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godot/servers/physics_3d/godot_collision_solver_3d_sat.cpp
Markus Mikonsaari 3f69af9e64 Fix separating axes for 3D cylinder-face collisions 
When checking for lateral surfaces of a cylinder against the points on a
face, the axis projection does not remove the cylinder position. This
results in the axis pointing to the wrong direction and reports
collisions when there shouldn't be.
2024-04-01 21:47:54 +03:00

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/**************************************************************************/
/* 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, Vector3 p_normal) {
if (p_normal.dot(p_point_B - p_point_A) < 0)
p_normal = -p_normal;
if (swap) {
callback(p_point_B, 0, p_point_A, 0, -p_normal, userdata);
} else {
callback(p_point_A, 0, p_point_B, 0, p_normal, 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, p_callback->normal);
}
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, p_callback->normal);
}
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
Plane plane(p_points_B[0], p_points_B[1], p_points_B[2]);
Vector3 closest_B = plane.project(*p_points_A);
p_callback->call(*p_points_A, closest_B, plane.get_normal());
}
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
Plane plane(p_points_B[0], p_points_B[1], p_points_B[2]);
Vector3 closest_B = plane.project(*p_points_A);
p_callback->call(*p_points_A, closest_B, plane.get_normal());
}
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<real_t> 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->normal);
p_callback->call(base_A + axis * dvec[2], base_B + axis * dvec[2], p_callback->normal);
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);
// The normal should be perpendicular to both edges.
Vector3 normal = rel_A.cross(rel_B);
real_t normal_len = normal.length();
if (normal_len > 1e-3)
normal /= normal_len;
else
normal = p_callback->normal;
p_callback->call(closest_A, closest_B, normal);
}
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, circle_plane.get_normal());
}
}
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, plane_B.get_normal());
}
}
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, circle_plane.get_normal());
}
}
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, circle_B_plane.get_normal());
}
}
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_NULL(contacts_func);
contacts_func(points_A, pointcount_A, points_B, pointcount_B, p_callback);
}
template <typename ShapeA, typename ShapeB, bool withMargin = false>
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, const Vector3 &normal, void *p_userdata) {
SeparatorAxisTest<ShapeA, ShapeB, withMargin> *separator = (SeparatorAxisTest<ShapeA, ShapeB, withMargin> *)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 <bool withMargin>
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, b_to_a); // 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, b_to_a); // Consider adding b_to_a vector
}
}
template <bool withMargin>
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<const GodotSphereShape3D *>(p_a);
const GodotSphereShape3D *sphere_B = static_cast<const GodotSphereShape3D *>(p_b);
// Perform an analytic sphere collision between the two spheres
analytic_sphere_collision<withMargin>(
p_transform_a.origin,
sphere_A->get_radius() * p_transform_a.basis[0].length(),
p_transform_b.origin,
sphere_B->get_radius() * p_transform_b.basis[0].length(),
p_collector,
p_margin_a,
p_margin_b);
}
template <bool withMargin>
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<const GodotSphereShape3D *>(p_a);
const GodotBoxShape3D *box_B = static_cast<const GodotBoxShape3D *>(p_b);
// Find the point on the box nearest to the center of the sphere.
Vector3 center = p_transform_b.affine_inverse().xform(p_transform_a.origin);
Vector3 extents = box_B->get_half_extents();
Vector3 nearest(MIN(MAX(center.x, -extents.x), extents.x),
MIN(MAX(center.y, -extents.y), extents.y),
MIN(MAX(center.z, -extents.z), extents.z));
nearest = p_transform_b.xform(nearest);
// See if it is inside the sphere.
