/*************************************************************************/ /* collision_solver_sat.cpp */ /*************************************************************************/ /* This file is part of: */ /* GODOT ENGINE */ /* https://godotengine.org */ /*************************************************************************/ /* Copyright (c) 2007-2018 Juan Linietsky, Ariel Manzur. */ /* Copyright (c) 2014-2018 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 "collision_solver_sat.h" #include "geometry.h" #define _EDGE_IS_VALID_SUPPORT_TRESHOLD 0.02 struct _CollectorCallback { CollisionSolverSW::CallbackResult callback; void *userdata; bool swap; bool collided; Vector3 normal; Vector3 *prev_axis; _FORCE_INLINE_ void call(const Vector3 &p_point_A, const Vector3 &p_point_B) { //if (normal.dot(p_point_A) >= normal.dot(p_point_B)) // return; // print_line("** A: "+p_point_A+" B: "+p_point_B+" D: "+rtos(p_point_A.distance_to(p_point_B))); if (swap) callback(p_point_B, p_point_A, userdata); else callback(p_point_A, p_point_B, userdata); } }; typedef void (*GenerateContactsFunc)(const Vector3 *, int, const Vector3 *, int, _CollectorCallback *); static void _generate_contacts_point_point(const Vector3 *p_points_A, int p_point_count_A, const Vector3 *p_points_B, int p_point_count_B, _CollectorCallback *p_callback) { #ifdef DEBUG_ENABLED ERR_FAIL_COND(p_point_count_A != 1); ERR_FAIL_COND(p_point_count_B != 1); #endif p_callback->call(*p_points_A, *p_points_B); } static void _generate_contacts_point_edge(const Vector3 *p_points_A, int p_point_count_A, const Vector3 *p_points_B, int p_point_count_B, _CollectorCallback *p_callback) { #ifdef DEBUG_ENABLED ERR_FAIL_COND(p_point_count_A != 1); ERR_FAIL_COND(p_point_count_B != 2); #endif Vector3 closest_B = Geometry::get_closest_point_to_segment_uncapped(*p_points_A, p_points_B); p_callback->call(*p_points_A, closest_B); } static void _generate_contacts_point_face(const Vector3 *p_points_A, int p_point_count_A, const Vector3 *p_points_B, int p_point_count_B, _CollectorCallback *p_callback) { #ifdef DEBUG_ENABLED ERR_FAIL_COND(p_point_count_A != 1); ERR_FAIL_COND(p_point_count_B < 3); #endif Vector3 closest_B = Plane(p_points_B[0], p_points_B[1], p_points_B[2]).project(*p_points_A); p_callback->call(*p_points_A, closest_B); } static void _generate_contacts_edge_edge(const Vector3 *p_points_A, int p_point_count_A, const Vector3 *p_points_B, int p_point_count_B, _CollectorCallback *p_callback) { #ifdef DEBUG_ENABLED ERR_FAIL_COND(p_point_count_A != 2); ERR_FAIL_COND(p_point_count_B != 2); // circle is actually a 4x3 matrix #endif Vector3 rel_A = p_points_A[1] - p_points_A[0]; Vector3 rel_B = p_points_B[1] - p_points_B[0]; Vector3 c = rel_A.cross(rel_B).cross(rel_B); // if ( Math::abs(rel_A.dot(c) )<_EDGE_IS_VALID_SUPPORT_TRESHOLD ) { if (Math::abs(rel_A.dot(c)) < CMP_EPSILON) { // should handle somehow.. //ERR_PRINT("TODO FIX"); //return; Vector3 axis = rel_A.normalized(); //make an axis Vector3 base_A = p_points_A[0] - axis * axis.dot(p_points_A[0]); Vector3 base_B = p_points_B[0] - axis * axis.dot(p_points_B[0]); //sort all 4 points in axis float dvec[4] = { axis.dot(p_points_A[0]), axis.dot(p_points_A[1]), axis.dot(p_points_B[0]), axis.dot(p_points_B[1]) }; SortArray sa; sa.sort(dvec, 4); //use the middle ones as contacts p_callback->call(base_A + axis * dvec[1], base_B + axis * dvec[1]); p_callback->call(base_A + axis * dvec[2], base_B + axis * dvec[2]); return; } real_t d = (c.dot(p_points_B[0]) - p_points_A[0].dot(c)) / rel_A.dot(c); if (d < 0.0) d = 0.0; else if (d > 1.0) d = 1.0; Vector3 closest_A = p_points_A[0] + rel_A * d; Vector3 closest_B = Geometry::get_closest_point_to_segment_uncapped(closest_A, p_points_B); p_callback->call(closest_A, closest_B); } static void _generate_contacts_face_face(const Vector3 *p_points_A, int p_point_count_A, const Vector3 *p_points_B, int p_point_count_B, _CollectorCallback *p_callback) { #ifdef DEBUG_ENABLED ERR_FAIL_COND(p_point_count_A < 2); ERR_FAIL_COND(p_point_count_B < 3); #endif static const int max_clip = 32; Vector3 _clipbuf1[max_clip]; Vector3 _clipbuf2[max_clip]; Vector3 *clipbuf_src = _clipbuf1; Vector3 *clipbuf_dst = _clipbuf2; int clipbuf_len = p_point_count_A; // copy A points to clipbuf_src for (int i = 0; i < p_point_count_A; i++) { clipbuf_src[i] = p_points_A[i]; } Plane plane_B(p_points_B[0], p_points_B[1], p_points_B[2]); // go through all of B points for (int i = 0; i < p_point_count_B; i++) { int i_n = (i + 1) % p_point_count_B; Vector3 edge0_B = p_points_B[i]; Vector3 edge1_B = p_points_B[i_n]; Vector3 clip_normal = (edge0_B - edge1_B).cross(plane_B.normal).normalized(); // make a clip plane Plane clip(edge0_B, clip_normal); // avoid double clip if A is edge int dst_idx = 0; bool edge = clipbuf_len == 2; for (int j = 0; j < clipbuf_len; j++) { int j_n = (j + 1) % clipbuf_len; Vector3 edge0_A = clipbuf_src[j]; Vector3 edge1_A = clipbuf_src[j_n]; real_t dist0 = clip.distance_to(edge0_A); real_t dist1 = clip.distance_to(edge1_A); if (dist0 <= 0) { // behind plane ERR_FAIL_COND(dst_idx >= max_clip); clipbuf_dst[dst_idx++] = clipbuf_src[j]; } // check for different sides and non coplanar // if ( (dist0*dist1) < -CMP_EPSILON && !