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godot/core/math/geometry.cpp

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/**************************************************************************/
/* geometry.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.h"
#include "core/local_vector.h"
#include "core/print_string.h"
#include "thirdparty/misc/clipper.hpp"
#include "thirdparty/misc/triangulator.h"
#define STB_RECT_PACK_IMPLEMENTATION
#include "thirdparty/stb_rect_pack/stb_rect_pack.h"
#define SCALE_FACTOR 100000.0 // Based on CMP_EPSILON.
// This implementation is very inefficient, commenting unless bugs happen. See the other one.
/*
bool Geometry::is_point_in_polygon(const Vector2 &p_point, const Vector<Vector2> &p_polygon) {
Vector<int> indices = Geometry::triangulate_polygon(p_polygon);
for (int j = 0; j + 3 <= indices.size(); j += 3) {
int i1 = indices[j], i2 = indices[j + 1], i3 = indices[j + 2];
if (Geometry::is_point_in_triangle(p_point, p_polygon[i1], p_polygon[i2], p_polygon[i3]))
return true;
}
return false;
}
*/
void Geometry::OccluderMeshData::clear() {
faces.clear();
vertices.clear();
}
void Geometry::MeshData::clear() {
faces.clear();
edges.clear();
vertices.clear();
}
void Geometry::MeshData::optimize_vertices() {
Map<int, int> vtx_remap;
for (int i = 0; i < faces.size(); i++) {
for (int j = 0; j < faces[i].indices.size(); j++) {
int idx = faces[i].indices[j];
if (!vtx_remap.has(idx)) {
int ni = vtx_remap.size();
vtx_remap[idx] = ni;
}
faces.write[i].indices.write[j] = vtx_remap[idx];
}
}
for (int i = 0; i < edges.size(); i++) {
int a = edges[i].a;
int b = edges[i].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;
}
edges.write[i].a = vtx_remap[a];
edges.write[i].b = vtx_remap[b];
}
Vector<Vector3> new_vertices;
new_vertices.resize(vtx_remap.size());
for (int i = 0; i < vertices.size(); i++) {
if (vtx_remap.has(i)) {
new_vertices.write[vtx_remap[i]] = vertices[i];
}
}
vertices = new_vertices;
}
struct _FaceClassify {
struct _Link {
int face;
int edge;
void clear() {
face = -1;
edge = -1;
}
_Link() {
face = -1;
edge = -1;
}
};
bool valid;
int group;
_Link links[3];
Face3 face;
_FaceClassify() {
group = -1;
valid = false;
};
};
static bool _connect_faces(_FaceClassify *p_faces, int len, int p_group) {
// Connect faces, error will occur if an edge is shared between more than 2 faces.
// Clear connections.
bool error = false;
for (int i = 0; i < len; i++) {
for (int j = 0; j < 3; j++) {
p_faces[i].links[j].clear();
}
}
for (int i = 0; i < len; i++) {
if (p_faces[i].group != p_group) {
continue;
}
for (int j = i + 1; j < len; j++) {
if (p_faces[j].group != p_group) {
continue;
}
for (int k = 0; k < 3; k++) {
Vector3 vi1 = p_faces[i].face.vertex[k];
Vector3 vi2 = p_faces[i].face.vertex[(k + 1) % 3];
for (int l = 0; l < 3; l++) {
Vector3 vj2 = p_faces[j].face.vertex[l];
Vector3 vj1 = p_faces[j].face.vertex[(l + 1) % 3];
if (vi1.distance_to(vj1) < 0.00001f &&
vi2.distance_to(vj2) < 0.00001f) {
if (p_faces[i].links[k].face != -1) {
ERR_PRINT("already linked\n");
error = true;
break;
}
if (p_faces[j].links[l].face != -1) {
ERR_PRINT("already linked\n");
error = true;
break;
}
p_faces[i].links[k].face = j;
p_faces[i].links[k].edge = l;
p_faces[j].links[l].face = i;
