/**************************************************************************/ /* godot_collision_solver_3d_sat.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 "godot_collision_solver_3d_sat.h" #include "gjk_epa.h" #include "core/math/geometry_3d.h" #define fallback_collision_solver gjk_epa_calculate_penetration #define _BACKFACE_NORMAL_THRESHOLD -0.0002 // Cylinder SAT analytic methods and face-circle contact points for cylinder-trimesh and cylinder-box collision are based on ODE colliders. /* * Cylinder-trimesh and Cylinder-box colliders by Alen Ladavac * Ported to ODE by Nguyen Binh */ /************************************************************************* * * * Open Dynamics Engine, Copyright (C) 2001-2003 Russell L. Smith. * * All rights reserved. Email: russ@q12.org Web: www.q12.org * * * * This library is free software; you can redistribute it and/or * * modify it under the terms of EITHER: * * (1) The GNU Lesser General Public License as published by the Free * * Software Foundation; either version 2.1 of the License, or (at * * your option) any later version. The text of the GNU Lesser * * General Public License is included with this library in the * * file LICENSE.TXT. * * (2) The BSD-style license that is included with this library in * * the file LICENSE-BSD.TXT. * * * * This library is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files * * LICENSE.TXT and LICENSE-BSD.TXT for more details. * * * *************************************************************************/ struct _CollectorCallback { GodotCollisionSolver3D::CallbackResult callback = nullptr; void *userdata = nullptr; bool swap = false; bool collided = false; Vector3 normal; Vector3 *prev_axis = nullptr; _FORCE_INLINE_ void call(const Vector3 &p_point_A, const Vector3 &p_point_B) { if (swap) { callback(p_point_B, 0, p_point_A, 0, userdata); } else { callback(p_point_A, 0, p_point_B, 0, 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 = Geometry3D::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_point_circle(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::is_zero_approx(rel_A.dot(c))) { // 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 real_t 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 = Geometry3D::get_closest_point_to_segment_uncapped(closest_A, p_points_B); p_callback->call(closest_A, closest_B); } static void _generate_contacts_edge_circle(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 const Vector3 &circle_B_pos = p_points_B[0]; Vector3 circle_B_line_1 = p_points_B[1] - circle_B_pos; Vector3 circle_B_line_2 = p_points_B[2] - circle_B_pos; real_t circle_B_radius = circle_B_line_1.length(); Vector3 circle_B_normal = circle_B_line_1.cross(circle_B_line_2).normalized(); Plane circle_plane(circle_B_normal, circle_B_pos); static const int max_clip = 2; Vector3 contact_points[max_clip]; int num_points = 0; // Project edge point in circle plane. const Vector3 &edge_A_1 = p_points_A[0]; Vector3 proj_point_1 = circle_plane.project(edge_A_1); Vector3 dist_vec = proj_point_1 - circle_B_pos; real_t dist_sq = dist_vec.length_squared(); // Point 1 is inside disk, add as contact point. if (dist_sq <= circle_B_radius * circle_B_radius) { contact_points[num_points] = edge_A_1; ++num_points; } const Vector3 &edge_A_2 = p_points_A[1]; Vector3 proj_point_2 = circle_plane.project(edge_A_2); Vector3 dist_vec_2 = proj_point_2 - circle_B_pos; real_t dist_sq_2 = dist_vec_2.length_squared(); // Point 2 is inside disk, add as contact point. if (dist_sq_2 <= circle_B_radius * circle_B_radius) { contact_points[num_points] = edge_A_2; ++num_points; } if (num_points < 2) { Vector3 line_vec = proj_point_2 - proj_point_1; real_t line_length_sq = line_vec.length_squared(); // Create a quadratic formula of the form ax^2 + bx + c = 0 real_t a, b, c; a = line_length_sq; b = 2.0 * dist_vec.dot(line_vec); c = dist_sq - circle_B_radius * circle_B_radius; // Solve for t. real_t sqrtterm = b * b - 4.0 * a * c; // If the term we intend to square root is less than 0 then the answer won't be real, // so the line doesn't intersect. if (sqrtterm >= 0) { sqrtterm = Math::sqrt(sqrtterm); Vector3 edge_dir = edge_A_2 - edge_A_1; real_t fraction_1 = (-b - sqrtterm) / (2.0 * a); if ((fraction_1 > 0.0) && (fraction_1 < 1.0)) { Vector3 face_point_1 = edge_A_1 + fraction_1 * edge_dir; ERR_FAIL_COND(num_points >= max_clip); contact_points[num_points] = face_point_1; ++num_points; } real_t fraction_2 = (-b + sqrtterm) / (2.0 * a); if ((fraction_2 > 0.0) && (fraction_2 < 1.0) && !Math::is_equal_approx(fraction_1, fraction_2)) { Vector3 face_point_2 = edge_A_1 + fraction_2 * edge_dir; ERR_FAIL_COND(num_points >= max_clip); contact_points[num_points] = face_point_2; ++num_points; } } } // Generate contact points. for (int i = 0; i < num_points; i++) { const Vector3 &contact_point_A = contact_points[i]; real_t d = circle_plane.distance_to(contact_point_A); Vector3 closest_B = contact_point_A - circle_plane.normal * d; if (p_callback->normal.dot(contact_point_A) >= p_callback->normal.dot(closest_B)) { continue; } p_callback->call(contact_point_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(clip_normal, edge0_B); // 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]); for (int i = 0; i < clipbuf_len; i++) { real_t d = plane_B.distance_to(clipbuf_src[i]); 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); } } static void _generate_contacts_face_circle(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 < 3); ERR_FAIL_COND(p_point_count_B != 3); #endif const Vector3 &circle_B_pos = p_points_B[0]; Vector3 circle_B_line_1 = p_points_B[1] - circle_B_pos; Vector3 circle_B_line_2 = p_points_B[2] - circle_B_pos; // Clip face with circle segments. static const int circle_segments = 8; Vector3 circle_points[circle_segments]; real_t angle_delta = 2.0 * Math_PI / circle_segments; for (int i = 0; i < circle_segments; ++i) { Vector3 point_pos = circle_B_pos; point_pos += circle_B_line_1 * Math::cos(i * angle_delta); point_pos += circle_B_line_2 * Math::sin(i * angle_delta); circle_points[i] = point_pos; } _generate_contacts_face_face(p_points_A, p_point_count_A, circle_points, circle_segments, p_callback); // Clip face with circle plane. Vector3 circle_B_normal = circle_B_line_1.cross(circle_B_line_2).normalized(); Plane circle_plane(circle_B_normal, circle_B_pos); static const int max_clip = 32; Vector3 contact_points[max_clip]; int num_points = 0; for (int i = 0; i < p_point_count_A; i++) { int i_n = (i + 1) % p_point_count_A; const Vector3 &edge0_A = p_points_A[i]; const Vector3 &edge1_A = p_points_A[i_n]; real_t dist0 = circle_plane.distance_to(edge0_A); real_t dist1 = circle_plane.distance_to(edge1_A); // First point in front of plane, generate contact point. if (dist0 * circle_plane.d >= 0) { ERR_FAIL_COND(num_points >= max_clip); contact_points[num_points] = edge0_A; ++num_points; } // Points on different sides, generate contact point. if (dist0 * dist1 < 0) { // calculate intersection Vector3 rel = edge1_A - edge0_A; real_t den = circle_plane.normal.dot(rel); real_t dist = -(circle_plane.normal.dot(edge0_A) - circle_plane.d) / den; Vector3 inters = edge0_A + rel * dist; ERR_FAIL_COND(num_points >= max_clip); contact_points[num_points] = inters; ++num_points; } } // Generate contact points. for (int i = 0; i < num_points; i++) { const Vector3 &contact_point_A = contact_points[i]; real_t d = circle_plane.distance_to(contact_point_A); Vector3 closest_B = contact_point_A - circle_plane.normal * d; if (p_callback->normal.dot(contact_point_A) >= p_callback->normal.dot(closest_B)) { continue; } p_callback->call(contact_point_A, closest_B); } } static void _generate_contacts_circle_circle(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 != 3); ERR_FAIL_COND(p_point_count_B != 3); #endif const Vector3 &circle_A_pos = p_points_A[0]; Vector3 circle_A_line_1 = p_points_A[1] - circle_A_pos; Vector3 circle_A_line_2 = p_points_A[2] - circle_A_pos; real_t circle_A_radius = circle_A_line_1.length(); Vector3 circle_A_normal = circle_A_line_1.cross(circle_A_line_2).normalized(); const Vector3 &circle_B_pos = p_points_B[0]; Vector3 circle_B_line_1 = p_points_B[1] - circle_B_pos; Vector3 circle_B_line_2 = p_points_B[2] - circle_B_pos; real_t circle_B_radius = circle_B_line_1.length(); Vector3 circle_B_normal = circle_B_line_1.cross(circle_B_line_2).normalized(); static const int max_clip = 4; Vector3 contact_points[max_clip]; int num_points = 0; Vector3 centers_diff = circle_B_pos - circle_A_pos; Vector3 norm_proj = circle_A_normal.dot(centers_diff) * circle_A_normal; Vector3 comp_proj = centers_diff - norm_proj; real_t proj_dist = comp_proj.length(); if (!Math::is_zero_approx(proj_dist)) { comp_proj /= proj_dist; if ((proj_dist > circle_A_radius - circle_B_radius) && (proj_dist > circle_B_radius - circle_A_radius)) { // Circles are overlapping, use the 2 points of intersection as contacts. real_t radius_a_sqr = circle_A_radius * circle_A_radius; real_t radius_b_sqr = circle_B_radius * circle_B_radius; real_t d_sqr = proj_dist * proj_dist; real_t s = (1.0 + (radius_a_sqr - radius_b_sqr) / d_sqr) * 0.5; real_t h = Math::sqrt(MAX(radius_a_sqr - d_sqr * s * s, 0.0)); Vector3 midpoint = circle_A_pos + s * comp_proj * proj_dist; Vector3 h_vec = h * circle_A_normal.cross(comp_proj); Vector3 point_A = midpoint + h_vec; contact_points[num_points] = point_A; ++num_points; point_A = midpoint - h_vec; contact_points[num_points] = point_A; ++num_points; // Add 2 points from circle A and B along the line between the centers. point_A = circle_A_pos + comp_proj * circle_A_radius; contact_points[num_points] = point_A; ++num_points; point_A = circle_B_pos - comp_proj * circle_B_radius - norm_proj; contact_points[num_points] = point_A; ++num_points; } // Otherwise one circle is inside the other one, use 3 arbitrary equidistant points. } // Otherwise circles are concentric, use 3 arbitrary equidistant points. if (num_points == 0) { // Generate equidistant points. if (circle_A_radius < circle_B_radius) { // Circle A inside circle B. for (int i = 0; i < 3; ++i) { Vector3 circle_A_point = circle_A_pos; circle_A_point += circle_A_line_1 * Math::cos(2.0 * Math_PI * i / 3.0); circle_A_point += circle_A_line_2 * Math::sin(2.0 * Math_PI * i / 3.0); contact_points[num_points] = circle_A_point; ++num_points; } } else { // Circle B inside circle A. for (int i = 0; i < 3; ++i) { Vector3 circle_B_point = circle_B_pos; circle_B_point += circle_B_line_1 * Math::cos(2.0 * Math_PI * i / 3.0); circle_B_point += circle_B_line_2 * Math::sin(2.0 * Math_PI * i / 3.0); Vector3 circle_A_point = circle_B_point - norm_proj; contact_points[num_points] = circle_A_point; ++num_points; } } } Plane circle_B_plane(circle_B_normal, circle_B_pos); // Generate contact points. for (int i = 0; i < num_points; i++) { const Vector3 &contact_point_A = contact_points[i]; real_t d = circle_B_plane.distance_to(contact_point_A); Vector3 closest_B = contact_point_A - circle_B_plane.normal * d; if (p_callback->normal.dot(contact_point_A) >= p_callback->normal.dot(closest_B)) { continue; } p_callback->call(contact_point_A, closest_B); } } static void _generate_contacts_from_supports(const Vector3 *p_points_A, int p_point_count_A, GodotShape3D::FeatureType p_feature_type_A, const Vector3 *p_points_B, int p_point_count_B, GodotShape3D::FeatureType p_feature_type_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[4][4] = { { _generate_contacts_point_point, _generate_contacts_point_edge, _generate_contacts_point_face, _generate_contacts_point_circle, }, { nullptr, _generate_contacts_edge_edge, _generate_contacts_face_face, _generate_contacts_edge_circle, }, { nullptr, nullptr, _generate_contacts_face_face, _generate_contacts_face_circle, }, { nullptr, nullptr, nullptr, _generate_contacts_circle_circle, }, }; int pointcount_B; int pointcount_A; const Vector3 *points_A; const Vector3 *points_B; int version_A; int version_B; if (p_feature_type_A > p_feature_type_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; version_A = p_feature_type_B; version_B = p_feature_type_A; } else { pointcount_B = p_point_count_B; pointcount_A = p_point_count_A; points_A = p_points_A; points_B = p_points_B; version_A = p_feature_type_A; version_B = p_feature_type_B; } 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 = nullptr; const ShapeB *shape_B = nullptr; const Transform3D *transform_A = nullptr; const Transform3D *transform_B = nullptr; real_t best_depth = 1e15; _CollectorCallback *callback = nullptr; real_t margin_A = 0.0; real_t margin_B = 0.0; Vector3 separator_axis; public: Vector3 best_axis; _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 (axis.is_zero_approx()) { // strange case, try an upwards separator axis = Vector3(0.0, 1.0, 0.0); } real_t min_A = 0.0, max_A = 0.0, min_B = 0.0, max_B = 0.0; 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; min_B -= (min_A + max_A) * 0.5; max_B -= (min_A + max_A) * 0.5; if (min_B > 0.0 || max_B < 0.0) { separator_axis = axis; return false; // doesn't contain 0 } //use the smallest depth if (min_B < 0.0) { // could be +0.0, we don't want it to become -0.0 min_B = -min_B; } if (max_B < min_B) { if (max_B < best_depth) { best_depth = max_B; best_axis = axis; } } else { if (min_B < best_depth) { best_depth = min_B; best_axis = -axis; // keep it as A axis } } return true; } static _FORCE_INLINE_ void test_contact_points(const Vector3 &p_point_A, int p_index_A, const Vector3 &p_point_B, int p_index_B, void *p_userdata) { SeparatorAxisTest *separator = (SeparatorAxisTest *)p_userdata; Vector3 axis = (p_point_B - p_point_A); real_t depth = axis.length(); // Filter out bogus directions with a threshold and re-testing axis. if (separator->best_depth - depth > 0.001) { separator->test_axis(axis / depth); } } _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; GodotShape3D::FeatureType support_type_A; shape_A->get_supports(transform_A->basis.xform_inv(-best_axis).normalized(), max_supports, supports_A, support_count_A, support_type_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; GodotShape3D::FeatureType support_type_B; shape_B->get_supports(transform_B->basis.xform_inv(best_axis).normalized(), max_supports, supports_B, support_count_B, support_type_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; } } callback->normal = best_axis; if (callback->prev_axis) { *callback->prev_axis = best_axis; } _generate_contacts_from_supports(supports_A, support_count_A, support_type_A, supports_B, support_count_B, support_type_B, callback); callback->collided = true; } _FORCE_INLINE_ SeparatorAxisTest(const ShapeA *p_shape_A, const Transform3D &p_transform_A, const ShapeB *p_shape_B, const Transform3D &p_transform_B, _CollectorCallback *p_callback, real_t p_margin_A = 0, real_t p_margin_B = 0) { 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 *******/ typedef void (*CollisionFunc)(const GodotShape3D *, const Transform3D &, const GodotShape3D *, const Transform3D &, _CollectorCallback *p_callback, real_t, real_t); // Perform analytic sphere-sphere collision and report results to collector template static void analytic_sphere_collision(const Vector3 &p_origin_a, real_t p_radius_a, const Vector3 &p_origin_b, real_t p_radius_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { // Expand the spheres by the margins if enabled if (withMargin) { p_radius_a += p_margin_a; p_radius_b += p_margin_b; } // Get the vector from sphere B to A Vector3 b_to_a = p_origin_a - p_origin_b; // Get the length from B to A real_t b_to_a_len = b_to_a.length(); // Calculate the sphere overlap, and bail if not overlapping real_t overlap = p_radius_a + p_radius_b - b_to_a_len; if (overlap < 0) return; // Report collision p_collector->collided = true; // Bail if there is no callback to receive the A and B collision points. if (!p_collector->callback) { return; } // Normalize the B to A vector if (b_to_a_len < CMP_EPSILON) { b_to_a = Vector3(0, 1, 0); // Spheres coincident, use arbitrary direction } else { b_to_a /= b_to_a_len; } // Report collision points. The operations below are intended to minimize // floating-point precision errors. This is done by calculating the first // collision point from the smaller sphere, and then jumping across to // the larger spheres collision point using the overlap distance. This // jump is usually small even if the large sphere is massive, and so the // second point will not suffer from precision errors. if (p_radius_a < p_radius_b) { Vector3 point_a = p_origin_a - b_to_a * p_radius_a; Vector3 point_b = point_a + b_to_a * overlap; p_collector->call(point_a, point_b); // Consider adding b_to_a vector } else { Vector3 point_b = p_origin_b + b_to_a * p_radius_b; Vector3 point_a = point_b - b_to_a * overlap; p_collector->call(point_a, point_b); // Consider adding b_to_a vector } } template static void _collision_sphere_sphere(const GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotSphereShape3D *sphere_A = static_cast(p_a); const GodotSphereShape3D *sphere_B = static_cast(p_b); // Perform an analytic sphere collision between the two spheres analytic_sphere_collision( p_transform_a.origin, sphere_A->get_radius(), p_transform_b.origin, sphere_B->get_radius(), p_collector, p_margin_a, p_margin_b); } template static void _collision_sphere_box(const GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotSphereShape3D *sphere_A = static_cast(p_a); const GodotBoxShape3D *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_column(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_column(i)).cross(p_transform_b.basis.get_column(i)).normalized(); if (!separator.test_axis(axis)) { return; } } separator.generate_contacts(); } template static void _collision_sphere_capsule(const GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotSphereShape3D *sphere_A = static_cast(p_a); const GodotCapsuleShape3D *capsule_B = static_cast(p_b); real_t capsule_B_radius = capsule_B->get_radius(); // Construct the capsule segment (ball-center to ball-center) Vector3 capsule_segment[2]; Vector3 capsule_axis = p_transform_b.basis.get_column(1) * (capsule_B->get_height() * 0.5 - capsule_B_radius); capsule_segment[0] = p_transform_b.origin + capsule_axis; capsule_segment[1] = p_transform_b.origin - capsule_axis; // Get the capsules closest segment-point to the sphere Vector3 capsule_closest = Geometry3D::get_closest_point_to_segment(p_transform_a.origin, capsule_segment); // Perform an analytic sphere collision between the sphere and the sphere-collider in the capsule analytic_sphere_collision( p_transform_a.origin, sphere_A->get_radius(), capsule_closest, capsule_B_radius, p_collector, p_margin_a, p_margin_b); } template static void _collision_sphere_cylinder(const GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotSphereShape3D *sphere_A = static_cast(p_a); const GodotCylinderShape3D *cylinder_B = static_cast(p_b); SeparatorAxisTest separator(sphere_A, p_transform_a, cylinder_B, p_transform_b, p_collector, p_margin_a, p_margin_b); if (!separator.test_previous_axis()) { return; } // Cylinder B end caps. Vector3 cylinder_B_axis = p_transform_b.basis.get_column(1).normalized(); if (!separator.test_axis(cylinder_B_axis)) { return; } Vector3 cylinder_diff = p_transform_b.origin - p_transform_a.origin; // Cylinder B lateral surface. if (!separator.test_axis(cylinder_B_axis.cross(cylinder_diff).cross(cylinder_B_axis).normalized())) { return; } // Closest point to cylinder caps. const Vector3 &sphere_center = p_transform_a.origin; Vector3 cyl_axis = p_transform_b.basis.get_column(1); Vector3 cap_axis = p_transform_b.basis.get_column(0); real_t height_scale = cyl_axis.length(); real_t cap_dist = cylinder_B->get_height() * 0.5 * height_scale; cyl_axis /= height_scale; real_t radius_scale = cap_axis.length(); real_t cap_radius = cylinder_B->get_radius() * radius_scale; for (int i = 0; i < 2; i++) { Vector3 cap_dir = ((i == 0) ? cyl_axis : -cyl_axis); Vector3 cap_pos = p_transform_b.origin + cap_dir * cap_dist; Vector3 closest_point; Vector3 diff = sphere_center - cap_pos; Vector3 proj = diff - cap_dir.dot(diff) * cap_dir; real_t proj_len = proj.length(); if (Math::is_zero_approx(proj_len)) { // Point is equidistant to all circle points. continue; } closest_point = cap_pos + (cap_radius / proj_len) * proj; if (!separator.test_axis((closest_point - sphere_center).normalized())) { return; } } separator.generate_contacts(); } template static void _collision_sphere_convex_polygon(const GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotSphereShape3D *sphere_A = static_cast(p_a); const GodotConvexPolygonShape3D *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 Geometry3D::MeshData &mesh = convex_polygon_B->get_mesh(); const Geometry3D::MeshData::Face *faces = mesh.faces.ptr(); int face_count = mesh.faces.size(); const Geometry3D::MeshData::Edge *edges = mesh.edges.ptr(); int edge_count = mesh.edges.size(); const Vector3 *vertices = mesh.vertices.ptr(); int vertex_count = mesh.vertices.size(); // Precalculating this makes the transforms faster. Basis b_xform_normal = p_transform_b.basis.inverse().transposed(); // faces of B for (int i = 0; i < face_count; i++) { Vector3 axis = b_xform_normal.xform(faces[i].plane.normal).normalized(); 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].vertex_a]); Vector3 v2 = p_transform_b.xform(vertices[edges[i].vertex_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 GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotSphereShape3D *sphere_A = static_cast(p_a); const GodotFaceShape3D *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]), }; Vector3 normal = (vertex[0] - vertex[2]).cross(vertex[0] - vertex[1]).normalized(); if (!separator.test_axis(normal)) { return; } // edges and points of B for (int i = 0; i < 3; i++) { Vector3 n1 = vertex[i] - p_transform_a.origin; if (n1.dot(normal) < 0.0) { n1 *= -1.0; } if (!separator.test_axis(n1.normalized())) { return; } Vector3 n2 = vertex[(i + 1) % 3] - vertex[i]; Vector3 axis = n1.cross(n2).cross(n2).normalized(); if (axis.dot(normal) < 0.0) { axis *= -1.0; } if (!separator.test_axis(axis)) { return; } } if (!face_B->backface_collision) { if (separator.best_axis.dot(normal) < _BACKFACE_NORMAL_THRESHOLD) { if (face_B->invert_backface_collision) { separator.best_axis = separator.best_axis.bounce(normal); } else { // Just ignore backface collision. return; } } } separator.generate_contacts(); } template static void _collision_box_box(const GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotBoxShape3D *box_A = static_cast(p_a); const GodotBoxShape3D *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_column(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_column(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_column(i).cross(p_transform_b.basis.get_column(j)); if (Math::is_zero_approx(axis.length_squared())) { 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_column(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_column(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 GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotBoxShape3D *box_A = static_cast(p_a); const GodotCapsuleShape3D *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_column(i).normalized(); if (!separator.test_axis(axis)) { return; } } Vector3 cyl_axis = p_transform_b.basis.get_column(1).normalized(); // edges of A, capsule cylinder for (int i = 0; i < 3; i++) { // cylinder Vector3 box_axis = p_transform_a.basis.get_column(i); Vector3 axis = box_axis.cross(cyl_axis); if (Math::is_zero_approx(axis.length_squared())) { 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_column(l) * he[l]; } //Vector3 axis = (point - cyl_axis * cyl_axis.dot(point)).normalized(); Vector3 axis = Plane(cyl_axis).