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godot/core/math/geometry_3d.cpp

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/**************************************************************************/
/* geometry_3d.cpp */
/**************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/**************************************************************************/
/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
/* */
/* Permission is hereby granted, free of charge, to any person obtaining */
/* a copy of this software and associated documentation files (the */
/* "Software"), to deal in the Software without restriction, including */
/* without limitation the rights to use, copy, modify, merge, publish, */
/* distribute, sublicense, and/or sell copies of the Software, and to */
/* permit persons to whom the Software is furnished to do so, subject to */
/* the following conditions: */
/* */
/* The above copyright notice and this permission notice shall be */
/* included in all copies or substantial portions of the Software. */
/* */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. */
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
/**************************************************************************/
#include "geometry_3d.h"
#include "thirdparty/misc/clipper.hpp"
#include "thirdparty/misc/polypartition.h"
void Geometry3D::get_closest_points_between_segments(const Vector3 &p_p0, const Vector3 &p_p1, const Vector3 &p_q0, const Vector3 &p_q1, Vector3 &r_ps, Vector3 &r_qt) {
// Based on David Eberly's Computation of Distance Between Line Segments algorithm.
Vector3 p = p_p1 - p_p0;
Vector3 q = p_q1 - p_q0;
Vector3 r = p_p0 - p_q0;
real_t a = p.dot(p);
real_t b = p.dot(q);
real_t c = q.dot(q);
real_t d = p.dot(r);
real_t e = q.dot(r);
real_t s = 0.0f;
real_t t = 0.0f;
real_t det = a * c - b * b;
if (det > CMP_EPSILON) {
// Non-parallel segments
real_t bte = b * e;
real_t ctd = c * d;
if (bte <= ctd) {
// s <= 0.0f
if (e <= 0.0f) {
// t <= 0.0f
s = (-d >= a ? 1 : (-d > 0.0f ? -d / a : 0.0f));
t = 0.0f;
} else if (e < c) {
// 0.0f < t < 1
s = 0.0f;
t = e / c;
} else {
// t >= 1
s = (b - d >= a ? 1 : (b - d > 0.0f ? (b - d) / a : 0.0f));
t = 1;
}
} else {
// s > 0.0f
s = bte - ctd;
if (s >= det) {
// s >= 1
if (b + e <= 0.0f) {
// t <= 0.0f
s = (-d <= 0.0f ? 0.0f : (-d < a ? -d / a : 1));
t = 0.0f;
} else if (b + e < c) {
// 0.0f < t < 1
s = 1;
t = (b + e) / c;
} else {
// t >= 1
s = (b - d <= 0.0f ? 0.0f : (b - d < a ? (b - d) / a : 1));
t = 1;
}
} else {
// 0.0f < s < 1
real_t ate = a * e;
real_t btd = b * d;
if (ate <= btd) {
// t <= 0.0f
s = (-d <= 0.0f ? 0.0f : (-d >= a ? 1 : -d / a));
t = 0.0f;
} else {
// t > 0.0f
t = ate - btd;
if (t >= det) {
// t >= 1
s = (b - d <= 0.0f ? 0.0f : (b - d >= a ? 1 : (b - d) / a));
t = 1;
} else {
// 0.0f < t < 1
s /= det;
t /= det;
}
}
}
}
} else {
// Parallel segments
if (e <= 0.0f) {
s = (-d <= 0.0f ? 0.0f : (-d >= a ? 1 : -d / a));
t = 0.0f;
} else if (e >= c) {
s = (b - d <= 0.0f ? 0.0f : (b - d >= a ? 1 : (b - d) / a));
t = 1;
} else {
s = 0.0f;
t = e / c;
}
}
r_ps = (1 - s) * p_p0 + s * p_p1;
r_qt = (1 - t) * p_q0 + t * p_q1;
}