(edge && j)) { if ((dist0 * dist1) < 0 && !(edge && j)) { // calculate intersection Vector3 rel = edge1_A - edge0_A; real_t den = clip.normal.dot(rel); real_t dist = -(clip.normal.dot(edge0_A) - clip.d) / den; Vector3 inters = edge0_A + rel * dist; ERR_FAIL_COND(dst_idx >= max_clip); clipbuf_dst[dst_idx] = inters; dst_idx++; } } clipbuf_len = dst_idx; SWAP(clipbuf_src, clipbuf_dst); } // generate contacts //Plane plane_A(p_points_A[0],p_points_A[1],p_points_A[2]); int added = 0; for (int i = 0; i < clipbuf_len; i++) { float d = plane_B.distance_to(clipbuf_src[i]); //if (d>CMP_EPSILON) // continue; Vector3 closest_B = clipbuf_src[i] - plane_B.normal * d; if (p_callback->normal.dot(clipbuf_src[i]) >= p_callback->normal.dot(closest_B)) continue; p_callback->call(clipbuf_src[i], closest_B); added++; } } static void _generate_contacts_from_supports(const Vector3 *p_points_A, int p_point_count_A, const Vector3 *p_points_B, int p_point_count_B, _CollectorCallback *p_callback) { #ifdef DEBUG_ENABLED ERR_FAIL_COND(p_point_count_A < 1); ERR_FAIL_COND(p_point_count_B < 1); #endif static const GenerateContactsFunc generate_contacts_func_table[3][3] = { { _generate_contacts_point_point, _generate_contacts_point_edge, _generate_contacts_point_face, }, { 0, _generate_contacts_edge_edge, _generate_contacts_face_face, }, { 0, 0, _generate_contacts_face_face, } }; int pointcount_B; int pointcount_A; const Vector3 *points_A; const Vector3 *points_B; if (p_point_count_A > p_point_count_B) { //swap p_callback->swap = !p_callback->swap; p_callback->normal = -p_callback->normal; pointcount_B = p_point_count_A; pointcount_A = p_point_count_B; points_A = p_points_B; points_B = p_points_A; } else { pointcount_B = p_point_count_B; pointcount_A = p_point_count_A; points_A = p_points_A; points_B = p_points_B; } int version_A = (pointcount_A > 3 ? 3 : pointcount_A) - 1; int version_B = (pointcount_B > 3 ? 3 : pointcount_B) - 1; GenerateContactsFunc contacts_func = generate_contacts_func_table[version_A][version_B]; ERR_FAIL_COND(!contacts_func); contacts_func(points_A, pointcount_A, points_B, pointcount_B, p_callback); } template class SeparatorAxisTest { const ShapeA *shape_A; const ShapeB *shape_B; const Transform *transform_A; const Transform *transform_B; real_t best_depth; Vector3 best_axis; _CollectorCallback *callback; real_t margin_A; real_t margin_B; Vector3 separator_axis; public: _FORCE_INLINE_ bool test_previous_axis() { if (callback && callback->prev_axis && *callback->prev_axis != Vector3()) return test_axis(*callback->prev_axis); else return true; } _FORCE_INLINE_ bool test_axis(const Vector3 &p_axis) { Vector3 axis = p_axis; if (Math::abs(axis.x) < CMP_EPSILON && Math::abs(axis.y) < CMP_EPSILON && Math::abs(axis.z) < CMP_EPSILON) { // strange case, try an upwards separator axis = Vector3(0.0, 1.0, 0.0); } real_t min_A, max_A, min_B, max_B; shape_A->project_range(axis, *transform_A, min_A, max_A); shape_B->project_range(axis, *transform_B, min_B, max_B); if (withMargin) { min_A -= margin_A; max_A += margin_A; min_B -= margin_B; max_B += margin_B; } min_B -= (max_A - min_A) * 0.5; max_B += (max_A - min_A) * 0.5; real_t dmin = min_B - (min_A + max_A) * 0.5; real_t dmax = max_B - (min_A + max_A) * 0.5; if (dmin > 0.0 || dmax < 0.0) { separator_axis = axis; return false; // doesn't contain 0 } //use the smallest depth dmin = Math::abs(dmin); if (dmax < dmin) { if (dmax < best_depth) { best_depth = dmax; best_axis = axis; } } else { if (dmin < best_depth) { best_depth = dmin; best_axis = -axis; // keep it as A axis } } return true; } _FORCE_INLINE_ void generate_contacts() { // nothing to do, don't generate if (best_axis == Vector3(0.0, 0.0, 0.0)) return; if (!callback->callback) { //just was checking intersection? callback->collided = true; if (callback->prev_axis) *callback->prev_axis = best_axis; return; } static const int max_supports = 16; Vector3 supports_A[max_supports]; int support_count_A; shape_A->get_supports(transform_A->basis.xform_inv(-best_axis).normalized(), max_supports, supports_A, support_count_A); for (int i = 0; i < support_count_A; i++) { supports_A[i] = transform_A->xform(supports_A[i]); } if (withMargin) { for (int i = 0; i < support_count_A; i++) { supports_A[i] += -best_axis * margin_A; } } Vector3 supports_B[max_supports]; int support_count_B; shape_B->get_supports(transform_B->basis.xform_inv(best_axis).normalized(), max_supports, supports_B, support_count_B); for (int i = 0; i < support_count_B; i++) { supports_B[i] = transform_B->xform(supports_B[i]); } if (withMargin) { for (int i = 0; i < support_count_B; i++) { supports_B[i] += best_axis * margin_B; } } /* print_line("best depth: "+rtos(best_depth)); print_line("best axis: "+(best_axis)); for(int i=0;inormal = best_axis; if (callback->prev_axis) *callback->prev_axis = best_axis; _generate_contacts_from_supports(supports_A, support_count_A, supports_B, support_count_B, callback); callback->collided = true; //CollisionSolverSW::CallbackResult cbk=NULL; //cbk(Vector3(),Vector3(),NULL); } _FORCE_INLINE_ SeparatorAxisTest(const ShapeA *p_shape_A, const Transform &p_transform_A, const ShapeB *p_shape_B, const Transform &p_transform_B, _CollectorCallback *p_callback, real_t p_margin_A = 0, real_t p_margin_B = 0) { best_depth = 1e15; shape_A = p_shape_A; shape_B = p_shape_B; transform_A = &p_transform_A; transform_B = &p_transform_B; callback = p_callback; margin_A = p_margin_A; margin_B = p_margin_B; } }; /****** SAT TESTS *******/ /****** SAT TESTS *******/ /****** SAT TESTS *******/ /****** SAT TESTS *******/ typedef void (*CollisionFunc)(const ShapeSW *, const Transform &, const ShapeSW *, const Transform &, _CollectorCallback *p_callback, float, float); template static void _collision_sphere_sphere(const ShapeSW *p_a, const Transform &p_transform_a, const ShapeSW *p_b, const Transform &p_transform_b, _CollectorCallback *p_collector, float p_margin_a, float p_margin_b) { const SphereShapeSW *sphere_A = static_cast(p_a); const SphereShapeSW *sphere_B = static_cast(p_b); SeparatorAxisTest separator(sphere_A, p_transform_a, sphere_B, p_transform_b, p_collector, p_margin_a, p_margin_b); // previous axis if (!separator.test_previous_axis()) return; if (!separator.test_axis((p_transform_a.origin - p_transform_b.origin).normalized())) return; separator.generate_contacts(); } template static void _collision_sphere_box(const ShapeSW *p_a, const Transform &p_transform_a, const ShapeSW *p_b, const Transform &p_transform_b, _CollectorCallback *p_collector, float p_margin_a, float p_margin_b) { const SphereShapeSW *sphere_A = static_cast(p_a); const BoxShapeSW *box_B = static_cast(p_b); SeparatorAxisTest separator(sphere_A, p_transform_a, box_B, p_transform_b, p_collector, p_margin_a, p_margin_b); if (!separator.test_previous_axis()) return; // test faces for (int i = 0; i < 3; i++) { Vector3 axis = p_transform_b.basis.get_axis(i).normalized(); if (!separator.test_axis(axis)) return; } // calculate closest point to sphere Vector3 cnormal = p_transform_b.xform_inv(p_transform_a.origin); Vector3 cpoint = p_transform_b.xform(Vector3( (cnormal.x < 0) ? -box_B->get_half_extents().x : box_B->get_half_extents().x, (cnormal.y < 0) ? -box_B->get_half_extents().y : box_B->get_half_extents().y, (cnormal.z < 0) ? -box_B->get_half_extents().z : box_B->get_half_extents().z)); // use point to test axis Vector3 point_axis = (p_transform_a.origin - cpoint).normalized(); if (!separator.test_axis(point_axis)) return; // test edges for (int i = 0; i < 3; i++) { Vector3 axis = point_axis.cross(p_transform_b.basis.get_axis(i)).cross(p_transform_b.basis.get_axis(i)).normalized(); if (!separator.test_axis(axis)) return; } separator.generate_contacts(); } template static void _collision_sphere_capsule(const ShapeSW *p_a, const Transform &p_transform_a, const ShapeSW *p_b, const Transform &p_transform_b, _CollectorCallback *p_collector, float p_margin_a, float p_margin_b) { const SphereShapeSW *sphere_A = static_cast(p_a); const CapsuleShapeSW *capsule_B = static_cast(p_b); SeparatorAxisTest separator(sphere_A, p_transform_a, capsule_B, p_transform_b, p_collector, p_margin_a, p_margin_b); if (!separator.test_previous_axis()) return; //capsule sphere 1, sphere Vector3 capsule_axis = p_transform_b.basis.get_axis(2) * (capsule_B->get_height() * 0.5); Vector3 capsule_ball_1 = p_transform_b.origin + capsule_axis; if (!separator.test_axis((capsule_ball_1 - p_transform_a.origin).normalized())) return; //capsule sphere 2, sphere Vector3 capsule_ball_2 = p_transform_b.origin - capsule_axis; if (!separator.test_axis((capsule_ball_2 - p_transform_a.origin).normalized())) return; //capsule edge, sphere Vector3 b2a = p_transform_a.origin - p_transform_b.origin; Vector3 axis = b2a.cross(capsule_axis).cross(capsule_axis).normalized(); if (!separator.test_axis(axis)) return; separator.generate_contacts(); } template static void _collision_sphere_convex_polygon(const ShapeSW *p_a, const Transform &p_transform_a, const ShapeSW *p_b, const Transform &p_transform_b, _CollectorCallback *p_collector, float p_margin_a, float p_margin_b) { const SphereShapeSW *sphere_A = static_cast(p_a); const ConvexPolygonShapeSW *convex_polygon_B = static_cast(p_b); SeparatorAxisTest separator(sphere_A, p_transform_a, convex_polygon_B, p_transform_b, p_collector, p_margin_a, p_margin_b); if (!separator.test_previous_axis()) return; const Geometry::MeshData &mesh = convex_polygon_B->get_mesh(); const Geometry::MeshData::Face *faces = mesh.faces.ptr(); int face_count = mesh.faces.size(); const Geometry::MeshData::Edge *edges = mesh.edges.ptr(); int edge_count = mesh.edges.size(); const Vector3 *vertices = mesh.vertices.ptr(); int vertex_count = mesh.vertices.size(); // faces of B for (int i = 0; i < face_count; i++) { Vector3 axis = p_transform_b.xform(faces[i].plane).normal; if (!separator.test_axis(axis)) return; } // edges of B for (int i = 0; i < edge_count; i++) { Vector3 v1 = p_transform_b.xform(vertices[edges[i].a]); Vector3 v2 = p_transform_b.xform(vertices[edges[i].b]); Vector3 v3 = p_transform_a.origin; Vector3 n1 = v2 - v1; Vector3 n2 = v2 - v3; Vector3 axis = n1.cross(n2).cross(n1).normalized(); if (!separator.test_axis(axis)) return; } // vertices of B for (int i = 0; i < vertex_count; i++) { Vector3 v1 = p_transform_b.xform(vertices[i]); Vector3 v2 = p_transform_a.origin; Vector3 axis = (v2 - v1).normalized(); if (!separator.test_axis(axis)) return; } separator.generate_contacts(); } template static void _collision_sphere_face(const ShapeSW *p_a, const Transform &p_transform_a, const ShapeSW *p_b, const Transform &p_transform_b, _CollectorCallback *p_collector, float p_margin_a, float p_margin_b) { const SphereShapeSW *sphere_A = static_cast(p_a); const FaceShapeSW *face_B = static_cast(p_b); SeparatorAxisTest separator(sphere_A, p_transform_a, face_B, p_transform_b, p_collector, p_margin_a, p_margin_b); Vector3 vertex[3] = { p_transform_b.xform(face_B->vertex[0]), p_transform_b.xform(face_B->vertex[1]), p_transform_b.xform(face_B->vertex[2]), }; if (!separator.test_axis((vertex[0] - vertex[2]).cross(vertex[0] - vertex[1]).normalized())) return; // edges and points of B for (int i = 0; i < 3; i++) { Vector3 n1 = vertex[i] - p_transform_a.origin; if (!separator.test_axis(n1.normalized())) { return; } Vector3 n2 = vertex[(i + 1) % 3] - vertex[i]; Vector3 axis = n1.cross(n2).cross(n2).normalized(); if (!separator.test_axis(axis)) { return; } } separator.generate_contacts(); } template static void _collision_box_box(const ShapeSW *p_a, const Transform &p_transform_a, const ShapeSW *p_b, const Transform &p_transform_b, _CollectorCallback *p_collector, float p_margin_a, float p_margin_b) { const BoxShapeSW *box_A = static_cast(p_a); const BoxShapeSW *box_B = static_cast(p_b); SeparatorAxisTest separator(box_A, p_transform_a, box_B, p_transform_b, p_collector, p_margin_a, p_margin_b); if (!separator.test_previous_axis()) return; // test faces of A for (int i = 0; i < 3; i++) { Vector3 axis = p_transform_a.basis.get_axis(i).normalized(); if (!separator.test_axis(axis)) return; } // test faces of B for (int i = 0; i < 3; i++) { Vector3 axis = p_transform_b.basis.get_axis(i).normalized(); if (!separator.test_axis(axis)) return; } // test combined edges for (int i = 0; i < 3; i++) { for (int j = 0; j < 3; j++) { Vector3 axis = p_transform_a.basis.get_axis(i).cross(p_transform_b.basis.get_axis(j)); if (axis.length_squared() < CMP_EPSILON) continue; axis.normalize(); if (!separator.test_axis(axis)) { return; } } } if (withMargin) { //add endpoint test between closest vertices and edges // calculate closest point to sphere Vector3 ab_vec = p_transform_b.origin - p_transform_a.origin; Vector3 cnormal_a = p_transform_a.basis.xform_inv(ab_vec); Vector3 support_a = p_transform_a.xform(Vector3( (cnormal_a.x < 0) ? -box_A->get_half_extents().x : box_A->get_half_extents().x, (cnormal_a.y < 0) ? -box_A->get_half_extents().y : box_A->get_half_extents().y, (cnormal_a.z < 0) ? -box_A->get_half_extents().z : box_A->get_half_extents().z)); Vector3 cnormal_b = p_transform_b.basis.xform_inv(-ab_vec); Vector3 support_b = p_transform_b.xform(Vector3( (cnormal_b.x < 0) ? -box_B->get_half_extents().x : box_B->get_half_extents().x, (cnormal_b.y < 0) ? -box_B->get_half_extents().y : box_B->get_half_extents().y, (cnormal_b.z < 0) ? -box_B->get_half_extents().z : box_B->get_half_extents().z)); Vector3 axis_ab = (support_a - support_b); if (!separator.test_axis(axis_ab.normalized())) { return; } //now try edges, which become cylinders! for (int i = 0; i < 3; i++) { //a ->b Vector3 axis_a = p_transform_a.basis.get_axis(i); if (!separator.test_axis(axis_ab.cross(axis_a).cross(axis_a).normalized())) return; //b ->a Vector3 axis_b = p_transform_b.basis.get_axis(i); if (!separator.test_axis(axis_ab.cross(axis_b).cross(axis_b).normalized())) return; } } separator.generate_contacts(); } template static void _collision_box_capsule(const ShapeSW *p_a, const Transform &p_transform_a, const ShapeSW *p_b, const Transform &p_transform_b, _CollectorCallback *p_collector, float p_margin_a, float p_margin_b) { const BoxShapeSW *box_A = static_cast(p_a); const CapsuleShapeSW *capsule_B = static_cast(p_b); SeparatorAxisTest separator(box_A, p_transform_a, capsule_B, p_transform_b, p_collector, p_margin_a, p_margin_b); if (!separator.test_previous_axis()) return; // faces of A for (int i = 0; i < 3; i++) { Vector3 axis = p_transform_a.basis.get_axis(i); if (!separator.test_axis(axis)) return; } Vector3 cyl_axis = p_transform_b.basis.get_axis(2).normalized(); // edges of A, capsule cylinder for (int i = 0; i < 3; i++) { // cylinder Vector3 box_axis = p_transform_a.basis.get_axis(i); Vector3 axis = box_axis.cross(cyl_axis); if (axis.length_squared() < CMP_EPSILON) continue; if (!separator.test_axis(axis.normalized())) return; } // points of A, capsule cylinder // this sure could be made faster somehow.. for (int i = 0; i < 2; i++) { for (int j = 0; j < 2; j++) { for (int k = 0; k < 2; k++) { Vector3 he = box_A->get_half_extents(); he.x *= (i * 2 - 1); he.y *= (j * 2 - 1); he.z *= (k * 2 - 1); Vector3 point = p_transform_a.origin; for (int l = 0; l < 