/*************************************************************************/ /* geometry_3d.cpp */ /*************************************************************************/ /* This file is part of: */ /* GODOT ENGINE */ /* https://godotengine.org */ /*************************************************************************/ /* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur. */ /* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md). */ /* */ /* 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 "core/string/print_string.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 (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 = -1; int edge = -1; void clear() { face = -1; edge = -1; } _Link() {} }; bool valid = false; int group = -1; _Link links[3]; Face3 face; _FaceClassify() {} }; 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; } Vector<Vector<Face3>> Geometry3D::separate_objects(Vector<Face3> p_array) { Vector<Vector<Face3>> objects; int len = p_array.size(); const Face3 *arrayptr = p_array.ptr(); Vector<_FaceClassify> fc; fc.resize(len); _FaceClassify *_fcptr = fc.ptrw(); 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, Vector<Vector<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); Vector<Face3> *group_faces = objects.ptrw(); 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_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.center(); // make a quad clockwise Vector<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; } 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; } 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; }