real_t Geometry3D::get_closest_distance_between_segments(const Vector3 &p_p0, const Vector3 &p_p1, const Vector3 &p_q0, const Vector3 &p_q1) {
Vector3 ps;
Vector3 qt;
get_closest_points_between_segments(p_p0, p_p1, p_q0, p_q1, ps, qt);
Vector3 st = qt - ps;
return st.length();
}
void Geometry3D::MeshData::optimize_vertices() {
HashMap<int, int> vtx_remap;
for (MeshData::Face &face : faces) {
for (int &index : face.indices) {
if (!vtx_remap.has(index)) {
int ni = vtx_remap.size();
vtx_remap[index] = ni;
}
index = vtx_remap[index];
}
}
for (MeshData::Edge edge : edges) {
int a = edge.vertex_a;
int b = edge.vertex_b;
if (!vtx_remap.has(a)) {
int ni = vtx_remap.size();
vtx_remap[a] = ni;
}
if (!vtx_remap.has(b)) {
int ni = vtx_remap.size();
vtx_remap[b] = ni;
}
edge.vertex_a = vtx_remap[a];
edge.vertex_b = vtx_remap[b];
}
LocalVector<Vector3> new_vertices;
new_vertices.resize(vtx_remap.size());
for (uint32_t i = 0; i < vertices.size(); i++) {
if (vtx_remap.has(i)) {
new_vertices[vtx_remap[i]] = vertices[i];
}
}
vertices = new_vertices;
}
struct _FaceClassify {
struct _Link {
int face = -1;
int edge = -1;
void clear() {
face = -1;
edge = -1;
}
_Link() {}
};
bool valid = false;
int group = -1;
_Link links[3];
Face3 face;
_FaceClassify() {}
};
/*** GEOMETRY WRAPPER ***/
enum _CellFlags {
_CELL_SOLID = 1,
_CELL_EXTERIOR = 2,
_CELL_STEP_MASK = 0x1C,
_CELL_STEP_NONE = 0 << 2,
_CELL_STEP_Y_POS = 1 << 2,
_CELL_STEP_Y_NEG = 2 << 2,
_CELL_STEP_X_POS = 3 << 2,
_CELL_STEP_X_NEG = 4 << 2,
_CELL_STEP_Z_POS = 5 << 2,
_CELL_STEP_Z_NEG = 6 << 2,
_CELL_STEP_DONE = 7 << 2,
_CELL_PREV_MASK = 0xE0,
_CELL_PREV_NONE = 0 << 5,
_CELL_PREV_Y_POS = 1 << 5,
_CELL_PREV_Y_NEG = 2 << 5,
_CELL_PREV_X_POS = 3 << 5,
_CELL_PREV_X_NEG = 4 << 5,
_CELL_PREV_Z_POS = 5 << 5,
_CELL_PREV_Z_NEG = 6 << 5,
_CELL_PREV_FIRST = 7 << 5,
};
static inline void _plot_face(uint8_t ***p_cell_status, int x, int y, int z, int len_x, int len_y, int len_z, const Vector3 &voxelsize, const Face3 &p_face) {
AABB aabb(Vector3(x, y, z), Vector3(len_x, len_y, len_z));
aabb.position = aabb.position * voxelsize;
aabb.size = aabb.size * voxelsize;
if (!p_face.intersects_aabb(aabb)) {
return;
}
if (len_x == 1 && len_y == 1 && len_z == 1) {
p_cell_status[x][y][z] = _CELL_SOLID;
return;
}
int div_x = len_x > 1 ? 2 : 1;
int div_y = len_y > 1 ? 2 : 1;
int div_z = len_z > 1 ? 2 : 1;
#define SPLIT_DIV(m_i, m_div, m_v, m_len_v, m_new_v, m_new_len_v) \
if (m_div == 1) { \
m_new_v = m_v; \
m_new_len_v = 1; \
} else if (m_i == 0) { \
m_new_v = m_v; \
m_new_len_v = m_len_v / 2; \
} else { \
m_new_v = m_v + m_len_v / 2; \
m_new_len_v = m_len_v - m_len_v / 2; \
}
int new_x;
int new_len_x;
int new_y;
int new_len_y;
int new_z;
int new_len_z;
for (int i = 0; i < div_x; i++) {
SPLIT_DIV(i, div_x, x, len_x, new_x, new_len_x);
for (int j = 0; j < div_y; j++) {
SPLIT_DIV(j, div_y, y, len_y, new_y, new_len_y);
for (int k = 0; k < div_z; k++) {
SPLIT_DIV(k, div_z, z, len_z, new_z, new_len_z);
_plot_face(p_cell_status, new_x, new_y, new_z, new_len_x, new_len_y, new_len_z, voxelsize, p_face);
}
}
}
#undef SPLIT_DIV
}
static inline void _mark_outside(uint8_t ***p_cell_status, int x, int y, int z, int len_x, int len_y, int len_z) {
if (p_cell_status[x][y][z] & 3) {
return; // Nothing to do, already used and/or visited.