Vector3 delta = nearest - p_transform_a.origin;
real_t length = delta.length();
real_t radius = sphere_A->get_radius() * p_transform_a.basis[0].length();
if (length > radius + p_margin_a + p_margin_b) {
return;
}
p_collector->collided = true;
if (!p_collector->callback) {
return;
}
Vector3 axis;
if (length == 0) {
// The box passes through the sphere center. Select an axis based on the box's center.
axis = (p_transform_b.origin - nearest).normalized();
} else {
axis = delta / length;
}
Vector3 point_a = p_transform_a.origin + (radius + p_margin_a) * axis;
Vector3 point_b = (withMargin ? nearest - p_margin_b * axis : nearest);
p_collector->call(point_a, point_b, axis);
}
template <bool withMargin>
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<const GodotSphereShape3D *>(p_a);
const GodotCapsuleShape3D *capsule_B = static_cast<const GodotCapsuleShape3D *>(p_b);
real_t scale_A = p_transform_a.basis[0].length();
real_t scale_B = p_transform_b.basis[0].length();
// 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->get_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<withMargin>(
p_transform_a.origin,
sphere_A->get_radius() * scale_A,
capsule_closest,
capsule_B->get_radius() * scale_B,
p_collector,
p_margin_a,
p_margin_b);
}
template <bool withMargin>
static void analytic_sphere_cylinder_collision(real_t p_radius_a, real_t p_radius_b, real_t p_height_b, const Transform3D &p_transform_a, const Transform3D &p_transform_b, _CollectorCallback *p_collector, real_t p_margin_a, real_t p_margin_b) {
// Find the point on the cylinder nearest to the center of the sphere.
Vector3 center = p_transform_b.affine_inverse().xform(p_transform_a.origin);
Vector3 nearest = center;
real_t scale_A = p_transform_a.basis[0].length();
real_t r = Math::sqrt(center.x * center.x + center.z * center.z);
if (r > p_radius_b) {
real_t scale = p_radius_b / r;
nearest.x *= scale;
nearest.z *= scale;
}
real_t half_height = p_height_b / 2;
nearest.y = MIN(MAX(center.y, -half_height), half_height);
nearest = p_transform_b.xform(nearest);
// See if it is inside the sphere.
Vector3 delta = nearest - p_transform_a.origin;
real_t length = delta.length();
if (length > p_radius_a * scale_A + p_margin_a + p_margin_b) {
return;
}
p_collector->collided = true;
if (!p_collector->callback) {
return;
}
Vector3 axis;
if (length == 0) {
// The cylinder passes through the sphere center. Select an axis based on the cylinder's center.
axis = (p_transform_b.origin - nearest).normalized();
} else {
axis = delta / length;
}
Vector3 point_a = p_transform_a.origin + (p_radius_a * scale_A + p_margin_a) * axis;
Vector3 point_b = (withMargin ? nearest - p_margin_b * axis : nearest);
p_collector->call(point_a, point_b, axis);
}
template <bool withMargin>
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<const GodotSphereShape3D *>(p_a);
const GodotCylinderShape3D *cylinder_B = static_cast<const GodotCylinderShape3D *>(p_b);
analytic_sphere_cylinder_collision<withMargin>(sphere_A->get_radius(), cylinder_B->get_radius(), cylinder_B->get_height(), p_transform_a, p_transform_b, p_collector, p_margin_a, p_margin_b);
}
template <bool withMargin>
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<const GodotSphereShape3D *>(p_a);
const GodotConvexPolygonShape3D *convex_polygon_B = static_cast<const GodotConvexPolygonShape3D *>(p_b);
SeparatorAxisTest<GodotSphereShape3D, GodotConvexPolygonShape3D, withMargin> 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 <bool withMargin>
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<const GodotSphereShape3D *>(p_a);
const GodotFaceShape3D *face_B = static_cast<const GodotFaceShape3D *>(p_b);
SeparatorAxisTest<GodotSphereShape3D, GodotFaceShape3D, withMargin> 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 <bool withMargin>
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<const GodotBoxShape3D *>(p_a);
const GodotBoxShape3D *box_B = static_cast<const GodotBoxShape3D *>(p_b);