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_column(1) * (capsule_B->get_height() * 0.5 - capsule_B->get_radius()); 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 j = 0; j < 3; j++) { Vector3 axis = point_axis.cross(p_transform_a.basis.get_column(j)).cross(p_transform_a.basis.get_column(j)).normalized(); if (!separator.test_axis(axis)) { return; } } } separator.generate_contacts(); } template static void _collision_box_cylinder(const GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotBoxShape3D *box_A = static_cast(p_a); const GodotCylinderShape3D *cylinder_B = static_cast(p_b); SeparatorAxisTest separator(box_A, p_transform_a, cylinder_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_column(i).normalized(); if (!separator.test_axis(axis)) { return; } } Vector3 cyl_axis = p_transform_b.basis.get_column(1).normalized(); // Cylinder end caps. { if (!separator.test_axis(cyl_axis)) { return; } } // Edges of A, cylinder lateral surface. for (int i = 0; i < 3; i++) { Vector3 box_axis = p_transform_a.basis.get_column(i); Vector3 axis = box_axis.cross(cyl_axis); if (Math::is_zero_approx(axis.length_squared())) { continue; } if (!separator.test_axis(axis.normalized())) { return; } } // Gather points of A. Vector3 vertices_A[8]; Vector3 box_extent = box_A->get_half_extents(); for (int i = 0; i < 2; i++) { for (int j = 0; j < 2; j++) { for (int k = 0; k < 2; k++) { Vector3 extent = box_extent; extent.x *= (i * 2 - 1); extent.y *= (j * 2 - 1); extent.z *= (k * 2 - 1); Vector3 &point = vertices_A[i * 2 * 2 + j * 2 + k]; point = p_transform_a.origin; for (int l = 0; l < 3; l++) { point += p_transform_a.basis.get_column(l) * extent[l]; } } } } // Points of A, cylinder lateral surface. for (int i = 0; i < 8; i++) { const Vector3 &point = vertices_A[i]; Vector3 axis = Plane(cyl_axis).project(point).normalized(); if (!separator.test_axis(axis)) { return; } } // Edges of A, cylinder end caps rim. int edges_start_A[12] = { 0, 2, 4, 6, 0, 1, 4, 5, 0, 1, 2, 3 }; int edges_end_A[12] = { 1, 3, 5, 7, 2, 3, 6, 7, 4, 5, 6, 7 }; Vector3 cap_axis = cyl_axis * (cylinder_B->get_height() * 0.5); for (int i = 0; i < 2; i++) { Vector3 cap_pos = p_transform_b.origin + ((i == 0) ? cap_axis : -cap_axis); for (int e = 0; e < 12; e++) { const Vector3 &edge_start = vertices_A[edges_start_A[e]]; const Vector3 &edge_end = vertices_A[edges_end_A[e]]; Vector3 edge_dir = (edge_end - edge_start); edge_dir.normalize(); real_t edge_dot = edge_dir.dot(cyl_axis); if (Math::is_zero_approx(edge_dot)) { // Edge is perpendicular to cylinder axis. continue; } // Calculate intersection between edge and circle plane. Vector3 edge_diff = cap_pos - edge_start; real_t diff_dot = edge_diff.dot(cyl_axis); Vector3 intersection = edge_start + edge_dir * diff_dot / edge_dot; // Calculate tangent that touches intersection. Vector3 tangent = (cap_pos - intersection).cross(cyl_axis); // Axis is orthogonal both to tangent and edge direction. Vector3 axis = tangent.cross(edge_dir); if (!separator.test_axis(axis.normalized())) { return; } } } separator.generate_contacts(); } template static void _collision_box_convex_polygon(const GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotBoxShape3D *box_A = static_cast(p_a); const GodotConvexPolygonShape3D *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 Geometry3D::MeshData &mesh = convex_polygon_B->get_mesh(); const Geometry3D::MeshData::Face *faces = mesh.faces.ptr(); int face_count = mesh.faces.size(); const Geometry3D::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_column(i).normalized(); if (!separator.test_axis(axis)) { return; } } // Precalculating this makes the transforms faster. Basis b_xform_normal = p_transform_b.basis.inverse().transposed(); // faces of B for (int i = 0; i < face_count; i++) { Vector3 axis = b_xform_normal.xform(faces[i].plane.normal).normalized(); if (!separator.test_axis(axis)) { return; } } // A<->B edges for (int i = 0; i < 3; i++) { Vector3 e1 = p_transform_a.basis.get_column(i); for (int j = 0; j < edge_count; j++) { Vector3 e2 = p_transform_b.basis.xform(vertices[edges[j].vertex_a]) - p_transform_b.basis.xform(vertices[edges[j].vertex_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_column(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_column(l) * he[l]; } for (int e = 0; e < edge_count; e++) { Vector3 p1 = p_transform_b.xform(vertices[edges[e].vertex_a]); Vector3 p2 = p_transform_b.xform(vertices[edges[e].vertex_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 GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotBoxShape3D *box_A = static_cast(p_a); const GodotFaceShape3D *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]), }; Vector3 normal = (vertex[0] - vertex[2]).cross(vertex[0] - vertex[1]).normalized(); if (!separator.test_axis(normal)) { return; } // faces of A for (int i = 0; i < 3; i++) { Vector3 axis = p_transform_a.basis.get_column(i).normalized(); if (axis.dot(normal) < 0.0) { axis *= -1.0; } 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 = e.cross(p_transform_a.basis.get_column(j)).normalized(); if (axis.dot(normal) < 0.0) { axis *= -1.0; } if (!separator.test_axis(axis)) { 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 (axis_ab.dot(normal) < 0.0) { axis_ab *= -1.0; } 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_column(i); Vector3 axis = axis_ab.cross(axis_a).cross(axis_a).normalized(); if (axis.dot(normal) < 0.0) { axis *= -1.0; } if (!separator.test_axis(axis)) { 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_column(l) * he[l]; } for (int e = 0; e < 3; e++) { Vector3 p1 = vertex[e]; Vector3 p2 = vertex[(e + 1) % 3]; Vector3 n = (p2 - p1); Vector3 axis = (point - p2).cross(n).cross(n).normalized(); if (axis.dot(normal) < 0.0) { axis *= -1.0; } if (!separator.test_axis(axis)) { return; } } } } } } if (!face_B->backface_collision) { if (separator.best_axis.dot(normal) < _BACKFACE_NORMAL_THRESHOLD) { if (face_B->invert_backface_collision) { separator.best_axis = separator.best_axis.bounce(normal); } else { // Just ignore backface collision. return; } } } separator.generate_contacts(); } template static void _collision_capsule_capsule(const GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotCapsuleShape3D *capsule_A = static_cast(p_a); const GodotCapsuleShape3D *capsule_B = static_cast(p_b); real_t capsule_A_radius = capsule_A->get_radius(); real_t capsule_B_radius = capsule_B->get_radius(); // Get the closest points between the capsule segments Vector3 capsule_A_closest; Vector3 capsule_B_closest; Vector3 capsule_A_axis = p_transform_a.basis.get_column(1) * (capsule_A->get_height() * 0.5 - capsule_A_radius); Vector3 capsule_B_axis = p_transform_b.basis.get_column(1) * (capsule_B->get_height() * 0.5 - capsule_B_radius); Geometry3D::get_closest_points_between_segments( p_transform_a.origin + capsule_A_axis, p_transform_a.origin - capsule_A_axis, p_transform_b.origin + capsule_B_axis, p_transform_b.origin - capsule_B_axis, capsule_A_closest, capsule_B_closest); // Perform the analytic collision between the two closest capsule spheres analytic_sphere_collision( capsule_A_closest, capsule_A_radius, capsule_B_closest, capsule_B_radius, p_collector, p_margin_a, p_margin_b); } template static void _collision_capsule_cylinder(const GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotCapsuleShape3D *capsule_A = static_cast(p_a); const GodotCylinderShape3D *cylinder_B = static_cast(p_b); SeparatorAxisTest separator(capsule_A, p_transform_a, cylinder_B, p_transform_b, p_collector, p_margin_a, p_margin_b); if (!separator.test_previous_axis()) { return; } // Cylinder B end caps. Vector3 cylinder_B_axis = p_transform_b.basis.get_column(1).normalized(); if (!separator.test_axis(cylinder_B_axis)) { return; } // Cylinder edge against capsule balls. Vector3 capsule_A_axis = p_transform_a.basis.get_column(1); Vector3 capsule_A_ball_1 = p_transform_a.origin + capsule_A_axis * (capsule_A->get_height() * 0.5 - capsule_A->get_radius()); Vector3 capsule_A_ball_2 = p_transform_a.origin - capsule_A_axis * (capsule_A->get_height() * 0.5 - capsule_A->get_radius()); if (!separator.test_axis((p_transform_b.origin - capsule_A_ball_1).cross(cylinder_B_axis).cross(cylinder_B_axis).normalized())) { return; } if (!separator.test_axis((p_transform_b.origin - capsule_A_ball_2).cross(cylinder_B_axis).cross(cylinder_B_axis).normalized())) { return; } // Cylinder edge against capsule edge. Vector3 center_diff = p_transform_b.origin - p_transform_a.origin; if (!separator.test_axis(capsule_A_axis.cross(center_diff).cross(capsule_A_axis).normalized())) { return; } if (!separator.test_axis(cylinder_B_axis.cross(center_diff).cross(cylinder_B_axis).normalized())) { return; } real_t proj = capsule_A_axis.cross(cylinder_B_axis).cross(cylinder_B_axis).dot(capsule_A_axis); if (Math::is_zero_approx(proj)) { // Parallel capsule and cylinder axes, handle with specific axes only. // Note: GJKEPA with no margin can lead to degenerate cases in this situation. separator.generate_contacts(); return; } GodotCollisionSolver3D::CallbackResult callback = SeparatorAxisTest::test_contact_points; // Fallback to generic algorithm to find the best separating axis. if (!fallback_collision_solver(p_a, p_transform_a, p_b, p_transform_b, callback, &separator, false, p_margin_a, p_margin_b)) { return; } separator.generate_contacts(); } template static void _collision_capsule_convex_polygon(const GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotCapsuleShape3D *capsule_A = static_cast(p_a); const GodotConvexPolygonShape3D *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 Geometry3D::MeshData &mesh = convex_polygon_B->get_mesh(); const Geometry3D::MeshData::Face *faces = mesh.faces.ptr(); int face_count = mesh.faces.size(); const Geometry3D::MeshData::Edge *edges = mesh.edges.ptr(); int edge_count = mesh.edges.size(); const Vector3 *vertices = mesh.vertices.ptr(); // Precalculating this makes the transforms faster. Basis b_xform_normal = p_transform_b.basis.inverse().transposed(); // faces of B for (int i = 0; i < face_count; i++) { Vector3 axis = b_xform_normal.xform(faces[i].plane.normal).normalized(); 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].vertex_a]) - p_transform_b.basis.xform(vertices[edges[i].vertex_b]); Vector3 axis = edge_axis.cross(p_transform_a.basis.get_column(1)).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_column(1) * (capsule_A->get_height() * 0.5 - capsule_A->get_radius()); 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].vertex_a]); Vector3 n2 = p_transform_b.basis.xform(vertices[edges[j].vertex_a]) - p_transform_b.basis.xform(vertices[edges[j].vertex_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 GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotCapsuleShape3D *capsule_A = static_cast(p_a); const GodotFaceShape3D *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]), }; Vector3 normal = (vertex[0] - vertex[2]).cross(vertex[0] - vertex[1]).normalized(); if (!separator.test_axis(normal)) { return; } // edges of B, capsule cylinder Vector3 capsule_axis = p_transform_a.basis.get_column(1) * (capsule_A->get_height() * 0.5 - capsule_A->get_radius()); 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 (axis.dot(normal) < 0.0) { axis *= -1.0; } if (!separator.test_axis(axis)) { return; } Vector3 dir_axis = (p_transform_a.origin - vertex[i]).cross(capsule_axis).cross(capsule_axis).normalized(); if (dir_axis.dot(normal) < 0.0) { dir_axis *= -1.0; } if (!separator.test_axis(dir_axis)) { 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 (n1.dot(normal) < 0.0) { n1 *= -1.0; } if (!separator.test_axis(n1.normalized())) { return; } Vector3 n2 = edge_axis; axis = n1.cross(n2).cross(n2); if (axis.dot(normal) < 0.0) { axis *= -1.0; } if (!separator.test_axis(axis.normalized())) { return; } } } if (!face_B->backface_collision) { if (separator.best_axis.dot(normal) < _BACKFACE_NORMAL_THRESHOLD) { if (face_B->invert_backface_collision) { separator.best_axis = separator.best_axis.bounce(normal); } else { // Just ignore backface collision. return; } } } separator.generate_contacts(); } template static void _collision_cylinder_cylinder(const GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotCylinderShape3D *cylinder_A = static_cast(p_a); const GodotCylinderShape3D *cylinder_B = static_cast(p_b); SeparatorAxisTest separator(cylinder_A, p_transform_a, cylinder_B, p_transform_b, p_collector, p_margin_a, p_margin_b); Vector3 cylinder_A_axis = p_transform_a.basis.get_column(1); Vector3 cylinder_B_axis = p_transform_b.basis.get_column(1); if (!separator.test_previous_axis()) { return; } // Cylinder A end caps. if (!separator.test_axis(cylinder_A_axis.normalized())) { return; } // Cylinder B end caps. if (!separator.test_axis(cylinder_B_axis.normalized())) { return; } Vector3 cylinder_diff = p_transform_b.origin - p_transform_a.origin; // Cylinder A lateral surface. if (!separator.test_axis(cylinder_A_axis.cross(cylinder_diff).cross(cylinder_A_axis).normalized())) { return; } // Cylinder B lateral surface. if (!separator.test_axis(cylinder_B_axis.cross(cylinder_diff).cross(cylinder_B_axis).normalized())) { return; } real_t proj = cylinder_A_axis.cross(cylinder_B_axis).cross(cylinder_B_axis).dot(cylinder_A_axis); if (Math::is_zero_approx(proj)) { // Parallel cylinders, handle with specific axes only. // Note: GJKEPA with no margin can lead to degenerate cases in this situation. separator.generate_contacts(); return; } GodotCollisionSolver3D::CallbackResult callback = SeparatorAxisTest::test_contact_points; // Fallback to generic algorithm to find the best separating axis. if (!fallback_collision_solver(p_a, p_transform_a, p_b, p_transform_b, callback, &separator, false, p_margin_a, p_margin_b)) { return; } separator.generate_contacts(); } template static void _collision_cylinder_convex_polygon(const GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotCylinderShape3D *cylinder_A = static_cast(p_a); const GodotConvexPolygonShape3D *convex_polygon_B = static_cast(p_b); SeparatorAxisTest separator(cylinder_A, p_transform_a, convex_polygon_B, p_transform_b, p_collector, p_margin_a, p_margin_b); GodotCollisionSolver3D::CallbackResult callback = SeparatorAxisTest::test_contact_points; // Fallback to generic algorithm to find the best separating axis. if (!fallback_collision_solver(p_a, p_transform_a, p_b, p_transform_b, callback, &separator, false, p_margin_a, p_margin_b)) { return; } separator.generate_contacts(); } template static void _collision_cylinder_face(const GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotCylinderShape3D *cylinder_A = static_cast(p_a); const GodotFaceShape3D *face_B = static_cast(p_b); SeparatorAxisTest separator(cylinder_A, p_transform_a, face_B, p_transform_b, p_collector, p_margin_a, p_margin_b); if (!separator.test_previous_axis()) { return; } 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]), }; Vector3 normal = (vertex[0] - vertex[2]).cross(vertex[0] - vertex[1]).normalized(); // Face B normal. if (!separator.test_axis(normal)) { return; } Vector3 cyl_axis = p_transform_a.basis.get_column(1).normalized(); if (cyl_axis.dot(normal) < 0.0) { cyl_axis *= -1.0; } // Cylinder end caps. if (!separator.test_axis(cyl_axis)) { return; } // Edges of B, cylinder lateral surface. for (int i = 0; i < 3; i++) { Vector3 edge_axis = vertex[i] - vertex[(i + 1) % 3]; Vector3 axis = edge_axis.cross(cyl_axis); if (Math::is_zero_approx(axis.length_squared())) { continue; } if (axis.dot(normal) < 0.0) { axis *= -1.0; } if (!separator.test_axis(axis.normalized())) { return; } } // Points of B, cylinder lateral surface. for (int i = 0; i < 3; i++) { const Vector3 &point = vertex[i]; Vector3 axis = Plane(cyl_axis).project(point).normalized(); if (axis.dot(normal) < 0.0) { axis *= -1.0; } if (!separator.test_axis(axis)) { return; } } // Edges of B, cylinder end caps rim. Vector3 cap_axis = cyl_axis * (cylinder_A->get_height() * 0.5); for (int i = 0; i < 2; i++) { Vector3 cap_pos = p_transform_a.origin + ((i == 0) ? cap_axis : -cap_axis); for (int j = 0; j < 3; j++) { const Vector3 &edge_start = vertex[j]; const Vector3 &edge_end = vertex[(j + 1) % 3]; Vector3 edge_dir = edge_end - edge_start; edge_dir.normalize(); real_t edge_dot = edge_dir.dot(cyl_axis); if (Math::is_zero_approx(edge_dot)) { // Edge is perpendicular to cylinder axis. continue; } // Calculate intersection between edge and circle plane. Vector3 edge_diff = cap_pos - edge_start; real_t diff_dot = edge_diff.dot(cyl_axis); Vector3 intersection = edge_start + edge_dir * diff_dot / edge_dot; // Calculate tangent that touches intersection. Vector3 tangent = (cap_pos - intersection).cross(cyl_axis); // Axis is orthogonal both to tangent and edge direction. Vector3 axis = tangent.cross(edge_dir); if (axis.dot(normal) < 0.0) { axis *= -1.0; } if (!separator.test_axis(axis.normalized())) { return; } } } if (!face_B->backface_collision) { if (separator.best_axis.dot(normal) < _BACKFACE_NORMAL_THRESHOLD) { if (face_B->invert_backface_collision) { separator.best_axis = separator.best_axis.bounce(normal); } else { // Just ignore backface collision. return; } } } separator.generate_contacts(); } static _FORCE_INLINE_ bool is_minkowski_face(const Vector3 &A, const Vector3 &B, const Vector3 &B_x_A, const Vector3 &C, const Vector3 &D, const Vector3 &D_x_C) { // Test if arcs AB and CD intersect on the unit sphere real_t CBA = C.dot(B_x_A); real_t DBA = D.dot(B_x_A); real_t ADC = A.dot(D_x_C); real_t BDC = B.dot(D_x_C); return (CBA * DBA < 0.0f) && (ADC * BDC < 0.0f) && (CBA * BDC > 0.0f); } template static void _collision_convex_polygon_convex_polygon(const GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotConvexPolygonShape3D *convex_polygon_A = static_cast(p_a); const GodotConvexPolygonShape3D *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 Geometry3D::MeshData &mesh_A = convex_polygon_A->get_mesh(); const Geometry3D::MeshData::Face *faces_A = mesh_A.faces.ptr(); int face_count_A = mesh_A.faces.size(); const Geometry3D::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 Geometry3D::MeshData &mesh_B = convex_polygon_B->get_mesh(); const Geometry3D::MeshData::Face *faces_B = mesh_B.faces.ptr(); int face_count_B = mesh_B.faces.size(); const Geometry3D::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(); // Precalculating this makes the transforms faster. Basis a_xform_normal = p_transform_b.basis.inverse().transposed(); // faces of A for (int i = 0; i < face_count_A; i++) { Vector3 axis = a_xform_normal.xform(faces_A[i].plane.normal).normalized(); if (!separator.test_axis(axis)) { return; } } // Precalculating this makes the transforms faster. Basis b_xform_normal = p_transform_b.basis.inverse().transposed(); // faces of B for (int i = 0; i < face_count_B; i++) { Vector3 axis = b_xform_normal.