}
p_cell_status[x][y][z] = _CELL_PREV_FIRST;
while (true) {
uint8_t &c = p_cell_status[x][y][z];
if ((c & _CELL_STEP_MASK) == _CELL_STEP_NONE) {
// Haven't been in here, mark as outside.
p_cell_status[x][y][z] |= _CELL_EXTERIOR;
}
if ((c & _CELL_STEP_MASK) != _CELL_STEP_DONE) {
// If not done, increase step.
c += 1 << 2;
}
if ((c & _CELL_STEP_MASK) == _CELL_STEP_DONE) {
// Go back.
switch (c & _CELL_PREV_MASK) {
case _CELL_PREV_FIRST: {
return;
} break;
case _CELL_PREV_Y_POS: {
y++;
ERR_FAIL_COND(y >= len_y);
} break;
case _CELL_PREV_Y_NEG: {
y--;
ERR_FAIL_COND(y < 0);
} break;
case _CELL_PREV_X_POS: {
x++;
ERR_FAIL_COND(x >= len_x);
} break;
case _CELL_PREV_X_NEG: {
x--;
ERR_FAIL_COND(x < 0);
} break;
case _CELL_PREV_Z_POS: {
z++;
ERR_FAIL_COND(z >= len_z);
} break;
case _CELL_PREV_Z_NEG: {
z--;
ERR_FAIL_COND(z < 0);
} break;
default: {
ERR_FAIL();
}
}
continue;
}
int next_x = x, next_y = y, next_z = z;
uint8_t prev = 0;
switch (c & _CELL_STEP_MASK) {
case _CELL_STEP_Y_POS: {
next_y++;
prev = _CELL_PREV_Y_NEG;
} break;
case _CELL_STEP_Y_NEG: {
next_y--;
prev = _CELL_PREV_Y_POS;
} break;
case _CELL_STEP_X_POS: {
next_x++;
prev = _CELL_PREV_X_NEG;
} break;
case _CELL_STEP_X_NEG: {
next_x--;
prev = _CELL_PREV_X_POS;
} break;
case _CELL_STEP_Z_POS: {
next_z++;
prev = _CELL_PREV_Z_NEG;
} break;
case _CELL_STEP_Z_NEG: {
next_z--;
prev = _CELL_PREV_Z_POS;
} break;
default:
ERR_FAIL();
}
if (next_x < 0 || next_x >= len_x) {
continue;
}
if (next_y < 0 || next_y >= len_y) {
continue;
}
if (next_z < 0 || next_z >= len_z) {
continue;
}
if (p_cell_status[next_x][next_y][next_z] & 3) {
continue;
}
x = next_x;
y = next_y;
z = next_z;
p_cell_status[x][y][z] |= prev;
}
}
static inline void _build_faces(uint8_t ***p_cell_status, int x, int y, int z, int len_x, int len_y, int len_z, Vector<Face3> &p_faces) {
ERR_FAIL_INDEX(x, len_x);
ERR_FAIL_INDEX(y, len_y);
ERR_FAIL_INDEX(z, len_z);
if (p_cell_status[x][y][z] & _CELL_EXTERIOR) {
return;
}
#define vert(m_idx) Vector3(((m_idx)&4) >> 2, ((m_idx)&2) >> 1, (m_idx)&1)
static const uint8_t indices[6][4] = {
{ 7, 6, 4, 5 },
{ 7, 3, 2, 6 },
{ 7, 5, 1, 3 },
{ 0, 2, 3, 1 },
{ 0, 1, 5, 4 },
{ 0, 4, 6, 2 },
};
for (int i = 0; i < 6; i++) {
Vector3 face_points[4];
int disp_x = x + ((i % 3) == 0 ? ((i < 3) ? 1 : -1) : 0);
int disp_y = y + (((i - 1) % 3) == 0 ? ((i < 3) ? 1 : -1) : 0);
int disp_z = z + (((i - 2) % 3) == 0 ? ((i < 3) ? 1 : -1) : 0);
bool plot = false;
if (disp_x < 0 || disp_x >= len_x) {
plot = true;
}
if (disp_y < 0 || disp_y >= len_y) {
plot = true;
}
if (disp_z < 0 || disp_z >= len_z) {
plot = true;
}
