Merge pull request #50637 from lawnjelly/fix_plane_xform_new

Fix Transform::xform(Plane) functions, add Transform unit tests

core/math/transform.h

@@ -76,16 +76,24 @@ public:
 	bool operator!=(const Transform &p_transform) const;
 
 	_FORCE_INLINE_ Vector3 xform(const Vector3 &p_vector) const;
-	_FORCE_INLINE_ Vector3 xform_inv(const Vector3 &p_vector) const;
+	_FORCE_INLINE_ AABB xform(const AABB &p_aabb) const;
+	_FORCE_INLINE_ PoolVector<Vector3> xform(const PoolVector<Vector3> &p_array) const;
 
+	// NOTE: These are UNSAFE with non-uniform scaling, and will produce incorrect results.
+	// They use the transpose.
+	// For safe inverse transforms, xform by the affine_inverse.
+	_FORCE_INLINE_ Vector3 xform_inv(const Vector3 &p_vector) const;
+	_FORCE_INLINE_ AABB xform_inv(const AABB &p_aabb) const;
+	_FORCE_INLINE_ PoolVector<Vector3> xform_inv(const PoolVector<Vector3> &p_array) const;
+
+	// Safe with non-uniform scaling (uses affine_inverse).
 	_FORCE_INLINE_ Plane xform(const Plane &p_plane) const;
 	_FORCE_INLINE_ Plane xform_inv(const Plane &p_plane) const;
 
-	_FORCE_INLINE_ AABB xform(const AABB &p_aabb) const;
+	// These fast versions use precomputed affine inverse, and should be used in bottleneck areas where
-	_FORCE_INLINE_ AABB xform_inv(const AABB &p_aabb) const;
+	// multiple planes are to be transformed.
-
+	_FORCE_INLINE_ Plane xform_fast(const Plane &p_plane, const Basis &p_basis_inverse_transpose) const;
-	_FORCE_INLINE_ PoolVector<Vector3> xform(const PoolVector<Vector3> &p_array) const;
+	static _FORCE_INLINE_ Plane xform_inv_fast(const Plane &p_plane, const Transform &p_inverse, const Basis &p_basis_transpose);
-	_FORCE_INLINE_ PoolVector<Vector3> xform_inv(const PoolVector<Vector3> &p_array) const;
 
 	void operator*=(const Transform &p_transform);
 	Transform operator*(const Transform &p_transform) const;
@@ -118,6 +126,7 @@ _FORCE_INLINE_ Vector3 Transform::xform(const Vector3 &p_vector) const {
 			basis[1].dot(p_vector) + origin.y,
 			basis[2].dot(p_vector) + origin.z);
 }
+
 _FORCE_INLINE_ Vector3 Transform::xform_inv(const Vector3 &p_vector) const {
 	Vector3 v = p_vector - origin;
 
@@ -127,29 +136,20 @@ _FORCE_INLINE_ Vector3 Transform::xform_inv(const Vector3 &p_vector) const {
 			(basis.elements[0][2] * v.x) + (basis.elements[1][2] * v.y) + (basis.elements[2][2] * v.z));
 }
 
+// Neither the plane regular xform or xform_inv are particularly efficient,
+// as they do a basis inverse. For xforming a large number
+// of planes it is better to pre-calculate the inverse transpose basis once
+// and reuse it for each plane, by using the 'fast' version of the functions.
 _FORCE_INLINE_ Plane Transform::xform(const Plane &p_plane) const {
-	Vector3 point = p_plane.normal * p_plane.d;
+	Basis b = basis.inverse();
-	Vector3 point_dir = point + p_plane.normal;
+	b.transpose();
-	point = xform(point);
+	return xform_fast(p_plane, b);
-	point_dir = xform(point_dir);
-
-	Vector3 normal = point_dir - point;
-	normal.normalize();
-	real_t d = normal.dot(point);
-
-	return Plane(normal, d);
 }
+
 _FORCE_INLINE_ Plane Transform::xform_inv(const Plane &p_plane) const {
-	Vector3 point = p_plane.normal * p_plane.d;
+	Transform inv = affine_inverse();
-	Vector3 point_dir = point + p_plane.normal;
+	Basis basis_transpose = basis.transposed();
-	point = xform_inv(point);
+	return xform_inv_fast(p_plane, inv, basis_transpose);
-	point_dir = xform_inv(point_dir);
-
-	Vector3 normal = point_dir - point;
-	normal.normalize();
-	real_t d = normal.dot(point);
-
-	return Plane(normal, d);
 }
 
 _FORCE_INLINE_ AABB Transform::xform(const AABB &p_aabb) const {
@@ -227,4 +227,37 @@ PoolVector<Vector3> Transform::xform_inv(const PoolVector<Vector3> &p_array) con
 	return array;
 }
 