SeparatorAxisTest<GodotBoxShape3D, GodotBoxShape3D, withMargin> 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 <bool withMargin>
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<const GodotBoxShape3D *>(p_a);
const GodotCapsuleShape3D *capsule_B = static_cast<const GodotCapsuleShape3D *>(p_b);
SeparatorAxisTest<GodotBoxShape3D, GodotCapsuleShape3D, withMargin> 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 <bool withMargin>
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<const GodotBoxShape3D *>(p_a);
const GodotCylinderShape3D *cylinder_B = static_cast<const GodotCylinderShape3D *>(p_b);
SeparatorAxisTest<GodotBoxShape3D, GodotCylinderShape3D, withMargin> 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 <bool withMargin>
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<const GodotBoxShape3D *>(p_a);
const GodotConvexPolygonShape3D *convex_polygon_B = static_cast<const GodotConvexPolygonShape3D *>(p_b);
SeparatorAxisTest<GodotBoxShape3D, GodotConvexPolygonShape3D, withMargin> 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 <bool withMargin>
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<const GodotBoxShape3D *>(p_a);
const GodotFaceShape3D *face_B = static_cast<const GodotFaceShape3D *>(p_b);
SeparatorAxisTest<GodotBoxShape3D, GodotFaceShape3D, withMargin> 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 <bool withMargin>
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<const GodotCapsuleShape3D *>(p_a);
const GodotCapsuleShape3D *capsule_B = static_cast<const GodotCapsuleShape3D *>(p_b);
real_t scale_A = p_transform_a.basis[0].length();
real_t scale_B = p_transform_b.basis[0].length();
// 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->get_radius());
Vector3 capsule_B_axis = p_transform_b.basis.get_column(1) * (capsule_B->get_height() * 0.5 - capsule_B->get_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<withMargin>(
capsule_A_closest,
capsule_A->get_radius() * scale_A,
capsule_B_closest,
capsule_B->get_radius() * scale_B,
p_collector,
p_margin_a,
p_margin_b);
}
template <bool withMargin>
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<const GodotCapsuleShape3D *>(p_a);
const GodotCylinderShape3D *cylinder_B = static_cast<const GodotCylinderShape3D *>(p_b);
// Find the closest points between the axes of the two objects.
Vector3 capsule_A_closest;
Vector3 cylinder_B_closest;
Vector3 capsule_A_axis = p_transform_a.basis.get_column(1) * (capsule_A->get_height() * 0.5 - capsule_A->get_radius());
Vector3 cylinder_B_axis = p_transform_b.basis.get_column(1) * (cylinder_B->get_height() * 0.5);
Geometry3D::get_closest_points_between_segments(
p_transform_a.origin + capsule_A_axis,
p_transform_a.origin - capsule_A_axis,
p_transform_b.origin + cylinder_B_axis,
p_transform_b.origin - cylinder_B_axis,
capsule_A_closest,
cylinder_B_closest);
// Perform the collision test between the cylinder and the nearest sphere on the capsule axis.
Transform3D sphere_transform(p_transform_a.basis, capsule_A_closest);
analytic_sphere_cylinder_collision<withMargin>(capsule_A->get_radius(), cylinder_B->get_radius(), cylinder_B->get_height(), sphere_transform, p_transform_b, p_collector, p_margin_a, p_margin_b);
}
template <bool withMargin>
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<const GodotCapsuleShape3D *>(p_a);
const GodotConvexPolygonShape3D *convex_polygon_B = static_cast<const GodotConvexPolygonShape3D *>(p_b);
SeparatorAxisTest<GodotCapsuleShape3D, GodotConvexPolygonShape3D, withMargin> 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 <bool withMargin>
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<const GodotCapsuleShape3D *>(p_a);
const GodotFaceShape3D *face_B = static_cast<const GodotFaceShape3D *>(p_b);
SeparatorAxisTest<GodotCapsuleShape3D, GodotFaceShape3D, withMargin> 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 <bool withMargin>
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<const GodotCylinderShape3D *>(p_a);