if (!plot && (p_cell_status[disp_x][disp_y][disp_z] & _CELL_EXTERIOR)) {
plot = true;
}
if (!plot) {
continue;
}
for (int j = 0; j < 4; j++) {
face_points[j] = vert(indices[i][j]) + Vector3(x, y, z);
}
p_faces.push_back(
Face3(
face_points[0],
face_points[1],
face_points[2]));
p_faces.push_back(
Face3(
face_points[2],
face_points[3],
face_points[0]));
}
}
Vector<Face3> Geometry3D::wrap_geometry(Vector<Face3> p_array, real_t *p_error) {
int face_count = p_array.size();
const Face3 *faces = p_array.ptr();
constexpr double min_size = 1.0;
constexpr int max_length = 20;
AABB global_aabb;
for (int i = 0; i < face_count; i++) {
if (i == 0) {
global_aabb = faces[i].get_aabb();
} else {
global_aabb.merge_with(faces[i].get_aabb());
}
}
global_aabb.grow_by(0.01f); // Avoid numerical error.
// Determine amount of cells in grid axis.
int div_x, div_y, div_z;
if (global_aabb.size.x / min_size < max_length) {
div_x = (int)(global_aabb.size.x / min_size) + 1;
} else {
div_x = max_length;
}
if (global_aabb.size.y / min_size < max_length) {
div_y = (int)(global_aabb.size.y / min_size) + 1;
} else {
div_y = max_length;
}
if (global_aabb.size.z / min_size < max_length) {
div_z = (int)(global_aabb.size.z / min_size) + 1;
} else {
div_z = max_length;
}
Vector3 voxelsize = global_aabb.size;
voxelsize.x /= div_x;
voxelsize.y /= div_y;
voxelsize.z /= div_z;
// Create and initialize cells to zero.
uint8_t ***cell_status = memnew_arr(uint8_t **, div_x);
for (int i = 0; i < div_x; i++) {
cell_status[i] = memnew_arr(uint8_t *, div_y);
for (int j = 0; j < div_y; j++) {
cell_status[i][j] = memnew_arr(uint8_t, div_z);
for (int k = 0; k < div_z; k++) {
cell_status[i][j][k] = 0;
}
}
}
// Plot faces into cells.
for (int i = 0; i < face_count; i++) {
Face3 f = faces[i];
for (int j = 0; j < 3; j++) {
f.vertex[j] -= global_aabb.position;
}
_plot_face(cell_status, 0, 0, 0, div_x, div_y, div_z, voxelsize, f);
}
// Determine which cells connect to the outside by traversing the outside and recursively flood-fill marking.
for (int i = 0; i < div_x; i++) {
for (int j = 0; j < div_y; j++) {
_mark_outside(cell_status, i, j, 0, div_x, div_y, div_z);
_mark_outside(cell_status, i, j, div_z - 1, div_x, div_y, div_z);
}
}
for (int i = 0; i < div_z; i++) {
for (int j = 0; j < div_y; j++) {
_mark_outside(cell_status, 0, j, i, div_x, div_y, div_z);
_mark_outside(cell_status, div_x - 1, j, i, div_x, div_y, div_z);
}
}
for (int i = 0; i < div_x; i++) {
for (int j = 0; j < div_z; j++) {
_mark_outside(cell_status, i, 0, j, div_x, div_y, div_z);
_mark_outside(cell_status, i, div_y - 1, j, div_x, div_y, div_z);
}
}
// Build faces for the inside-outside cell divisors.
