R128 rel2_z = p_simplex.circum_center_z - v_z;
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R128 radius2 = rel2_x * rel2_x + rel2_y * rel2_y + rel2_z * rel2_z;
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return radius2 < (p_simplex.circum_r2 - R128(0.0000000001));
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// When this tolerance is too big, it can result in overlapping simplices.
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// When it's too small, large amounts of planar simplices are created.
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}
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static bool simplex_is_coplanar(const Vector3 *p_points, const Simplex &p_simplex) {
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// Checking every possible distance like this is overkill, but only checking
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// one is not enough. If the simplex is almost planar then the vectors p1-p2
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// and p1-p3 can be practically collinear, which makes Plane unreliable.
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for (uint32_t i = 0; i < 4; i++) {
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Plane p(p_points[p_simplex.points[i]], p_points[p_simplex.points[(i + 1) % 4]], p_points[p_simplex.points[(i + 2) % 4]]);
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// This tolerance should not be smaller than the one used with
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// Plane::has_point() when creating the LightmapGI probe BSP tree.
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if (ABS(p.distance_to(p_points[p_simplex.points[(i + 3) % 4]])) < 0.001) {
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return true;
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}
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}
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return false;
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}
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public:
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struct OutputSimplex {
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uint32_t points[4];
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};
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static Vector<OutputSimplex> tetrahedralize(const Vector<Vector3> &p_points) {
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uint32_t point_count = p_points.size();
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Vector3 *points = (Vector3 *)memalloc(sizeof(Vector3) * (point_count + 4));
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const Vector3 *src_points = p_points.ptr();
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Vector3 proportions;
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{
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AABB rect;
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for (uint32_t i = 0; i < point_count; i++) {
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Vector3 point = src_points[i];
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if (i == 0) {
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rect.position = point;
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} else {
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rect.expand_to(point);
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}
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}
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real_t longest_axis = rect.size[rect.get_longest_axis_index()];
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proportions = Vector3(longest_axis, longest_axis, longest_axis) / rect.size;
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for (uint32_t i = 0; i < point_count; i++) {
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// Scale points to the unit cube to better utilize R128 precision
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// and quantize to stabilize triangulation over a wide range of
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// distances.
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points[i] = Vector3(Vector3i((src_points[i] - rect.position) / longest_axis * QUANTIZATION_MAX)) / QUANTIZATION_MAX;
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}
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const real_t delta_max = Math::sqrt(2.0) * 100.0;
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Vector3 center = Vector3(0.5, 0.5, 0.5);
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// The larger the root simplex is, the more likely it is that the
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// triangulation is convex. If it's not absolutely huge, there can
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// be missing simplices that are not created for the outermost faces
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// of the point cloud if the point density is very low there.
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points[point_count + 0] = center + Vector3(0, 1, 0) * delta_max;
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points[point_count + 1] = center + Vector3(0, -1, 1) * delta_max;
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points[point_count + 2] = center + Vector3(1, -1, -1) * delta_max;
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points[point_count + 3] = center + Vector3(-1, -1, -1) * delta_max;
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}
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List<Simplex *> acceleration_grid[ACCEL_GRID_SIZE][ACCEL_GRID_SIZE][ACCEL_GRID_SIZE];
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List<Simplex *> simplex_list;
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{
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//create root simplex
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Simplex *root = memnew(Simplex(point_count + 0, point_count + 1, point_count + 2, point_count + 3));
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root->SE = simplex_list.push_back(root);
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for (uint32_t i = 0; i < ACCEL_GRID_SIZE; i++) {
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for (uint32_t j = 0; j < ACCEL_GRID_SIZE; j++) {
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for (uint32_t k = 0; k < ACCEL_GRID_SIZE; k++) {
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GridPos gp;
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gp.E = acceleration_grid[i][j][k].push_back(root);
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gp.pos = Vector3i(i, j, k);
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root->grid_positions.push_back(gp);
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}
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}
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}
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circum_sphere_compute(points, root);
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}
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OAHashMap<Triangle, uint32_t, TriangleHasher> triangles_inserted;
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LocalVector<Triangle> triangles;
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for (uint32_t i = 0; i < point_count; i++) {
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bool unique = true;
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for (uint32_t j = i + 1; j < point_count; j++) {
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if (points[i] == points[j]) {
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unique = false;
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break;
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}
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}
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if (!unique) {
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continue;
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}
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Vector3i grid_pos = Vector3i(points[i] * proportions * ACCEL_GRID_SIZE);
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grid_pos = grid_pos.clamp(Vector3i(), Vector3i(ACCEL_GRID_SIZE - 1, ACCEL_GRID_SIZE - 1, ACCEL_GRID_SIZE - 1));
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for (List<Simplex *>::Element *E = acceleration_grid[grid_pos.x][grid_pos.y][grid_pos.z].front(); E;) {
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List<Simplex *>::Element *N = E->next(); //may be deleted
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Simplex *simplex = E->get();
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if (simplex_contains(points, *simplex, i)) {
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static const uint32_t triangle_order[4][3] = {
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{ 0, 1, 2 },
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{ 0, 1, 3 },
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{ 0, 2, 3 },
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{ 1, 2, 3 },
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};
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for (uint32_t k = 0; k < 4; k++) {
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Triangle t = Triangle(simplex->points[triangle_order[k][0]], simplex->points[triangle_order[k][1]], simplex->points[triangle_order[k][2]]);
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uint32_t *p = triangles_inserted.lookup_ptr(t);
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if (p) {
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// This Delaunay implementation uses the Bowyer-Watson algorithm.