p_faces[j].links[l].edge = k;
}
}
if (error) {
break;
}
}
if (error) {
break;
}
}
if (error) {
break;
}
}
for (int i = 0; i < len; i++) {
p_faces[i].valid = true;
for (int j = 0; j < 3; j++) {
if (p_faces[i].links[j].face == -1) {
p_faces[i].valid = false;
}
}
}
return error;
}
static bool _group_face(_FaceClassify *p_faces, int len, int p_index, int p_group) {
if (p_faces[p_index].group >= 0) {
return false;
}
p_faces[p_index].group = p_group;
for (int i = 0; i < 3; i++) {
ERR_FAIL_INDEX_V(p_faces[p_index].links[i].face, len, true);
_group_face(p_faces, len, p_faces[p_index].links[i].face, p_group);
}
return true;
}
PoolVector<PoolVector<Face3>> Geometry::separate_objects(PoolVector<Face3> p_array) {
PoolVector<PoolVector<Face3>> objects;
int len = p_array.size();
PoolVector<Face3>::Read r = p_array.read();
const Face3 *arrayptr = r.ptr();
PoolVector<_FaceClassify> fc;
fc.resize(len);
PoolVector<_FaceClassify>::Write fcw = fc.write();
_FaceClassify *_fcptr = fcw.ptr();
for (int i = 0; i < len; i++) {
_fcptr[i].face = arrayptr[i];
}
bool error = _connect_faces(_fcptr, len, -1);
ERR_FAIL_COND_V_MSG(error, PoolVector<PoolVector<Face3>>(), "Invalid geometry.");
// Group connected faces in separate objects.
int group = 0;
for (int i = 0; i < len; i++) {
if (!_fcptr[i].valid) {
continue;
}
if (_group_face(_fcptr, len, i, group)) {
group++;
}
}
// Group connected faces in separate objects.
for (int i = 0; i < len; i++) {
_fcptr[i].face = arrayptr[i];
}
if (group >= 0) {
objects.resize(group);
PoolVector<PoolVector<Face3>>::Write obw = objects.write();
PoolVector<Face3> *group_faces = obw.ptr();
for (int i = 0; i < len; i++) {
if (!_fcptr[i].valid) {
continue;
}
if (_fcptr[i].group >= 0 && _fcptr[i].group < group) {
group_faces[_fcptr[i].group].push_back(_fcptr[i].face);
}
}
}
return objects;
}
/*** 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(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(i, div_x, x, len_x, new_x, new_len_x);
for (int j = 0; j < div_y; j++) {
_SPLIT(j, div_y, y, len_y, new_y, new_len_y);
for (int k = 0; k < div_z; k++) {
_SPLIT(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);
}
}
}
}
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, PoolVector<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]));
}
}
PoolVector<Face3> Geometry::wrap_geometry(PoolVector<Face3> p_array, real_t *p_error) {
#define _MIN_SIZE 1.0f
#define _MAX_LENGTH 20
int face_count = p_array.size();
PoolVector<Face3>::Read facesr = p_array.read();
const Face3 *faces = facesr.ptr();
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.
PoolVector<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();
PoolVector<Face3>::Write wrapped_facesw = wrapped_faces.write();
Face3 *wrapped_faces_ptr = wrapped_facesw.ptr();
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;
}
Vector<Vector<Vector2>> Geometry::decompose_polygon_in_convex(Vector<Point2> polygon) {
Vector<Vector<Vector2>> decomp;
List<TriangulatorPoly> in_poly, out_poly;
TriangulatorPoly inp;
inp.Init(polygon.size());
for (int i = 0; i < polygon.size(); i++) {
inp.GetPoint(i) = polygon[i];
}
inp.SetOrientation(TRIANGULATOR_CCW);
in_poly.push_back(inp);
TriangulatorPartition tpart;
if (tpart.ConvexPartition_HM(&in_poly, &out_poly) == 0) { // Failed.