Vector<Face3> wrapped_faces;
for (int i = 0; i < div_x; i++) {
for (int j = 0; j < div_y; j++) {
for (int k = 0; k < div_z; k++) {
_build_faces(cell_status, i, j, k, div_x, div_y, div_z, wrapped_faces);
}
}
}
// Transform face vertices to global coords.
int wrapped_faces_count = wrapped_faces.size();
Face3 *wrapped_faces_ptr = wrapped_faces.ptrw();
for (int i = 0; i < wrapped_faces_count; i++) {
for (int j = 0; j < 3; j++) {
Vector3 &v = wrapped_faces_ptr[i].vertex[j];
v = v * voxelsize;
v += global_aabb.position;
}
}
// clean up grid
for (int i = 0; i < div_x; i++) {
for (int j = 0; j < div_y; j++) {
memdelete_arr(cell_status[i][j]);
}
memdelete_arr(cell_status[i]);
}
memdelete_arr(cell_status);
if (p_error) {
*p_error = voxelsize.length();
}
return wrapped_faces;
}
Geometry3D::MeshData Geometry3D::build_convex_mesh(const Vector<Plane> &p_planes) {
MeshData mesh;
#define SUBPLANE_SIZE 1024.0
real_t subplane_size = 1024.0; // Should compute this from the actual plane.
for (int i = 0; i < p_planes.size(); i++) {
Plane p = p_planes[i];
Vector3 ref = Vector3(0.0, 1.0, 0.0);
if (ABS(p.normal.dot(ref)) > 0.95f) {
ref = Vector3(0.0, 0.0, 1.0); // Change axis.
}
Vector3 right = p.normal.cross(ref).normalized();
Vector3 up = p.normal.cross(right).normalized();
Vector3 center = p.get_center();
// make a quad clockwise
LocalVector<Vector3> vertices = {
center - up * subplane_size + right * subplane_size,
center - up * subplane_size - right * subplane_size,
center + up * subplane_size - right * subplane_size,
center + up * subplane_size + right * subplane_size
};
for (int j = 0; j < p_planes.size(); j++) {
if (j == i) {
continue;
}
LocalVector<Vector3> new_vertices;
Plane clip = p_planes[j];
if (clip.normal.dot(p.normal) > 0.95f) {
continue;
}
if (vertices.size() < 3) {
break;
}
for (uint32_t k = 0; k < vertices.size(); k++) {
int k_n = (k + 1) % vertices.size();
Vector3 edge0_A = vertices[k];
Vector3 edge1_A = vertices[k_n];
real_t dist0 = clip.distance_to(edge0_A);
real_t dist1 = clip.distance_to(edge1_A);
if (dist0 <= 0) { // Behind plane.
new_vertices.push_back(vertices[k]);
}
// Check for different sides and non coplanar.
if ((dist0 * dist1) < 0) {
// Calculate intersection.
Vector3 rel = edge1_A - edge0_A;
real_t den = clip.normal.dot(rel);
if (Math::is_zero_approx(den)) {
continue; // Point too short.
}
real_t dist = -(clip.normal.dot(edge0_A) - clip.d) / den;
Vector3 inters = edge0_A + rel * dist;
new_vertices.push_back(inters);
}
}
vertices = new_vertices;
}
if (vertices.size() < 3) {
continue;
}
// Result is a clockwise face.
MeshData::Face face;
// Add face indices.
for (const Vector3 &vertex : vertices) {
int idx = -1;
for (uint32_t k = 0; k < mesh.vertices.size(); k++) {
if (mesh.vertices[k].distance_to(vertex) < 0.001f) {
idx = k;
break;
}
}
if (idx == -1) {
idx = mesh.vertices.size();
mesh.vertices.push_back(vertex);
}
face.indices.push_back(idx);
}
face.plane = p;
mesh.faces.push_back(face);
// Add edge.