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 p1 = p_transform_a.xform(vertices_A[edges_A[i].vertex_a]); Vector3 q1 = p_transform_a.xform(vertices_A[edges_A[i].vertex_b]); Vector3 e1 = q1 - p1; Vector3 u1 = p_transform_a.basis.xform(faces_A[edges_A[i].face_a].plane.normal).normalized(); Vector3 v1 = p_transform_a.basis.xform(faces_A[edges_A[i].face_b].plane.normal).normalized(); for (int j = 0; j < edge_count_B; j++) { Vector3 p2 = p_transform_b.xform(vertices_B[edges_B[j].vertex_a]); Vector3 q2 = p_transform_b.xform(vertices_B[edges_B[j].vertex_b]); Vector3 e2 = q2 - p2; Vector3 u2 = p_transform_b.basis.xform(faces_B[edges_B[j].face_a].plane.normal).normalized(); Vector3 v2 = p_transform_b.basis.xform(faces_B[edges_B[j].face_b].plane.normal).normalized(); if (is_minkowski_face(u1, v1, -e1, -u2, -v2, -e2)) { 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 (shell) for (int i = 0; i < edge_count_A; i++) { Vector3 e1 = p_transform_a.basis.xform(vertices_A[edges_A[i].vertex_a]); Vector3 e2 = p_transform_a.basis.xform(vertices_A[edges_A[i].vertex_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].vertex_a]); Vector3 e2 = p_transform_b.basis.xform(vertices_B[edges_B[i].vertex_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 GodotShape3D *p_a, const Transform3D &p_transform_a, const GodotShape3D *p_b, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) { const GodotConvexPolygonShape3D *convex_polygon_A = static_cast(p_a); const GodotFaceShape3D *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 Geometry3D::MeshData &mesh = convex_polygon_A->get_mesh(); const Geometry3D::MeshData::Face *faces = mesh.faces.ptr(); int face_count = mesh.faces.size(); const Geometry3D::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]), }; Vector3 normal = (vertex[0] - vertex[2]).cross(vertex[0] - vertex[1]).normalized(); if (!separator.test_axis(normal)) { 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 (axis.dot(normal) < 0.0) { axis *= -1.0; } 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].vertex_a]) - p_transform_a.xform(vertices[edges[i].vertex_b]); for (int j = 0; j < 3; j++) { Vector3 e2 = vertex[j] - vertex[(j + 1) % 3]; Vector3 axis = e1.cross(e2).normalized(); if (axis.dot(normal) < 0.0) { axis *= -1.0; } 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++) { Vector3 axis = (va - vertex[j]).normalized(); if (axis.dot(normal) < 0.0) { axis *= -1.0; } if (!separator.test_axis(axis)) { return; } } } //edge-vertex (shell) for (int i = 0; i < edge_count; i++) { Vector3 e1 = p_transform_a.basis.xform(vertices[edges[i].vertex_a]); Vector3 e2 = p_transform_a.basis.xform(vertices[edges[i].vertex_b]); Vector3 n = (e2 - e1); for (int j = 0; j < 3; j++) { Vector3 e3 = vertex[j]; Vector3 axis = (e1 - e3).cross(n).cross(n).normalized(); if (axis.dot(normal) < 0.0) { axis *= -1.0; } if (!separator.test_axis(axis)) { 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]); Vector3 axis = (e1 - e3).cross(n).cross(n).normalized(); if (axis.dot(normal) < 0.0) { axis *= -1.0; } if (!separator.test_axis(axis)) { return; } } } } if (!face_B->backface_collision) { if (separator.best_axis.dot(normal) < _BACKFACE_NORMAL_THRESHOLD) { if (face_B->invert_backface_collision) { separator.best_axis = separator.best_axis.bounce(normal); } else { // Just ignore backface collision. return; } } } separator.generate_contacts(); } bool sat_calculate_penetration(const GodotShape3D *p_shape_A, const Transform3D &p_transform_A, const GodotShape3D *p_shape_B, const Transform3D &p_transform_B, GodotCollisionSolver3D::CallbackResult p_result_callback, void *p_userdata, bool p_swap, Vector3 *r_prev_axis, real_t p_margin_a, real_t p_margin_b) { PhysicsServer3D::ShapeType type_A = p_shape_A->get_type(); ERR_FAIL_COND_V(type_A == PhysicsServer3D::SHAPE_WORLD_BOUNDARY, false); ERR_FAIL_COND_V(type_A == PhysicsServer3D::SHAPE_SEPARATION_RAY, false); ERR_FAIL_COND_V(p_shape_A->is_concave(), false); PhysicsServer3D::ShapeType type_B = p_shape_B->get_type(); ERR_FAIL_COND_V(type_B == PhysicsServer3D::SHAPE_WORLD_BOUNDARY, false); ERR_FAIL_COND_V(type_B == PhysicsServer3D::SHAPE_SEPARATION_RAY, false); ERR_FAIL_COND_V(p_shape_B->is_concave(), false); static const CollisionFunc collision_table[6][6] = { { _collision_sphere_sphere, _collision_sphere_box, _collision_sphere_capsule, _collision_sphere_cylinder, _collision_sphere_convex_polygon, _collision_sphere_face }, { nullptr, _collision_box_box, _collision_box_capsule, _collision_box_cylinder, _collision_box_convex_polygon, _collision_box_face }, { nullptr, nullptr, _collision_capsule_capsule, _collision_capsule_cylinder, _collision_capsule_convex_polygon, _collision_capsule_face }, { nullptr, nullptr, nullptr, _collision_cylinder_cylinder, _collision_cylinder_convex_polygon, _collision_cylinder_face }, { nullptr, nullptr, nullptr, nullptr, _collision_convex_polygon_convex_polygon, _collision_convex_polygon_face }, { nullptr, nullptr, nullptr, nullptr, nullptr, nullptr }, }; static const CollisionFunc collision_table_margin[6][6] = { { _collision_sphere_sphere, _collision_sphere_box, _collision_sphere_capsule, _collision_sphere_cylinder, _collision_sphere_convex_polygon, _collision_sphere_face }, { nullptr, _collision_box_box, _collision_box_capsule, _collision_box_cylinder, _collision_box_convex_polygon, _collision_box_face }, { nullptr, nullptr, _collision_capsule_capsule, _collision_capsule_cylinder, _collision_capsule_convex_polygon, _collision_capsule_face }, { nullptr, nullptr, nullptr, _collision_cylinder_cylinder, _collision_cylinder_convex_polygon, _collision_cylinder_face }, { nullptr, nullptr, nullptr, nullptr, _collision_convex_polygon_convex_polygon, _collision_convex_polygon_face }, { nullptr, nullptr, nullptr, nullptr, nullptr, nullptr }, }; _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 GodotShape3D *A = p_shape_A; const GodotShape3D *B = p_shape_B; const Transform3D *transform_A = &p_transform_A; const Transform3D *transform_B = &p_transform_B; real_t margin_A = p_margin_a; real_t 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; }