ERR_PRINT("Convex decomposing failed!");
return decomp;
}
decomp.resize(out_poly.size());
int idx = 0;
for (List<TriangulatorPoly>::Element *I = out_poly.front(); I; I = I->next()) {
TriangulatorPoly &tp = I->get();
decomp.write[idx].resize(tp.GetNumPoints());
for (int64_t i = 0; i < tp.GetNumPoints(); i++) {
decomp.write[idx].write[i] = tp.GetPoint(i);
}
idx++;
}
return decomp;
}
Geometry::MeshData Geometry::build_convex_mesh(const PoolVector<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();
Vector<Vector3> vertices;
Vector3 center = p.get_any_point();
// make a quad clockwise
vertices.push_back(center - up * subplane_size + right * subplane_size);
vertices.push_back(center - up * subplane_size - right * subplane_size);
vertices.push_back(center + up * subplane_size - right * subplane_size);
vertices.push_back(center + up * subplane_size + right * subplane_size);
for (int j = 0; j < p_planes.size(); j++) {
if (j == i) {
continue;
}
Vector<Vector3> new_vertices;
Plane clip = p_planes[j];
if (clip.normal.dot(p.normal) > 0.95f) {
continue;
}
if (vertices.size() < 3) {
break;
}
for (int 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 (int j = 0; j < vertices.size(); j++) {
int idx = -1;
for (int k = 0; k < mesh.vertices.size(); k++) {
if (mesh.vertices[k].distance_to(vertices[j]) < 0.001f) {
idx = k;
break;
}
}
if (idx == -1) {
idx = mesh.vertices.size();
mesh.vertices.push_back(vertices[j]);
}
face.indices.push_back(idx);
}
face.plane = p;
mesh.faces.push_back(face);
// Add edge.
for (int j = 0; j < face.indices.size(); j++) {
int a = face.indices[j];
int b = face.indices[(j + 1) % face.indices.size()];
bool found = false;
for (int k = 0; k < mesh.edges.size(); k++) {
if (mesh.edges[k].a == a && mesh.edges[k].b == b) {
found = true;
break;
}
if (mesh.edges[k].b == a && mesh.edges[k].a == b) {
found = true;
break;
}
}
if (found) {
continue;
}
MeshData::Edge edge;
edge.a = a;
edge.b = b;
mesh.edges.push_back(edge);
}
}
return mesh;
}
PoolVector<Plane> Geometry::build_box_planes(const Vector3 &p_extents) {
PoolVector<Plane> planes;
planes.push_back(Plane(Vector3(1, 0, 0), p_extents.x));
planes.push_back(Plane(Vector3(-1, 0, 0), p_extents.x));
planes.push_back(Plane(Vector3(0, 1, 0), p_extents.y));
planes.push_back(Plane(Vector3(0, -1, 0), p_extents.y));
planes.push_back(Plane(Vector3(0, 0, 1), p_extents.z));
planes.push_back(Plane(Vector3(0, 0, -1), p_extents.z));
return planes;
}
PoolVector<Plane> Geometry::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, PoolVector<Plane>());
PoolVector<Plane> planes;
for (int i = 0; i < p_sides; i++) {
Vector3 normal;
normal[(p_axis + 1) % 3] = Math::cos(i * (real_t)(2.0 * Math_PI) / p_sides);
normal[(p_axis + 2) % 3] = Math::sin(i * (real_t)(2.0 * Math_PI) / p_sides);
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;
}
PoolVector<Plane> Geometry::build_sphere_planes(real_t p_radius, int p_lats, int p_lons, Vector3::Axis p_axis) {
ERR_FAIL_INDEX_V(p_axis, 3, PoolVector<Plane>());
PoolVector<Plane> planes;
Vector3 axis;
axis[p_axis] = 1;
Vector3 axis_neg;
axis_neg[(p_axis + 1) % 3] = 1;
axis_neg[(p_axis + 2) % 3] = 1;
axis_neg[p_axis] = -1;
for (int i = 0; i < p_lons; i++) {
Vector3 normal;
normal[(p_axis + 1) % 3] = Math::cos(i * (real_t)(2.0 * Math_PI) / p_lons);
normal[(p_axis + 2) % 3] = Math::sin(i * (real_t)(2.0 * Math_PI) / p_lons);
planes.push_back(Plane(normal, p_radius));
for (int j = 1; j <= p_lats; j++) {
// FIXME: This is stupid.
