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

The Transform::xform and xform_inv are made safe for Planes when using non-uniform scaling.

Basic unit tests for Transform.

Optimization of calling sites to prevent loss of performance from the changes to xform(Plane).
This commit is contained in:
lawnjelly 2021-07-17 12:28:29 +01:00
parent 8db0bd4424
commit 37f20e1d78
5 changed files with 397 additions and 34 deletions
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85
core/math/transform.h
View File

@ -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;
_FORCE_INLINE_ AABB xform_inv(const AABB &p_aabb) const;
_FORCE_INLINE_ PoolVector<Vector3> xform(const PoolVector<Vector3> &p_array) const;
_FORCE_INLINE_ PoolVector<Vector3> xform_inv(const PoolVector<Vector3> &p_array) const;
// These fast versions use precomputed affine inverse, and should be used in bottleneck areas where
// multiple planes are to be transformed.
_FORCE_INLINE_ Plane xform_fast(const Plane &p_plane, const Basis &p_basis_inverse_transpose) const;
static _FORCE_INLINE_ Plane xform_inv_fast(const Plane &p_plane, const Transform &p_inverse, const Basis &p_basis_transpose);
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;
Vector3 point_dir = point + p_plane.normal;
point = xform(point);
point_dir = xform(point_dir);
Vector3 normal = point_dir - point;
normal.normalize();
real_t d = normal.dot(point);
return Plane(normal, d);
Basis b = basis.inverse();
b.transpose();
return xform_fast(p_plane, b);
}
_FORCE_INLINE_ Plane Transform::xform_inv(const Plane &p_plane) const {
Vector3 point = p_plane.normal * p_plane.d;
Vector3 point_dir = point + p_plane.normal;
point = xform_inv(point);
point_dir = xform_inv(point_dir);
Vector3 normal = point_dir - point;
normal.normalize();
real_t d = normal.dot(point);
return Plane(normal, d);
Transform inv = affine_inverse();
Basis basis_transpose = basis.transposed();
return xform_inv_fast(p_plane, inv, basis_transpose);
}
_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

6
main/tests/test_main.cpp
View File

@ -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();
}

270
main/tests/test_transform.cpp Normal file
View File

@ -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

40
main/tests/test_transform.h Normal file
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@ -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

30
servers/physics/collision_solver_sat.cpp
View File

@ -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 = p_transform_a.basis.xform( faces_A[i].plane.normal ).normalized();
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 = p_transform_b.xform(faces_B[i].plane).normal;
//Vector3 axis = p_transform_b.basis.xform( faces_B[i].plane.normal ).normalized();
Vector3 axis = b_xform_normal.xform(faces_B[i].plane.normal).normalized();
if (!separator.test_axis(axis)) {
return;