3; l++) point += p_transform_a.basis.get_axis(l) * he[l]; //Vector3 axis = (point - cyl_axis * cyl_axis.dot(point)).normalized(); Vector3 axis = Plane(cyl_axis, 0).project(point).normalized(); if (!separator.test_axis(axis)) return; } } } // capsule balls, edges of A for (int i = 0; i < 2; i++) { Vector3 capsule_axis = p_transform_b.basis.get_axis(2) * (capsule_B->get_height() * 0.5); Vector3 sphere_pos = p_transform_b.origin + ((i == 0) ? capsule_axis : -capsule_axis); Vector3 cnormal = p_transform_a.xform_inv(sphere_pos); Vector3 cpoint = p_transform_a.xform(Vector3( (cnormal.x < 0) ? -box_A->get_half_extents().x : box_A->get_half_extents().x, (cnormal.y < 0) ? -box_A->get_half_extents().y : box_A->get_half_extents().y, (cnormal.z < 0) ? -box_A->get_half_extents().z : box_A->get_half_extents().z)); // use point to test axis Vector3 point_axis = (sphere_pos - cpoint).normalized(); if (!separator.test_axis(point_axis)) return; // test edges of A for (int i = 0; i < 3; i++) { Vector3 axis = point_axis.cross(p_transform_a.basis.get_axis(i)).cross(p_transform_a.basis.get_axis(i)).normalized(); if (!separator.test_axis(axis)) return; } } separator.generate_contacts(); } template static void _collision_box_convex_polygon(const ShapeSW *p_a, const Transform &p_transform_a, const ShapeSW *p_b, const Transform &p_transform_b, _CollectorCallback *p_collector, float p_margin_a, float p_margin_b) { const BoxShapeSW *box_A = static_cast(p_a); const ConvexPolygonShapeSW *convex_polygon_B = static_cast(p_b); SeparatorAxisTest separator(box_A, p_transform_a, convex_polygon_B, p_transform_b, p_collector, p_margin_a, p_margin_b); if (!separator.test_previous_axis()) return; const Geometry::MeshData &mesh = convex_polygon_B->get_mesh(); const Geometry::MeshData::Face *faces = mesh.faces.ptr(); int face_count = mesh.faces.size(); const Geometry::MeshData::Edge *edges = mesh.edges.ptr(); int edge_count = mesh.edges.size(); const Vector3 *vertices = mesh.vertices.ptr(); int vertex_count = mesh.vertices.size(); // faces of A for (int i = 0; i < 3; i++) { Vector3 axis = p_transform_a.basis.get_axis(i).normalized(); if (!separator.test_axis(axis)) return; } // faces of B for (int i = 0; i < face_count; i++) { Vector3 axis = p_transform_b.xform(faces[i].plane).normal; if (!separator.test_axis(axis)) return; } // A<->B edges for (int i = 0; i < 3; i++) { Vector3 e1 = p_transform_a.basis.get_axis(i); for (int j = 0; j < edge_count; j++) { Vector3 e2 = p_transform_b.basis.xform(vertices[edges[j].a]) - p_transform_b.basis.xform(vertices[edges[j].b]); Vector3 axis = e1.cross(e2).normalized(); if (!separator.test_axis(axis)) return; } } if (withMargin) { // calculate closest points between vertices and box edges for (int v = 0; v < vertex_count; v++) { Vector3 vtxb = p_transform_b.xform(vertices[v]); Vector3 ab_vec = vtxb - p_transform_a.origin; Vector3 cnormal_a = p_transform_a.basis.xform_inv(ab_vec); Vector3 support_a = p_transform_a.xform(Vector3( (cnormal_a.x < 0) ? -box_A->get_half_extents().x : box_A->get_half_extents().x, (cnormal_a.y < 0) ? -box_A->get_half_extents().y : box_A->get_half_extents().y, (cnormal_a.z < 0) ? -box_A->get_half_extents().z : box_A->get_half_extents().z)); Vector3 axis_ab = support_a - vtxb; if (!separator.test_axis(axis_ab.normalized())) { return; } //now try edges, which become cylinders! for (int i = 0; i < 3; i++) { //a ->b Vector3 axis_a = p_transform_a.basis.get_axis(i); if (!separator.test_axis(axis_ab.cross(axis_a).cross(axis_a).normalized())) return; } } //convex edges and box points for (int i = 0; i < 2; i++) { for (int j = 0; j < 2; j++) { for (int k = 0; k < 2; k++) { Vector3 he = box_A->get_half_extents(); he.x *= (i * 2 - 1); he.y *= (j * 2 - 1); he.z *= (k * 2 - 1); Vector3 point = p_transform_a.origin; for (int l = 0; l < 3; l++) point += p_transform_a.basis.get_axis(l) * he[l]; for (int e = 0; e < edge_count; e++) { Vector3 p1 = p_transform_b.xform(vertices[edges[e].a]); Vector3 p2 = p_transform_b.xform(vertices[edges[e].b]); Vector3 n = (p2 - p1); if (!separator.test_axis((point - p2).cross(n).cross(n).normalized())) return; } } } } } separator.generate_contacts(); } template static void _collision_box_face(const ShapeSW *p_a, const Transform &p_transform_a, const ShapeSW *p_b, const Transform &p_transform_b, _CollectorCallback *p_collector, float p_margin_a, float p_margin_b) { const BoxShapeSW *box_A = static_cast(p_a); const FaceShapeSW *face_B = static_cast(p_b); SeparatorAxisTest separator(box_A, p_transform_a, face_B, p_transform_b, p_collector, p_margin_a, p_margin_b); Vector3 vertex[3] = { p_transform_b.xform(face_B->vertex[0]), p_transform_b.xform(face_B->vertex[1]), p_transform_b.xform(face_B->vertex[2]), }; if (!separator.test_axis((vertex[0] - vertex[2]).cross(vertex[0] - vertex[1]).normalized())) return; // faces of A for (int i = 0; i < 3; i++) { Vector3 axis = p_transform_a.basis.get_axis(i).normalized(); if (!separator.test_axis(axis)) return; } // combined edges for (int i = 0; i < 3; i++) { Vector3 e = vertex[i] - vertex[(i + 1) % 3]; for (int j = 0; j < 3; j++) { Vector3 