Vector3 angle = normal.linear_interpolate(axis, j / (real_t)p_lats).normalized();
Vector3 pos = angle * p_radius;
planes.push_back(Plane(pos, angle));
planes.push_back(Plane(pos * axis_neg, angle * axis_neg));
}
}
return planes;
}
PoolVector<Plane> Geometry::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, PoolVector<Plane>());
PoolVector<Plane> planes;
Vector3 axis;
axis[p_axis] = 1;
Vector3 axis_neg;
axis_neg[(p_axis + 1) % 3] = 1;
axis_neg[(p_axis + 2) % 3] = 1;
axis_neg[p_axis] = -1;
for (int i = 0; i < p_sides; i++) {
Vector3 normal;
normal[(p_axis + 1) % 3] = Math::cos(i * (real_t)(2.0 * Math_PI) / p_sides);
normal[(p_axis + 2) % 3] = Math::sin(i * (real_t)(2.0 * Math_PI) / p_sides);
planes.push_back(Plane(normal, p_radius));
for (int j = 1; j <= p_lats; j++) {
Vector3 angle = normal.linear_interpolate(axis, j / (real_t)p_lats).normalized();
Vector3 pos = axis * p_height * 0.5f + angle * p_radius;
planes.push_back(Plane(pos, angle));
planes.push_back(Plane(pos * axis_neg, angle * axis_neg));
}
}
return planes;
}
struct _AtlasWorkRect {
Size2i s;
Point2i p;
int idx;
_FORCE_INLINE_ bool operator<(const _AtlasWorkRect &p_r) const { return s.width > p_r.s.width; }
};
struct _AtlasWorkRectResult {
Vector<_AtlasWorkRect> result;
int max_w;
int max_h;
};
void Geometry::make_atlas(const Vector<Size2i> &p_rects, Vector<Point2i> &r_result, Size2i &r_size) {
// Super simple, almost brute force scanline stacking fitter.
// It's pretty basic for now, but it tries to make sure that the aspect ratio of the
// resulting atlas is somehow square. This is necessary because video cards have limits.
// On texture size (usually 2048 or 4096), so the more square a texture, the more chances.
// It will work in every hardware.
// For example, it will prioritize a 1024x1024 atlas (works everywhere) instead of a
// 256x8192 atlas (won't work anywhere).
ERR_FAIL_COND(p_rects.size() == 0);
for (int i = 0; i < p_rects.size(); i++) {
ERR_FAIL_COND(p_rects[i].width <= 0);
ERR_FAIL_COND(p_rects[i].height <= 0);
}
Vector<_AtlasWorkRect> wrects;
wrects.resize(p_rects.size());
for (int i = 0; i < p_rects.size(); i++) {
wrects.write[i].s = p_rects[i];
wrects.write[i].idx = i;
}
wrects.sort();
int widest = wrects[0].s.width;
Vector<_AtlasWorkRectResult> results;
for (int i = 0; i <= 12; i++) {
int w = 1 << i;
int max_h = 0;
int max_w = 0;
if (w < widest) {
continue;
}
Vector<int> hmax;
hmax.resize(w);
for (int j = 0; j < w; j++) {
hmax.write[j] = 0;
}
// Place them.
int ofs = 0;
int limit_h = 0;
for (int j = 0; j < wrects.size(); j++) {
if (ofs + wrects[j].s.width > w) {
ofs = 0;
}
int from_y = 0;
for (int k = 0; k < wrects[j].s.width; k++) {
if (hmax[ofs + k] > from_y) {
from_y = hmax[ofs + k];
}
}
wrects.write[j].p.x = ofs;
wrects.write[j].p.y = from_y;
int end_h = from_y + wrects[j].s.height;
int end_w = ofs + wrects[j].s.width;
if (ofs == 0) {
limit_h = end_h;
}
for (int k = 0; k < wrects[j].s.width; k++) {
hmax.write[ofs + k] = end_h;
}
if (end_h > max_h) {
max_h = end_h;
}
if (end_w > max_w) {
max_w = end_w;
}
if (ofs == 0 || end_h > limit_h) { // While h limit not reached, keep stacking.
ofs += wrects[j].s.width;
}
}
_AtlasWorkRectResult result;
result.result = wrects;
result.max_h = max_h;
result.max_w = max_w;
results.push_back(result);
}
// Find the result with the best aspect ratio.