+_FORCE_INLINE_ Plane Transform::xform_fast(const Plane &p_plane, const Basis &p_basis_inverse_transpose) const {
+	// Transform a single point on the plane.
+	Vector3 point = p_plane.normal * p_plane.d;
+	point = xform(point);
+
+	// Use inverse transpose for correct normals with non-uniform scaling.
+	Vector3 normal = p_basis_inverse_transpose.xform(p_plane.normal);
+	normal.normalize();
+
+	real_t d = normal.dot(point);
+	return Plane(normal, d);
+}
+
+_FORCE_INLINE_ Plane Transform::xform_inv_fast(const Plane &p_plane, const Transform &p_inverse, const Basis &p_basis_transpose) {
+	// Transform a single point on the plane.
+	Vector3 point = p_plane.normal * p_plane.d;
+	point = p_inverse.xform(point);
+
+	// Note that instead of precalculating the transpose, an alternative
+	// would be to use the transpose for the basis transform.
+	// However that would be less SIMD friendly (requiring a swizzle).
+	// So the cost is one extra precalced value in the calling code.
+	// This is probably worth it, as this could be used in bottleneck areas. And
+	// where it is not a bottleneck, the non-fast method is fine.
+
+	// Use transpose for correct normals with non-uniform scaling.
+	Vector3 normal = p_basis_transpose.xform(p_plane.normal);
+	normal.normalize();
+
+	real_t d = normal.dot(point);
+	return Plane(normal, d);
+}
+
 #endif // TRANSFORM_H

main/tests/test_main.cpp

@@ -47,6 +47,7 @@
 #include "test_render.h"
 #include "test_shader_lang.h"
 #include "test_string.h"
+#include "test_transform.h"
 #include "test_xml_parser.h"
 
 const char **tests_get_names() {
@@ -54,6 +55,7 @@ const char **tests_get_names() {
 		"string",
 		"math",
 		"basis",
+		"transform",
 		"physics",
 		"physics_2d",
 		"render",
@@ -86,6 +88,10 @@ MainLoop *test_main(String p_test, const List<String> &p_args) {
 		return TestBasis::test();
 	}
 
+	if (p_test == "transform") {
+		return TestTransform::test();
+	}
+
 	if (p_test == "physics") {
 		return TestPhysics::test();
 	}