for (uint32_t j = 0; j < face.indices.size(); j++) {
int a = face.indices[j];
int b = face.indices[(j + 1) % face.indices.size()];
bool found = false;
int found_idx = -1;
for (uint32_t k = 0; k < mesh.edges.size(); k++) {
if (mesh.edges[k].vertex_a == a && mesh.edges[k].vertex_b == b) {
found = true;
found_idx = k;
break;
}
if (mesh.edges[k].vertex_b == a && mesh.edges[k].vertex_a == b) {
found = true;
found_idx = k;
break;
}
}
if (found) {
mesh.edges[found_idx].face_b = j;
continue;
}
MeshData::Edge edge;
edge.vertex_a = a;
edge.vertex_b = b;
edge.face_a = j;
edge.face_b = -1;
mesh.edges.push_back(edge);
}
}
return mesh;
}
Vector<Plane> Geometry3D::build_box_planes(const Vector3 &p_extents) {
Vector<Plane> planes = {
Plane(Vector3(1, 0, 0), p_extents.x),
Plane(Vector3(-1, 0, 0), p_extents.x),
Plane(Vector3(0, 1, 0), p_extents.y),
Plane(Vector3(0, -1, 0), p_extents.y),
Plane(Vector3(0, 0, 1), p_extents.z),
Plane(Vector3(0, 0, -1), p_extents.z)
};
return planes;
}
Vector<Plane> Geometry3D::build_cylinder_planes(real_t p_radius, real_t p_height, int p_sides, Vector3::Axis p_axis) {
ERR_FAIL_INDEX_V(p_axis, 3, Vector<Plane>());
Vector<Plane> planes;
const double sides_step = Math_TAU / p_sides;
for (int i = 0; i < p_sides; i++) {
Vector3 normal;
normal[(p_axis + 1) % 3] = Math::cos(i * sides_step);
normal[(p_axis + 2) % 3] = Math::sin(i * sides_step);
planes.push_back(Plane(normal, p_radius));
}
Vector3 axis;
axis[p_axis] = 1.0;
planes.push_back(Plane(axis, p_height * 0.5f));
planes.push_back(Plane(-axis, p_height * 0.5f));
return planes;
}
Vector<Plane> Geometry3D::build_sphere_planes(real_t p_radius, int p_lats, int p_lons, Vector3::Axis p_axis) {
ERR_FAIL_INDEX_V(p_axis, 3, Vector<Plane>());
Vector<Plane> planes;
Vector3 axis;
axis[p_axis] = 1.0;
Vector3 axis_neg;
axis_neg[(p_axis + 1) % 3] = 1.0;
axis_neg[(p_axis + 2) % 3] = 1.0;
axis_neg[p_axis] = -1.0;
const double lon_step = Math_TAU / p_lons;
for (int i = 0; i < p_lons; i++) {
Vector3 normal;
normal[(p_axis + 1) % 3] = Math::cos(i * lon_step);
normal[(p_axis + 2) % 3] = Math::sin(i * lon_step);
planes.push_back(Plane(normal, p_radius));
for (int j = 1; j <= p_lats; j++) {
Vector3 plane_normal = normal.lerp(axis, j / (real_t)p_lats).normalized();
planes.push_back(Plane(plane_normal, p_radius));
planes.push_back(Plane(plane_normal * axis_neg, p_radius));
}
}
return planes;
}
Vector<Plane> Geometry3D::build_capsule_planes(real_t p_radius, real_t p_height, int p_sides, int p_lats, Vector3::Axis p_axis) {
ERR_FAIL_INDEX_V(p_axis, 3, Vector<Plane>());
Vector<Plane> planes;
Vector3 axis;
axis[p_axis] = 1.0;
Vector3 axis_neg;
axis_neg[(p_axis + 1) % 3] = 1.0;
axis_neg[(p_axis + 2) % 3] = 1.0;
axis_neg[p_axis] = -1.0;
const double sides_step = Math_TAU / p_sides;
for (int i = 0; i < p_sides; i++) {
Vector3 normal;
normal[(p_axis + 1) % 3] = Math::cos(i * sides_step);
normal[(p_axis + 2) % 3] = Math::sin(i * sides_step);
planes.push_back(Plane(normal, p_radius));
for (int j = 1; j <= p_lats; j++) {
Vector3 plane_normal = normal.lerp(axis, j / (real_t)p_lats).normalized();
Vector3 position = axis * p_height * 0.5f + plane_normal * p_radius;
planes.push_back(Plane(plane_normal, position));
planes.push_back(Plane(plane_normal * axis_neg, position * axis_neg));
}
}
return planes;
}
Vector<Vector3> Geometry3D::compute_convex_mesh_points(const Plane *p_planes, int p_plane_count) {
Vector<Vector3> points;
// Iterate through every unique combination of any three planes.
for (int i = p_plane_count - 1; i >= 0; i--) {
for (int j = i - 1; j >= 0; j--) {
for (int k = j - 1; k >= 0; k--) {
// Find the point where these planes all cross over (if they
// do at all).