int best = -1;
real_t best_aspect = 1e20;
for (int i = 0; i < results.size(); i++) {
real_t h = next_power_of_2(results[i].max_h);
real_t w = next_power_of_2(results[i].max_w);
real_t aspect = h > w ? h / w : w / h;
if (aspect < best_aspect) {
best = i;
best_aspect = aspect;
}
}
r_result.resize(p_rects.size());
for (int i = 0; i < p_rects.size(); i++) {
r_result.write[results[best].result[i].idx] = results[best].result[i].p;
}
r_size = Size2(results[best].max_w, results[best].max_h);
}
Vector<Vector<Point2>> Geometry::_polypaths_do_operation(PolyBooleanOperation p_op, const Vector<Point2> &p_polypath_a, const Vector<Point2> &p_polypath_b, bool is_a_open) {
using namespace ClipperLib;
ClipType op = ctUnion;
switch (p_op) {
case OPERATION_UNION:
op = ctUnion;
break;
case OPERATION_DIFFERENCE:
op = ctDifference;
break;
case OPERATION_INTERSECTION:
op = ctIntersection;
break;
case OPERATION_XOR:
op = ctXor;
break;
}
Path path_a, path_b;
// Need to scale points (Clipper's requirement for robust computation).
for (int i = 0; i != p_polypath_a.size(); ++i) {
path_a << IntPoint(p_polypath_a[i].x * (real_t)SCALE_FACTOR, p_polypath_a[i].y * (real_t)SCALE_FACTOR);
}
for (int i = 0; i != p_polypath_b.size(); ++i) {
path_b << IntPoint(p_polypath_b[i].x * (real_t)SCALE_FACTOR, p_polypath_b[i].y * (real_t)SCALE_FACTOR);
}
Clipper clp;
clp.AddPath(path_a, ptSubject, !is_a_open); // Forward compatible with Clipper 10.0.0.
clp.AddPath(path_b, ptClip, true); // Polylines cannot be set as clip.
Paths paths;
if (is_a_open) {
PolyTree tree; // Needed to populate polylines.
clp.Execute(op, tree);
OpenPathsFromPolyTree(tree, paths);
} else {
clp.Execute(op, paths); // Works on closed polygons only.
}
// Have to scale points down now.
Vector<Vector<Point2>> polypaths;
for (Paths::size_type i = 0; i < paths.size(); ++i) {
Vector<Vector2> polypath;
const Path &scaled_path = paths[i];
for (Paths::size_type j = 0; j < scaled_path.size(); ++j) {
polypath.push_back(Point2(
static_cast<real_t>(scaled_path[j].X) / (real_t)SCALE_FACTOR,
static_cast<real_t>(scaled_path[j].Y) / (real_t)SCALE_FACTOR));
}
polypaths.push_back(polypath);
}
return polypaths;
}
Vector<Vector<Point2>> Geometry::_polypath_offset(const Vector<Point2> &p_polypath, real_t p_delta, PolyJoinType p_join_type, PolyEndType p_end_type) {
using namespace ClipperLib;
JoinType jt = jtSquare;
switch (p_join_type) {
case JOIN_SQUARE:
jt = jtSquare;
break;
case JOIN_ROUND:
jt = jtRound;
break;
case JOIN_MITER:
jt = jtMiter;
break;
}
EndType et = etClosedPolygon;
switch (p_end_type) {
case END_POLYGON:
et = etClosedPolygon;
break;
case END_JOINED:
et = etClosedLine;
break;
case END_BUTT:
et = etOpenButt;
break;
case END_SQUARE:
et = etOpenSquare;
break;
case END_ROUND:
et = etOpenRound;
break;
}
ClipperOffset co(2.0f, 0.25f * (real_t)SCALE_FACTOR); // Defaults from ClipperOffset.
Path path;
// Need to scale points (Clipper's requirement for robust computation).
for (int i = 0; i != p_polypath.size(); ++i) {
path << IntPoint(p_polypath[i].x * (real_t)SCALE_FACTOR, p_polypath[i].y * (real_t)SCALE_FACTOR);
}
co.AddPath(path, jt, et);
Paths paths;
co.Execute(paths, p_delta * (real_t)SCALE_FACTOR); // Inflate/deflate.
// Have to scale points down now.