main/tests/test_transform.cpp

@@ -0,0 +1,270 @@
+/*************************************************************************/
+/*  test_transform.cpp                                                   */
+/*************************************************************************/
+/*                       This file is part of:                           */
+/*                           GODOT ENGINE                                */
+/*                      https://godotengine.org                          */
+/*************************************************************************/
+/* Copyright (c) 2007-2021 Juan Linietsky, Ariel Manzur.                 */
+/* Copyright (c) 2014-2021 Godot Engine contributors (cf. AUTHORS.md).   */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "test_transform.h"
+
+#include "core/math/random_number_generator.h"
+#include "core/math/transform.h"
+#include "core/math/vector3.h"
+#include "core/os/os.h"
+#include "core/ustring.h"
+
+// #define GODOT_TEST_TRANSFORM_NON_UNIFORM_SCALE_TESTS_ENABLED
+
+namespace TestTransform {
+
+bool test_plane() {
+	bool pass = true;
+
+	// test non-uniform scaling, forward and inverse
+	Transform tr;
+	tr.scale(Vector3(1, 2, 3));
+
+	Plane p(Vector3(1, 1, 1), Vector3(1, 1, 1).normalized());
+
+	Plane p2 = tr.xform(p);
+	Plane p3 = tr.xform_inv(p2);
+
+	if (!p3.normal.is_equal_approx(p.normal)) {
+		OS::get_singleton()->print("Fail due to Transform::xform(Plane)\n");
+		pass = false;
+	}
+
+	return pass;
+}
+
+bool test_aabb_regular() {
+	bool pass = true;
+
+	Transform tr;
+	tr.basis = Basis(Vector3(Math_PI, 0, 0));
+	tr.origin = Vector3(1, 2, 3);
+
+	AABB bb(Vector3(1, 1, 1), Vector3(2, 3, 4));
+
+	// Test forward xform.
+	AABB bb2 = tr.xform(bb);
+	AABB bb3 = tr.xform_inv(bb2);
+
+	if (!bb3.position.is_equal_approx(bb.position)) {
+		OS::get_singleton()->print("Fail due to Transform::xform_inv(AABB) position\n");
+		pass = false;
+	}
+
+	if (!bb3.size.is_equal_approx(bb.size)) {
+		OS::get_singleton()->print("Fail due to Transform::xform_inv(AABB) size\n");
+		pass = false;
+	}
+
+	if (!pass) {
+		String string = String("bb2 : ") + String(Variant(bb2));
+		OS::get_singleton()->print("\t%ls\n", string.c_str());
+		string = String("bb3 : ") + String(Variant(bb3));
+		OS::get_singleton()->print("\t%ls\n", string.c_str());
+	}
+
+	return pass;
+}
+
+bool test_aabb_non_uniform_scale() {
+	bool pass = true;
+
+	Transform tr;
+	tr.scale(Vector3(1, 2, 3));
+
+	AABB bb(Vector3(1, 1, 1), Vector3(2, 3, 4));
+
+	// Test forward xform.
+	AABB bb2 = tr.xform(bb);
+
+	if (!bb2.position.is_equal_approx(Vector3(1, 2, 3))) {
+		OS::get_singleton()->print("Fail with non-uniform scale due to Transform::xform(AABB) position\n");
+		pass = false;
+	}
+
+	if (!bb2.size.is_equal_approx(Vector3(2, 6, 12))) {
+		OS::get_singleton()->print("Fail with non-uniform scale due to Transform::xform(AABB) size\n");
+		pass = false;
+	}
+
+	// Now test inverse.
+	// This will fail if using the transpose and not the affine_inverse.
+	bb2.position = Vector3(1, 2, 3);
+	bb2.size = Vector3(2, 6, 12);
+
+	AABB bb3 = tr.xform_inv(bb2);
+
+	if (!bb3.position.is_equal_approx(bb.position)) {
+		OS::get_singleton()->print("Fail with non-uniform scale due to Transform::xform_inv(AABB) position\n");
+		pass = false;
+	}
+
+	if (!bb3.size.is_equal_approx(bb.size)) {
+		OS::get_singleton()->print("Fail with non-uniform scale due to Transform::xform_inv(AABB) size\n");
+		pass = false;
+	}
+
+	if (!pass) {
+		String string = String("bb2 : ") + String(Variant(bb2));
+		OS::get_singleton()->print("\t%ls\n", string.c_str());
+		string = String("bb3 : ") + String(Variant(bb3));
+		OS::get_singleton()->print("\t%ls\n", string.c_str());
+	}
+
+	return pass;
+}
+
+bool test_aabb() {
+	bool pass = true;
+	if (!test_aabb_regular()) {
+		pass = false;
+	}
+
+#ifdef GODOT_TEST_TRANSFORM_NON_UNIFORM_SCALE_TESTS_ENABLED
+	if (!test_aabb_non_uniform_scale()) {
+		pass = false;
+	}
+#endif
+
+	return pass;
+}
+
+bool test_vector3_regular() {
+	bool pass = true;
+
+	Transform tr;
+
+	RandomNumberGenerator rng;
+	const real_t range = 1800.0;
+	const real_t range_rot = Math_PI;
+
+	bool passed_multi = true;
+	for (int n = 0; n < 1000; n++) {
+		Vector3 pt_test = Vector3(rng.randf_range(-range, range), rng.randf_range(-range, range), rng.randf_range(-range, range));
+
+		tr.origin = Vector3(rng.randf_range(-range, range), rng.randf_range(-range, range), rng.randf_range(-range, range));
+		tr.basis = Basis(Vector3(rng.randf_range(-range_rot, range_rot), rng.randf_range(-range_rot, range_rot), rng.randf_range(-range_rot, range_rot)));
+
+		Vector3 pt = tr.xform(pt_test);
+		pt = tr.xform_inv(pt);
+
+		if (!pt.is_equal_approx(pt_test, 0.1)) {
+			passed_multi = false;
+		}
+	}
+	if (!passed_multi) {
+		OS::get_singleton()->print("Failed multitest due to Transform::xform and xform_inv(Vector3)\n");
+		pass = false;
+	}
+
+	return pass;
+}
+
+bool test_vector3_non_uniform_scale() {
+	bool pass = true;
+
+	// Regular scale.
+	Transform tr;
+	tr.scale(Vector3(3, 3, 3));
+	Vector3 pt(1, 1, 1);
+	Vector3 res = tr.xform(pt);
+
+	if (!res.is_equal_approx(Vector3(3, 3, 3))) {
+		OS::get_singleton()->print("Fail with scale due to Transform::xform(Vector3)\n");
+		pass = false;
+	}
+
+	res = tr.xform_inv(res);
+	if (!res.is_equal_approx(pt)) {
+		OS::get_singleton()->print("Fail with scale due to Transform::xform_inv(Vector3)\n");
+		pass = false;
+	}
+
+	// Non uniform scale.
+	tr.scale(Vector3(1, 2, 3));
+	res = tr.xform(pt);
+
+	if (!res.is_equal_approx(Vector3(1, 2, 3))) {
+		OS::get_singleton()->print("Fail with non-uniform scale due to Transform::xform(Vector3)\n");
+		pass = false;
+	}
+
+	pt = Vector3(1, 2, 3);
+	res = tr.xform_inv(pt);
+	if (!res.is_equal_approx(Vector3(1, 1, 1))) {
+		OS::get_singleton()->print("Fail with non-uniform scale due to Transform::xform_inv(Vector3)\n");
+		pass = false;
+	}
+
+	return pass;
+}
+
+bool test_vector3() {
+	bool pass = true;
+	if (!test_vector3_regular()) {
+		pass = false;
+	}
+
+#ifdef GODOT_TEST_TRANSFORM_NON_UNIFORM_SCALE_TESTS_ENABLED
+	if (!test_vector3_non_uniform_scale()) {
+		pass = false;
+	}
+#endif
+
+	return pass;
+}
+
+MainLoop *test() {
+	OS::get_singleton()->print("Start Transform checks.\n");
+
+	bool success = true;
+
+	if (!test_vector3()) {
+		success = false;
+	}
+
+	if (!test_plane()) {
+		success = false;
+	}
+
+	if (!test_aabb()) {
+		success = false;
+	}
+
+	if (success) {
+		OS::get_singleton()->print("Transform checks passed.\n");
+	} else {
+		OS::get_singleton()->print("Transform checks FAILED.\n");
+	}
+
+	return nullptr;
+}
+
+} // namespace TestTransform