Vector3 convex_shape_point;
if (p_planes[i].intersect_3(p_planes[j], p_planes[k], &convex_shape_point)) {
// See if any *other* plane excludes this point because it's
// on the wrong side.
bool excluded = false;
for (int n = 0; n < p_plane_count; n++) {
if (n != i && n != j && n != k) {
real_t dp = p_planes[n].normal.dot(convex_shape_point);
if (dp - p_planes[n].d > (real_t)CMP_EPSILON) {
excluded = true;
break;
}
}
}
// Only add the point if it passed all tests.
if (!excluded) {
points.push_back(convex_shape_point);
}
}
}
}
}
return points;
}
#define square(m_s) ((m_s) * (m_s))
#define INF 1e20
/* dt of 1d function using squared distance */
static void edt(float *f, int stride, int n) {
float *d = (float *)alloca(sizeof(float) * n + sizeof(int) * n + sizeof(float) * (n + 1));
int *v = reinterpret_cast<int *>(&(d[n]));
float *z = reinterpret_cast<float *>(&v[n]);
int k = 0;
v[0] = 0;
z[0] = -INF;
z[1] = +INF;
for (int q = 1; q <= n - 1; q++) {
float s = ((f[q * stride] + square(q)) - (f[v[k] * stride] + square(v[k]))) / (2 * q - 2 * v[k]);
while (s <= z[k]) {
k--;
s = ((f[q * stride] + square(q)) - (f[v[k] * stride] + square(v[k]))) / (2 * q - 2 * v[k]);
}
k++;
v[k] = q;
z[k] = s;
z[k + 1] = +INF;
}
k = 0;
for (int q = 0; q <= n - 1; q++) {
while (z[k + 1] < q) {
k++;
}
d[q] = square(q - v[k]) + f[v[k] * stride];
}
for (int i = 0; i < n; i++) {
f[i * stride] = d[i];
}
}
#undef square
Vector<uint32_t> Geometry3D::generate_edf(const Vector<bool> &p_voxels, const Vector3i &p_size, bool p_negative) {
uint32_t float_count = p_size.x * p_size.y * p_size.z;
ERR_FAIL_COND_V((uint32_t)p_voxels.size() != float_count, Vector<uint32_t>());
float *work_memory = memnew_arr(float, float_count);
for (uint32_t i = 0; i < float_count; i++) {
work_memory[i] = INF;
}
uint32_t y_mult = p_size.x;
uint32_t z_mult = y_mult * p_size.y;
//plot solid cells
{
const bool *voxr = p_voxels.ptr();
for (uint32_t i = 0; i < float_count; i++) {
bool plot = voxr[i];
if (p_negative) {
plot = !plot;
}
if (plot) {
work_memory[i] = 0;
}
}
}
//process in each direction
//xy->z
for (int i = 0; i < p_size.x; i++) {
for (int j = 0; j < p_size.y; j++) {
edt(&work_memory[i + j * y_mult], z_mult, p_size.z);
}
}
//xz->y
for (int i = 0; i < p_size.x; i++) {
for (int j = 0; j < p_size.z; j++) {
edt(&work_memory[i + j * z_mult], y_mult, p_size.y);
}
}
//yz->x
for (int i = 0; i < p_size.y; i++) {
for (int j = 0; j < p_size.z; j++) {
edt(&work_memory[i * y_mult + j * z_mult], 1, p_size.x);
}
}
Vector<uint32_t> ret;
ret.resize(float_count);
{
uint32_t *w = ret.ptrw();
for (uint32_t i = 0; i < float_count; i++) {
w[i] = uint32_t(Math::sqrt(work_memory[i]));
}
}
memdelete_arr(work_memory);
return ret;
}
Vector<int8_t> Geometry3D::generate_sdf8(const Vector<uint32_t> &p_positive, const Vector<uint32_t> &p_negative) {
ERR_FAIL_COND_V(p_positive.size() != p_negative.size(), Vector<int8_t>());
Vector<int8_t> sdf8;
int s = p_positive.size();
sdf8.resize(s);
const uint32_t *rpos = p_positive.ptr();
const uint32_t *rneg = p_negative.ptr();
int8_t *wsdf = sdf8.ptrw();
for (int i = 0; i < s; i++) {
int32_t diff = int32_t(rpos[i]) - int32_t(rneg[i]);
wsdf[i] = CLAMP(diff, -128, 127);
}
return sdf8;
}
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