Fix Transform::xform(Plane) functions

The Transform::xform and xform_inv are made safe for Planes when using non-uniform scaling.
Optimization of calling sites to prevent loss of performance from the changes to xform(Plane).

2 files changed, 76 insertions, 32 deletions

diff --git a/core/math/transform_3d.h b/core/math/transform_3d.h
index 3d8e70cec7..cadfdc13d1 100644
--- a/core/math/transform_3d.h
+++ b/core/math/transform_3d.h
@@ -75,16 +75,24 @@ public:
 	bool operator!=(const Transform3D &p_transform) const;
 
 	_FORCE_INLINE_ Vector3 xform(const Vector3 &p_vector) const;
+	_FORCE_INLINE_ AABB xform(const AABB &p_aabb) const;
+	_FORCE_INLINE_ Vector<Vector3> xform(const Vector<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_ Vector<Vector3> xform_inv(const Vector<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_ Vector<Vector3> xform(const Vector<Vector3> &p_array) const;
-	_FORCE_INLINE_ Vector<Vector3> xform_inv(const Vector<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 Transform3D &p_inverse, const Basis &p_basis_transpose);
 
 	void operator*=(const Transform3D &p_transform);
 	Transform3D operator*(const Transform3D &p_transform) const;
@@ -130,30 +138,20 @@ _FORCE_INLINE_ Vector3 Transform3D::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 Transform3D::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 Transform3D::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);
+	Transform3D inv = affine_inverse();
+	Basis basis_transpose = basis.transposed();
+	return xform_inv_fast(p_plane, inv, basis_transpose);
 }
 
 _FORCE_INLINE_ AABB Transform3D::xform(const AABB &p_aabb) const {
@@ -231,4 +229,37 @@ Vector<Vector3> Transform3D::xform_inv(const Vector<Vector3> &p_array) const {
 	return array;
 }
 
+_FORCE_INLINE_ Plane Transform3D::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 Transform3D::xform_inv_fast(const Plane &p_plane, const Transform3D &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
diff --git a/servers/physics_3d/collision_solver_3d_sat.cpp b/servers/physics_3d/collision_solver_3d_sat.cpp
index 6a7f2b73c5..852e9ecd74 100644
--- a/servers/physics_3d/collision_solver_3d_sat.cpp
+++ b/servers/physics_3d/collision_solver_3d_sat.cpp
@@ -956,9 +956,12 @@ static void _collision_sphere_convex_polygon(const Shape3DSW *p_a, const Transfo
 	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;
@@ -1379,9 +1382,12 @@ static void _collision_box_convex_polygon(const Shape3DSW *p_a, const Transform3
 		}
 	}
 
+	// 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;
@@ -1733,9 +1739,12 @@ static void _collision_capsule_convex_polygon(const Shape3DSW *p_a, const Transf
 	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;
@@ -2057,20 +2066,24 @@ static void _collision_convex_polygon_convex_polygon(const Shape3DSW *p_a, const
 	const Vector3 *vertices_B = mesh_B.vertices.ptr();
 	int vertex_count_B = mesh_B.vertices.size();
 
+	// Precalculating this makes the transforms faster.
+	Basis a_xform_normal = p_transform_b.basis.inverse().transposed();
+
 	// faces of A
 	for (int i = 0; i < face_count_A; i++) {
-		Vector3 axis = 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;