main/tests/test_transform.h

@@ -0,0 +1,40 @@
+/*************************************************************************/
+/*  test_transform.h                                                     */
+/*************************************************************************/
+/*                       This file is part of:                           */
+/*                           GODOT ENGINE                                */
+/*                      https://godotengine.org                          */
+/*************************************************************************/
+/* Copyright (c) 2007-2021 Juan Linietsky, Ariel Manzur.                 */
+/* Copyright (c) 2014-2021 Godot Engine contributors (cf. AUTHORS.md).   */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#ifndef TEST_TRANSFORM_H
+#define TEST_TRANSFORM_H
+
+#include "core/os/main_loop.h"
+
+namespace TestTransform {
+MainLoop *test();
+}
+
+#endif

servers/physics/collision_solver_sat.cpp

@@ -953,9 +953,12 @@ static void _collision_sphere_convex_polygon(const ShapeSW *p_a, const Transform
 	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 = p_transform_b.xform(faces[i].plane).normal;
+		Vector3 axis = b_xform_normal.xform(faces[i].plane.normal).normalized();
 
 		if (!separator.test_axis(axis)) {
 			return;
@@ -1191,13 +1194,14 @@ static void _collision_box_capsule(const ShapeSW *p_a, const Transform &p_transf
 	}
 
 	// capsule balls, edges of A
+	Transform transform_a_inverse = p_transform_a.affine_inverse();
 
 	for (int i = 0; i < 2; i++) {
 		Vector3 capsule_axis = p_transform_b.basis.get_axis(2) * (capsule_B->get_height() * 0.5);
 
 		Vector3 sphere_pos = p_transform_b.origin + ((i == 0) ? capsule_axis : -capsule_axis);
 
-		Vector3 cnormal = p_transform_a.xform_inv(sphere_pos);
+		Vector3 cnormal = transform_a_inverse.xform(sphere_pos);
 
 		Vector3 cpoint = p_transform_a.xform(Vector3(
 
@@ -1368,9 +1372,12 @@ static void _collision_box_convex_polygon(const ShapeSW *p_a, const Transform &p
 		}
 	}
 
+	// 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 = p_transform_b.xform(faces[i].plane).normal;
+		Vector3 axis = b_xform_normal.xform(faces[i].plane.normal).normalized();
 
 		if (!separator.test_axis(axis)) {
 			return;
@@ -1701,9 +1708,12 @@ static void _collision_capsule_convex_polygon(const ShapeSW *p_a, const Transfor
 	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 = p_transform_b.xform(faces[i].plane).normal;
+		Vector3 axis = b_xform_normal.xform(faces[i].plane.normal).normalized();
 
 		if (!separator.test_axis(axis)) {
 			return;
@@ -1995,20 +2005,24 @@ static void _collision_convex_polygon_convex_polygon(const ShapeSW *p_a, const T
 	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 = p_transform_a.xform(faces_A[i].plane).normal;
+		Vector3 axis = a_xform_normal.xform(faces_A[i].plane.normal).normalized();
-		//Vector3 axis = p_transform_a.basis.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 = p_transform_b.xform(faces_B[i].plane).normal;
+		Vector3 axis = b_xform_normal.xform(faces_B[i].plane.normal).normalized();
-		//Vector3 axis = p_transform_b.basis.xform( faces_B[i].plane.normal ).normalized();
 
 		if (!separator.test_axis(axis)) {
 			return;