Vector<Vector<Point2>> polypaths;
for (Paths::size_type i = 0; i < paths.size(); ++i) {
Vector<Vector2> polypath;
const Path &scaled_path = paths[i];
for (Paths::size_type j = 0; j < scaled_path.size(); ++j) {
polypath.push_back(Point2(
static_cast<real_t>(scaled_path[j].X) / (real_t)SCALE_FACTOR,
static_cast<real_t>(scaled_path[j].Y) / (real_t)SCALE_FACTOR));
}
polypaths.push_back(polypath);
}
return polypaths;
}
real_t Geometry::calculate_convex_hull_volume(const Geometry::MeshData &p_md) {
if (!p_md.vertices.size()) {
return 0;
}
// find center
Vector3 center;
for (int n = 0; n < p_md.vertices.size(); n++) {
center += p_md.vertices[n];
}
center /= p_md.vertices.size();
Face3 fa;
real_t volume = 0.0;
// volume of each cone is 1/3 * height * area of face
for (int f = 0; f < p_md.faces.size(); f++) {
const Geometry::MeshData::Face &face = p_md.faces[f];
real_t height = 0.0;
real_t face_area = 0.0;
for (int c = 0; c < face.indices.size() - 2; c++) {
fa.vertex[0] = p_md.vertices[face.indices[0]];
fa.vertex[1] = p_md.vertices[face.indices[c + 1]];
fa.vertex[2] = p_md.vertices[face.indices[c + 2]];
if (!c) {
// calculate height
Plane plane(fa.vertex[0], fa.vertex[1], fa.vertex[2]);
height = -plane.distance_to(center);
}
face_area += Math::sqrt(fa.get_twice_area_squared());
}
volume += face_area * height;
}
volume *= (real_t)((1.0 / 3.0) * 0.5);
return volume;
}
// note this function is slow, because it builds meshes etc. Not ideal to use in realtime.
// Planes must face OUTWARD from the center of the convex hull, by convention.
bool Geometry::convex_hull_intersects_convex_hull(const Plane *p_planes_a, int p_plane_count_a, const Plane *p_planes_b, int p_plane_count_b) {
if (!p_plane_count_a || !p_plane_count_b) {
return false;
}
// OR alternative approach, we can call compute_convex_mesh_points()
// with both sets of planes, to get an intersection. Not sure which method is
// faster... this may be faster with more complex hulls.
// the usual silliness to get from one vector format to another...
PoolVector<Plane> planes_a;
PoolVector<Plane> planes_b;
{
planes_a.resize(p_plane_count_a);
PoolVector<Plane>::Write w = planes_a.write();
memcpy(w.ptr(), p_planes_a, p_plane_count_a * sizeof(Plane));
}
{
planes_b.resize(p_plane_count_b);
PoolVector<Plane>::Write w = planes_b.write();
memcpy(w.ptr(), p_planes_b, p_plane_count_b * sizeof(Plane));
}
Geometry::MeshData md_A = build_convex_mesh(planes_a);
Geometry::MeshData md_B = build_convex_mesh(planes_b);
// hull can't be built
if (!md_A.vertices.size() || !md_B.vertices.size()) {
return false;
}
// first check the points against the planes
for (int p = 0; p < p_plane_count_a; p++) {
const Plane &plane = p_planes_a[p];
for (int n = 0; n < md_B.vertices.size(); n++) {
if (!plane.is_point_over(md_B.vertices[n])) {
return true;
}
}
}
for (int p = 0; p < p_plane_count_b; p++) {
const Plane &plane = p_planes_b[p];
for (int n = 0; n < md_A.vertices.size(); n++) {
if (!plane.is_point_over(md_A.vertices[n])) {
return true;
}
}
}
// now check edges
for (int n = 0; n < md_A.edges.size(); n++) {
const Vector3 &pt_a = md_A.vertices[md_A.edges[n].a];
const Vector3 &pt_b = md_A.vertices[md_A.edges[n].b];
if (segment_intersects_convex(pt_a, pt_b, p_planes_b, p_plane_count_b, nullptr, nullptr)) {
return true;
}
}
for (int n = 0; n < md_B.edges.size(); n++) {
const Vector3 &pt_a = md_B.vertices[md_B.edges[n].a];
const Vector3 &pt_b = md_B.vertices[md_B.edges[n].b];
if (segment_intersects_convex(pt_a, pt_b, p_planes_a, p_plane_count_a, nullptr, nullptr)) {
return true;
}
}
return false;
}
Vector<Vector3> Geometry::compute_convex_mesh_points(const Plane *p_planes, int p_plane_count, real_t p_epsilon) {
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 dist = p_planes[n].distance_to(convex_shape_point);
if (dist > p_epsilon) {
excluded = true;
break;
}
}
}
// Only add the point if it passed all tests.