const GodotCylinderShape3D *cylinder_B = static_cast<const GodotCylinderShape3D *>(p_b);
SeparatorAxisTest<GodotCylinderShape3D, GodotCylinderShape3D, withMargin> 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<GodotCylinderShape3D, GodotCylinderShape3D, withMargin>::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 <bool withMargin>
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<const GodotCylinderShape3D *>(p_a);
const GodotConvexPolygonShape3D *convex_polygon_B = static_cast<const GodotConvexPolygonShape3D *>(p_b);
SeparatorAxisTest<GodotCylinderShape3D, GodotConvexPolygonShape3D, withMargin> separator(cylinder_A, p_transform_a, convex_polygon_B, p_transform_b, p_collector, p_margin_a, p_margin_b);
GodotCollisionSolver3D::CallbackResult callback = SeparatorAxisTest<GodotCylinderShape3D, GodotConvexPolygonShape3D, withMargin>::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 <bool withMargin>
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<const GodotCylinderShape3D *>(p_a);
const GodotFaceShape3D *face_B = static_cast<const GodotFaceShape3D *>(p_b);
SeparatorAxisTest<GodotCylinderShape3D, GodotFaceShape3D, withMargin> 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] - p_transform_a.origin;
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 <bool withMargin>
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<const GodotConvexPolygonShape3D *>(p_a);
const GodotConvexPolygonShape3D *convex_polygon_B = static_cast<const GodotConvexPolygonShape3D *>(p_b);
SeparatorAxisTest<GodotConvexPolygonShape3D, GodotConvexPolygonShape3D, withMargin> 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_a.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 <bool withMargin>
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<const GodotConvexPolygonShape3D *>(p_a);
const GodotFaceShape3D *face_B = static_cast<const GodotFaceShape3D *>(p_b);
SeparatorAxisTest<GodotConvexPolygonShape3D, GodotFaceShape3D, withMargin> 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<false>,
_collision_sphere_box<false>,
_collision_sphere_capsule<false>,
_collision_sphere_cylinder<false>,
_collision_sphere_convex_polygon<false>,
_collision_sphere_face<false> },
{ nullptr,
_collision_box_box<false>,
_collision_box_capsule<false>,
_collision_box_cylinder<false>,
_collision_box_convex_polygon<false>,
_collision_box_face<false> },
{ nullptr,
nullptr,
_collision_capsule_capsule<false>,
_collision_capsule_cylinder<false>,
_collision_capsule_convex_polygon<false>,
_collision_capsule_face<false> },
{ nullptr,
nullptr,
nullptr,
_collision_cylinder_cylinder<false>,
_collision_cylinder_convex_polygon<false>,
_collision_cylinder_face<false> },
{ nullptr,
nullptr,
nullptr,
nullptr,
_collision_convex_polygon_convex_polygon<false>,
_collision_convex_polygon_face<false> },
{ nullptr,
nullptr,
nullptr,
nullptr,
nullptr,
nullptr },
};
static const CollisionFunc collision_table_margin[6][6] = {
{ _collision_sphere_sphere<true>,
_collision_sphere_box<true>,
_collision_sphere_capsule<true>,
_collision_sphere_cylinder<true>,
_collision_sphere_convex_polygon<true>,
_collision_sphere_face<true> },
{ nullptr,
_collision_box_box<true>,
_collision_box_capsule<true>,
_collision_box_cylinder<true>,
_collision_box_convex_polygon<true>,
_collision_box_face<true> },
{ nullptr,
nullptr,
_collision_capsule_capsule<true>,
_collision_capsule_cylinder<true>,
_collision_capsule_convex_polygon<true>,
_collision_capsule_face<true> },
{ nullptr,
nullptr,
nullptr,
_collision_cylinder_cylinder<true>,
_collision_cylinder_convex_polygon<true>,
_collision_cylinder_face<true> },
{ nullptr,
nullptr,
nullptr,
nullptr,
_collision_convex_polygon_convex_polygon<true>,
_collision_convex_polygon_face<true> },
{ 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_NULL_V(collision_func, false);
collision_func(A, *transform_A, B, *transform_B, &callback, margin_A, margin_B);
return callback.collided;
}
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