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// The rule is that you don't reuse any triangles that were
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// shared by any of the retriangulated simplices.
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triangles[*p].bad = true;
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} else {
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triangles_inserted.insert(t, triangles.size());
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triangles.push_back(t);
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}
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}
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simplex_list.erase(simplex->SE);
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for (const GridPos &gp : simplex->grid_positions) {
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Vector3i p = gp.pos;
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acceleration_grid[p.x][p.y][p.z].erase(gp.E);
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}
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memdelete(simplex);
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}
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E = N;
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}
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for (const Triangle &triangle : triangles) {
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if (triangle.bad) {
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continue;
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}
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Simplex *new_simplex = memnew(Simplex(triangle.triangle[0], triangle.triangle[1], triangle.triangle[2], i));
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circum_sphere_compute(points, new_simplex);
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new_simplex->SE = simplex_list.push_back(new_simplex);
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{
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Vector3 center;
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center.x = double(new_simplex->circum_center_x);
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center.y = double(new_simplex->circum_center_y);
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center.z = double(new_simplex->circum_center_z);
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const real_t radius2 = Math::sqrt(double(new_simplex->circum_r2)) + 0.0001;
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Vector3 extents = Vector3(radius2, radius2, radius2);
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Vector3i from = Vector3i((center - extents) * proportions * ACCEL_GRID_SIZE);
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Vector3i to = Vector3i((center + extents) * proportions * ACCEL_GRID_SIZE);
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from = from.clamp(Vector3i(), Vector3i(ACCEL_GRID_SIZE - 1, ACCEL_GRID_SIZE - 1, ACCEL_GRID_SIZE - 1));
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to = to.clamp(Vector3i(), Vector3i(ACCEL_GRID_SIZE - 1, ACCEL_GRID_SIZE - 1, ACCEL_GRID_SIZE - 1));
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for (int32_t x = from.x; x <= to.x; x++) {
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for (int32_t y = from.y; y <= to.y; y++) {
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for (int32_t z = from.z; z <= to.z; z++) {
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GridPos gp;
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gp.pos = Vector3(x, y, z);
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gp.E = acceleration_grid[x][y][z].push_back(new_simplex);
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new_simplex->grid_positions.push_back(gp);
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}
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}
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}
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}
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}
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triangles.clear();
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triangles_inserted.clear();
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}
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//print_line("end with simplices: " + itos(simplex_list.size()));
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Vector<OutputSimplex> ret_simplices;
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ret_simplices.resize(simplex_list.size());
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OutputSimplex *ret_simplicesw = ret_simplices.ptrw();
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uint32_t simplices_written = 0;
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for (Simplex *simplex : simplex_list) {
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bool invalid = false;
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for (int j = 0; j < 4; j++) {
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if (simplex->points[j] >= point_count) {
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invalid = true;
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break;
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}
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}
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if (invalid || simplex_is_coplanar(src_points, *simplex)) {
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memdelete(simplex);
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continue;
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}
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ret_simplicesw[simplices_written].points[0] = simplex->points[0];
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ret_simplicesw[simplices_written].points[1] = simplex->points[1];
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ret_simplicesw[simplices_written].points[2] = simplex->points[2];
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ret_simplicesw[simplices_written].points[3] = simplex->points[3];
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simplices_written++;
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memdelete(simplex);
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}
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ret_simplices.resize(simplices_written);
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memfree(points);
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return ret_simplices;
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}
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};
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#endif // DELAUNAY_3D_H
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