if (!excluded) {
points.push_back(convex_shape_point);
}
}
}
}
}
return points;
}
Vector<Geometry::PackRectsResult> Geometry::partial_pack_rects(const Vector<Vector2i> &p_sizes, const Size2i &p_atlas_size) {
Vector<stbrp_node> nodes;
nodes.resize(p_atlas_size.width);
memset(nodes.ptrw(), 0, sizeof(stbrp_node) * nodes.size());
stbrp_context context;
stbrp_init_target(&context, p_atlas_size.width, p_atlas_size.height, nodes.ptrw(), p_atlas_size.width);
Vector<stbrp_rect> rects;
rects.resize(p_sizes.size());
for (int i = 0; i < p_sizes.size(); i++) {
rects.write[i].id = i;
rects.write[i].w = p_sizes[i].width;
rects.write[i].h = p_sizes[i].height;
rects.write[i].x = 0;
rects.write[i].y = 0;
rects.write[i].was_packed = 0;
}
stbrp_pack_rects(&context, rects.ptrw(), rects.size());
Vector<PackRectsResult> ret;
ret.resize(p_sizes.size());
for (int i = 0; i < p_sizes.size(); i++) {
ret.write[rects[i].id] = { rects[i].x, rects[i].y, static_cast<bool>(rects[i].was_packed) };
}
return ret;
}
// Expects polygon as a triangle fan
real_t Geometry::find_polygon_area(const Vector3 *p_verts, int p_num_verts) {
if (!p_verts || (p_num_verts < 3)) {
return 0.0;
}
Face3 f;
f.vertex[0] = p_verts[0];
f.vertex[1] = p_verts[1];
f.vertex[2] = p_verts[1];
real_t area = 0.0;
for (int n = 2; n < p_num_verts; n++) {
f.vertex[1] = f.vertex[2];
f.vertex[2] = p_verts[n];
area += Math::sqrt(f.get_twice_area_squared());
}
return area * 0.5f;
}
// adapted from:
// https://stackoverflow.com/questions/6989100/sort-points-in-clockwise-order
void Geometry::sort_polygon_winding(Vector<Vector2> &r_verts, bool p_clockwise) {
// sort winding order of a (primarily convex) polygon.
// It can handle some concave polygons, but not
// where a vertex 'goes back on' a previous vertex ..
// i.e. it will change the shape in some concave cases.
struct ElementComparator {
Vector2 center;
bool operator()(const Vector2 &a, const Vector2 &b) const {
if (a.x - center.x >= 0 && b.x - center.x < 0) {
return true;
}
if (a.x - center.x < 0 && b.x - center.x >= 0) {
return false;
}
if (a.x - center.x == 0 && b.x - center.x == 0) {
if (a.y - center.y >= 0 || b.y - center.y >= 0) {
return a.y > b.y;
}
return b.y > a.y;
}
// compute the cross product of vectors (center -> a) x (center -> b)
real_t det = (a.x - center.x) * (b.y - center.y) - (b.x - center.x) * (a.y - center.y);
if (det < 0) {
return true;
}
if (det > 0) {
return false;
}
// points a and b are on the same line from the center
// check which point is closer to the center
real_t d1 = (a.x - center.x) * (a.x - center.x) + (a.y - center.y) * (a.y - center.y);
real_t d2 = (b.x - center.x) * (b.x - center.x) + (b.y - center.y) * (b.y - center.y);
return d1 > d2;
}
};
int npoints = r_verts.size();
if (!npoints) {
return;
}
// first calculate center
Vector2 center;
for (int n = 0; n < npoints; n++) {
center += r_verts[n];
}
center /= npoints;
SortArray<Vector2, ElementComparator> sorter;
sorter.compare.center = center;
sorter.sort(r_verts.ptrw(), r_verts.size());
// if not clockwise, reverse order
if (!p_clockwise) {
r_verts.invert();
}
}
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