axis = p_transform_a.basis.get_axis(j); if (!separator.test_axis(e.cross(axis).normalized())) return; } } if (withMargin) { // calculate closest points between vertices and box edges for (int v = 0; v < 3; v++) { Vector3 ab_vec = vertex[v] - p_transform_a.origin; Vector3 cnormal_a = p_transform_a.basis.xform_inv(ab_vec); Vector3 support_a = p_transform_a.xform(Vector3( (cnormal_a.x < 0) ? -box_A->get_half_extents().x : box_A->get_half_extents().x, (cnormal_a.y < 0) ? -box_A->get_half_extents().y : box_A->get_half_extents().y, (cnormal_a.z < 0) ? -box_A->get_half_extents().z : box_A->get_half_extents().z)); Vector3 axis_ab = support_a - vertex[v]; if (!separator.test_axis(axis_ab.normalized())) { return; } //now try edges, which become cylinders! for (int i = 0; i < 3; i++) { //a ->b Vector3 axis_a = p_transform_a.basis.get_axis(i); if (!separator.test_axis(axis_ab.cross(axis_a).cross(axis_a).normalized())) return; } } //convex edges and box points, there has to be a way to speed up this (get closest point?) for (int i = 0; i < 2; i++) { for (int j = 0; j < 2; j++) { for (int k = 0; k < 2; k++) { Vector3 he = box_A->get_half_extents(); he.x *= (i * 2 - 1); he.y *= (j * 2 - 1); he.z *= (k * 2 - 1); Vector3 point = p_transform_a.origin; for (int l = 0; l < 3; l++) point += p_transform_a.basis.get_axis(l) * he[l]; for (int e = 0; e < 3; e++) { Vector3 p1 = vertex[e]; Vector3 p2 = vertex[(e + 1) % 3]; Vector3 n = (p2 - p1); if (!separator.test_axis((point - p2).cross(n).cross(n).normalized())) return; } } } } } separator.generate_contacts(); } template static void _collision_capsule_capsule(const ShapeSW *p_a, const Transform &p_transform_a, const ShapeSW *p_b, const Transform &p_transform_b, _CollectorCallback *p_collector, float p_margin_a, float p_margin_b) { const CapsuleShapeSW *capsule_A = static_cast(p_a); const CapsuleShapeSW *capsule_B = static_cast(p_b); SeparatorAxisTest separator(capsule_A, p_transform_a, capsule_B, p_transform_b, p_collector, p_margin_a, p_margin_b); if (!separator.test_previous_axis()) return; // some values Vector3 capsule_A_axis = p_transform_a.basis.get_axis(2) * (capsule_A->get_height() * 0.5); Vector3 capsule_B_axis = p_transform_b.basis.get_axis(2) * (capsule_B->get_height() * 0.5); Vector3 capsule_A_ball_1 = p_transform_a.origin + capsule_A_axis; Vector3 capsule_A_ball_2 = p_transform_a.origin - capsule_A_axis; Vector3 capsule_B_ball_1 = p_transform_b.origin + capsule_B_axis; Vector3 capsule_B_ball_2 = p_transform_b.origin - capsule_B_axis; //balls-balls if (!separator.test_axis((capsule_A_ball_1 - capsule_B_ball_1).normalized())) return; if (!separator.test_axis((capsule_A_ball_1 - capsule_B_ball_2).normalized())) return; if (!separator.test_axis((capsule_A_ball_2 - capsule_B_ball_1).normalized())) return; if (!separator.test_axis((capsule_A_ball_2 - capsule_B_ball_2).normalized())) return; // edges-balls if (!separator.test_axis((capsule_A_ball_1 - capsule_B_ball_1).cross(capsule_A_axis).cross(capsule_A_axis).normalized())) return; if (!separator.test_axis((capsule_A_ball_1 - capsule_B_ball_2).cross(capsule_A_axis).cross(capsule_A_axis).normalized())) return; if (!separator.test_axis((capsule_B_ball_1 - capsule_A_ball_1).cross(capsule_B_axis).cross(capsule_B_axis).normalized())) return; if (!separator.test_axis((capsule_B_ball_1 - capsule_A_ball_2).cross(capsule_B_axis).cross(capsule_B_axis).normalized())) return; // edges if (!separator.test_axis(capsule_A_axis.cross(capsule_B_axis).normalized())) return; separator.generate_contacts(); } template static void _collision_capsule_convex_polygon(const ShapeSW *p_a, const Transform &p_transform_a, const ShapeSW *p_b, const Transform &p_transform_b, _CollectorCallback *p_collector, float p_margin_a, float p_margin_b) { const CapsuleShapeSW *capsule_A = static_cast(p_a); const ConvexPolygonShapeSW *convex_polygon_B = static_cast(p_b); SeparatorAxisTest separator(capsule_A, p_transform_a, convex_polygon_B, p_transform_b, p_collector, p_margin_a, p_margin_b); if (!separator.test_previous_axis()) return; const Geometry::MeshData &mesh = convex_polygon_B->get_mesh(); const Geometry::MeshData::Face *faces = mesh.faces.ptr(); int face_count = mesh.faces.size(); const Geometry::MeshData::Edge *edges = mesh.edges.ptr(); int edge_count = mesh.edges.size(); const Vector3 *vertices = mesh.vertices.ptr(); // faces of B for (int i = 0; i < face_count; i++) { Vector3 axis = p_transform_b.xform(faces[i].plane).normal; if (!separator.test_axis(axis)) return; } // edges of B, capsule cylinder for (int i = 0; i < edge_count; i++) { // cylinder Vector3 edge_axis = p_transform_b.basis.xform(vertices[edges[i].a]) - p_transform_b.basis.xform(vertices[edges[i].b]); Vector3 axis = edge_axis.cross(p_transform_a.basis.get_axis(2)).normalized(); if (!separator.test_axis(axis)) return; } // capsule balls, edges of B for (int i = 0; i < 2; i++) { // edges of B, capsule cylinder Vector3 capsule_axis = p_transform_a.basis.get_axis(2) * (capsule_A->get_height() * 0.5); Vector3 sphere_pos = p_transform_a.origin + ((i == 0) ? capsule_axis : -capsule_axis); for (int j = 0; j < edge_count; j++) { Vector3 n1 = sphere_pos - p_transform_b.xform(vertices[edges[j].a]); Vector3 n2 = p_transform_b.basis.xform(vertices[edges[j].a]) - p_transform_b.basis.xform(vertices[edges[j].b]); Vector3 axis = n1.cross(n2).cross(n2).normalized(); if (!separator.test_axis(axis)) return; } } separator.generate_contacts(); } template static void _collision_capsule_face(const ShapeSW *p_a, const Transform &p_transform_a, const ShapeSW *p_b, const Transform &p_transform_b, _CollectorCallback *p_collector, float p_margin_a, float p_margin_b) { const CapsuleShapeSW *capsule_A = static_cast(p_a); const FaceShapeSW *face_B = static_cast(p_b); SeparatorAxisTest separator(capsule_A, p_transform_a, face_B, p_transform_b, p_collector, p_margin_a, p_margin_b); Vector3 vertex[3] = { p_transform_b.xform(face_B->vertex[0]), p_transform_b.xform(face_B->vertex[1]), p_transform_b.xform(face_B->vertex[2]), }; if (!separator.test_axis((vertex[0] - vertex[2]).cross(vertex[0] - vertex[1]).normalized())) return; // edges of B, capsule cylinder Vector3 capsule_axis = p_transform_a.basis.get_axis(2) * (capsule_A->get_height() * 0.5); for (int i = 0; i < 3; i++) { // edge-cylinder Vector3 edge_axis = vertex[i] - vertex[(i + 1) % 3]; Vector3 axis = edge_axis.cross(capsule_axis).normalized(); if (!separator.test_axis(axis)) return; if (!separator.test_axis((p_transform_a.origin - vertex[i]).cross(capsule_axis).cross(capsule_axis).normalized())) return; for (int j = 0; j < 2; j++) { // point-spheres Vector3 sphere_pos = p_transform_a.origin + ((j == 0) ? capsule_axis : -capsule_axis); Vector3 n1 = sphere_pos - vertex[i]; if (!separator.test_axis(n1.normalized())) return; Vector3 n2 = edge_axis; axis = n1.cross(n2).cross(n2); if (!separator.test_axis(axis.normalized())) return; } } separator.generate_contacts(); } template static void _collision_convex_polygon_convex_polygon(const ShapeSW *p_a, const Transform &p_transform_a, const ShapeSW *p_b, const Transform &p_transform_b, _CollectorCallback *p_collector, float p_margin_a, float p_margin_b) { const ConvexPolygonShapeSW *convex_polygon_A = static_cast(p_a); const ConvexPolygonShapeSW *convex_polygon_B = static_cast(p_b); SeparatorAxisTest separator(convex_polygon_A, p_transform_a, convex_polygon_B, p_transform_b, p_collector, p_margin_a, p_margin_b); if (!separator.test_previous_axis()) return; const Geometry::MeshData &mesh_A = convex_polygon_A->get_mesh(); const Geometry::MeshData::Face *faces_A = mesh_A.faces.ptr(); int face_count_A = mesh_A.faces.size(); const Geometry::MeshData::Edge *edges_A = mesh_A.edges.ptr(); int edge_count_A = mesh_A.edges.size(); const Vector3 *vertices_A = mesh_A.vertices.ptr(); int vertex_count_A = mesh_A.vertices.size(); const Geometry::MeshData &mesh_B = convex_polygon_B->get_mesh(); const Geometry::MeshData::Face *faces_B = mesh_B.faces.ptr(); int face_count_B = mesh_B.faces.size(); const Geometry::MeshData::Edge *edges_B = mesh_B.edges.ptr(); int edge_count_B = mesh_B.edges.size(); const Vector3 *vertices_B = mesh_B.vertices.ptr(); int vertex_count_B = mesh_B.vertices.size(); // faces of A for (int i = 0; i < face_count_A; i++) { Vector3 axis = p_transform_a.xform(faces_A[i].plane).normal; // Vector3 axis = p_transform_a.basis.xform( faces_A[i].plane.normal ).normalized(); if (!separator.test_axis(axis)) return; } // faces of B for (int i = 0; i < face_count_B; i++) { Vector3 axis = p_transform_b.xform(faces_B[i].plane).normal; // Vector3 axis = p_transform_b.basis.xform( faces_B[i].plane.normal ).normalized(); if (!separator.test_axis(axis)) return; } // A<->B edges for (int i = 0; i < edge_count_A; i++) { Vector3 e1 = p_transform_a.basis.xform(vertices_A[edges_A[i].a]) - p_transform_a.basis.xform(vertices_A[edges_A[i].b]); for (int j = 0; j < edge_count_B; j++) { Vector3 e2 = p_transform_b.basis.xform(vertices_B[edges_B[j].a]) - p_transform_b.basis.xform(vertices_B[edges_B[j].b]); Vector3 axis = e1.cross(e2).normalized(); if (!separator.test_axis(axis)) return; } } if (withMargin) { //vertex-vertex for (int i = 0; i < vertex_count_A; i++) { Vector3 va = p_transform_a.xform(vertices_A[i]); for (int j = 0; j < vertex_count_B; j++) { if (!separator.test_axis((va - p_transform_b.xform(vertices_B[j])).normalized())) return; } } //edge-vertex( hsell) for (int i = 0; i < edge_count_A; i++) { Vector3 e1 = p_transform_a.basis.xform(vertices_A[edges_A[i].a]); Vector3 e2 = p_transform_a.basis.xform(vertices_A[edges_A[i].b]); Vector3 n = (e2 - e1); for (int j = 0; j < vertex_count_B; j++) { Vector3 e3 = p_transform_b.xform(vertices_B[j]); if (!separator.test_axis((e1 - e3).cross(n).cross(n).normalized())) return; } } for (int i = 0; i < edge_count_B; i++) { Vector3 e1 = p_transform_b.basis.xform(vertices_B[edges_B[i].a]); Vector3 e2 = p_transform_b.basis.xform(vertices_B[edges_B[i].b]); Vector3 n = (e2 - e1); for (int j = 0; j < vertex_count_A; j++) { Vector3 e3 = p_transform_a.xform(vertices_A[j]); if (!separator.test_axis((e1 - e3).cross(n).cross(n).normalized())) return; } } } separator.generate_contacts(); } template static void _collision_convex_polygon_face(const ShapeSW *p_a, const Transform &p_transform_a, const ShapeSW *p_b, const Transform &p_transform_b, _CollectorCallback *p_collector, float p_margin_a, float p_margin_b) { const ConvexPolygonShapeSW *convex_polygon_A = static_cast(p_a); const FaceShapeSW *face_B = static_cast(p_b); SeparatorAxisTest separator(convex_polygon_A, p_transform_a, face_B, p_transform_b, p_collector, p_margin_a, p_margin_b); const Geometry::MeshData &mesh = convex_polygon_A->get_mesh(); const Geometry::MeshData::Face *faces = mesh.faces.ptr(); int face_count = mesh.faces.size(); const Geometry::MeshData::Edge *edges = mesh.edges.ptr(); int edge_count = mesh.edges.size(); const Vector3 *vertices = mesh.vertices.ptr(); int vertex_count = mesh.vertices.size(); Vector3 vertex[3] = { p_transform_b.xform(face_B->vertex[0]), p_transform_b.xform(face_B->vertex[1]), p_transform_b.xform(face_B->vertex[2]), }; if (!separator.test_axis((vertex[0] - vertex[2]).cross(vertex[0] - vertex[1]).normalized())) return; // faces of A for (int i = 0; i < face_count; i++) { // Vector3 axis = p_transform_a.xform( faces[i].plane ).normal; Vector3 axis = p_transform_a.basis.xform(faces[i].plane.normal).normalized(); if (!separator.test_axis(axis)) return; } // A<->B edges for (int i = 0; i < edge_count; i++) { Vector3 e1 = p_transform_a.xform(vertices[edges[i].a]) - p_transform_a.xform(vertices[edges[i].b]); for (int j = 0; j < 3; j++) { Vector3 e2 = vertex[j] - vertex[(j + 1) % 3]; Vector3 axis = e1.cross(e2).normalized(); if (!separator.test_axis(axis)) return; } } if (withMargin) { //vertex-vertex for (int i = 0; i < vertex_count; i++) { Vector3 va = p_transform_a.xform(vertices[i]); for (int j = 0; j < 3; j++) { if (!separator.test_axis((va - vertex[j]).normalized())) return; } } //edge-vertex( hsell) for (int i = 0; i < edge_count; i++) { Vector3 e1 = p_transform_a.basis.xform(vertices[edges[i].a]); Vector3 e2 = p_transform_a.basis.xform(vertices[edges[i].b]); Vector3 n = (e2 - e1); for (int j = 0; j < 3; j++) { Vector3 e3 = vertex[j]; if (!separator.test_axis((e1 - e3).cross(n).cross(n).normalized())) return; } } for (int i = 0; i < 3; i++) { Vector3 e1 = vertex[i]; Vector3 e2 = vertex[(i + 1) % 3]; Vector3 n = (e2 - e1); for (int j = 0; j < vertex_count; j++) { Vector3 e3 = p_transform_a.xform(vertices[j]); if (!separator.test_axis((e1 - e3).cross(n).cross(n).normalized())) return; } } } separator.generate_contacts(); } bool sat_calculate_penetration(const ShapeSW *p_shape_A, const Transform &p_transform_A, const ShapeSW *p_shape_B, const Transform &p_transform_B, CollisionSolverSW::CallbackResult p_result_callback, void *p_userdata, bool p_swap, Vector3 *r_prev_axis, float p_margin_a, float p_margin_b) { PhysicsServer::ShapeType type_A = p_shape_A->get_type(); ERR_FAIL_COND_V(type_A == PhysicsServer::SHAPE_PLANE, false); ERR_FAIL_COND_V(type_A == PhysicsServer::SHAPE_RAY, false); ERR_FAIL_COND_V(p_shape_A->is_concave(), false); PhysicsServer::ShapeType type_B = p_shape_B->get_type(); ERR_FAIL_COND_V(type_B == PhysicsServer::SHAPE_PLANE, false); ERR_FAIL_COND_V(type_B == PhysicsServer::SHAPE_RAY, false); ERR_FAIL_COND_V(p_shape_B->is_concave(), false); static const CollisionFunc collision_table[5][5] = { { _collision_sphere_sphere, _collision_sphere_box, _collision_sphere_capsule, _collision_sphere_convex_polygon, _collision_sphere_face }, { 0, _collision_box_box, _collision_box_capsule, _collision_box_convex_polygon, _collision_box_face }, { 0, 0, _collision_capsule_capsule, _collision_capsule_convex_polygon, _collision_capsule_face }, { 0, 0, 0, _collision_convex_polygon_convex_polygon, _collision_convex_polygon_face }, { 0, 0, 0, 0, 0 }, }; static const CollisionFunc collision_table_margin[5][5] = { { _collision_sphere_sphere, _collision_sphere_box, _collision_sphere_capsule, _collision_sphere_convex_polygon, _collision_sphere_face }, { 0, _collision_box_box, _collision_box_capsule, _collision_box_convex_polygon, _collision_box_face }, { 0, 0, _collision_capsule_capsule, _collision_capsule_convex_polygon, _collision_capsule_face }, { 0, 0, 0, _collision_convex_polygon_convex_polygon, _collision_convex_polygon_face }, { 0, 0, 0, 0, 0 }, }; _CollectorCallback callback; callback.callback = p_result_callback; callback.swap = p_swap; callback.userdata = p_userdata; callback.collided = false; callback.prev_axis = r_prev_axis; const ShapeSW *A = p_shape_A; const ShapeSW *B = p_shape_B; const Transform *transform_A = &p_transform_A; const Transform *transform_B = &p_transform_B; float margin_A = p_margin_a; float margin_B = p_margin_b; if (type_A > type_B) { SWAP(A, B); SWAP(transform_A, transform_B); SWAP(type_A, type_B); SWAP(margin_A, margin_B); callback.swap = !callback.swap; } CollisionFunc collision_func; if (margin_A != 0.0 || margin_B != 0.0) { collision_func = collision_table_margin[type_A - 2][type_B - 2]; } else { collision_func = collision_table[type_A - 2][type_B - 2]; } ERR_FAIL_COND_V(!collision_func, false); collision_func(A, *transform_A, B, *transform_B, &callback, margin_A, margin_B); return callback.collided; }