Merge pull request #63428 from fabriceci/fix-basis-get-axis-angle

Test, refactor and fix a bug in Basis.get_axis_angle

core/math/basis.cpp

@@ -754,29 +754,28 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
 #ifdef MATH_CHECKS
 	ERR_FAIL_COND(!is_rotation());
 #endif
-*/
-	real_t angle, x, y, z; // variables for result
-	real_t angle_epsilon = 0.1; // margin to distinguish between 0 and 180 degrees
-
-	if ((Math::abs(rows[1][0] - rows[0][1]) < CMP_EPSILON) && (Math::abs(rows[2][0] - rows[0][2]) < CMP_EPSILON) && (Math::abs(rows[2][1] - rows[1][2]) < CMP_EPSILON)) {
-		// singularity found
-		// first check for identity matrix which must have +1 for all terms
-		// in leading diagonal and zero in other terms
-		if ((Math::abs(rows[1][0] + rows[0][1]) < angle_epsilon) && (Math::abs(rows[2][0] + rows[0][2]) < angle_epsilon) && (Math::abs(rows[2][1] + rows[1][2]) < angle_epsilon) && (Math::abs(rows[0][0] + rows[1][1] + rows[2][2] - 3) < angle_epsilon)) {
-			// this singularity is identity matrix so angle = 0
+	*/
+
+	// https://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToAngle/index.htm
+	real_t x, y, z; // Variables for result.
+	if (Math::is_zero_approx(rows[0][1] - rows[1][0]) && Math::is_zero_approx(rows[0][2] - rows[2][0]) && Math::is_zero_approx(rows[1][2] - rows[2][1])) {
+		// Singularity found.
+		// First check for identity matrix which must have +1 for all terms in leading diagonal and zero in other terms.
+		if (is_diagonal() && (Math::abs(rows[0][0] + rows[1][1] + rows[2][2] - 3) < 3 * CMP_EPSILON)) {
+			// This singularity is identity matrix so angle = 0.
 			r_axis = Vector3(0, 1, 0);
 			r_angle = 0;
 			return;
 		}
-		// otherwise this singularity is angle = 180
-		angle = Math_PI;
+		// Otherwise this singularity is angle = 180.
 		real_t xx = (rows[0][0] + 1) / 2;
 		real_t yy = (rows[1][1] + 1) / 2;
 		real_t zz = (rows[2][2] + 1) / 2;
-		real_t xy = (rows[1][0] + rows[0][1]) / 4;
-		real_t xz = (rows[2][0] + rows[0][2]) / 4;
-		real_t yz = (rows[2][1] + rows[1][2]) / 4;
-		if ((xx > yy) && (xx > zz)) { // rows[0][0] is the largest diagonal term
+		real_t xy = (rows[0][1] + rows[1][0]) / 4;
+		real_t xz = (rows[0][2] + rows[2][0]) / 4;
+		real_t yz = (rows[1][2] + rows[2][1]) / 4;
+
+		if ((xx > yy) && (xx > zz)) { // rows[0][0] is the largest diagonal term.
 			if (xx < CMP_EPSILON) {
 				x = 0;
 				y = Math_SQRT12;
@@ -786,7 +785,7 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
 				y = xy / x;
 				z = xz / x;
 			}
-		} else if (yy > zz) { // rows[1][1] is the largest diagonal term
+		} else if (yy > zz) { // rows[1][1] is the largest diagonal term.
 			if (yy < CMP_EPSILON) {
 				x = Math_SQRT12;
 				y = 0;
@@ -796,7 +795,7 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
 				x = xy / y;
 				z = yz / y;
 			}
-		} else { // rows[2][2] is the largest diagonal term so base result on this
+		} else { // rows[2][2] is the largest diagonal term so base result on this.
 			if (zz < CMP_EPSILON) {
 				x = Math_SQRT12;
 				y = Math_SQRT12;
@@ -808,22 +807,24 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
 			}
 		}
 		r_axis = Vector3(x, y, z);
-		r_angle = angle;
+		r_angle = Math_PI;
 		return;
 	}
-	// as we have reached here there are no singularities so we can handle normally
-	real_t s = Math::sqrt((rows[1][2] - rows[2][1]) * (rows[1][2] - rows[2][1]) + (rows[2][0] - rows[0][2]) * (rows[2][0] - rows[0][2]) + (rows[0][1] - rows[1][0]) * (rows[0][1] - rows[1][0])); // s=|axis||sin(angle)|, used to normalise
+	// As we have reached here there are no singularities so we can handle normally.
+	double s = Math::sqrt((rows[2][1] - rows[1][2]) * (rows[2][1] - rows[1][2]) + (rows[0][2] - rows[2][0]) * (rows[0][2] - rows[2][0]) + (rows[1][0] - rows[0][1]) * (rows[1][0] - rows[0][1])); // Used to normalise.
 
-	angle = Math::acos((rows[0][0] + rows[1][1] + rows[2][2] - 1) / 2);
-	if (angle < 0) {
-		s = -s;
+	if (Math::abs(s) < CMP_EPSILON) {
+		// Prevent divide by zero, should not happen if matrix is orthogonal and should be caught by singularity test above.
+		s = 1;
 	}
+
 	x = (rows[2][1] - rows[1][2]) / s;
 	y = (rows[0][2] - rows[2][0]) / s;
 	z = (rows[1][0] - rows[0][1]) / s;
 
 	r_axis = Vector3(x, y, z);
-	r_angle = angle;
+	// CLAMP to avoid NaN if the value passed to acos is not in [0,1].
+	r_angle = Math::acos(CLAMP((rows[0][0] + rows[1][1] + rows[2][2] - 1) / 2, (real_t)0.0, (real_t)1.0));
 }
 
 void Basis::set_quaternion(const Quaternion &p_quaternion) {

tests/core/math/test_basis.h

@@ -47,7 +47,7 @@ enum RotOrder {
 	EulerZYX
 };
 
-Vector3 deg2rad(const Vector3 &p_rotation) {
+Vector3 deg_to_rad(const Vector3 &p_rotation) {
 	return p_rotation / 180.0 * Math_PI;
 }
 
@@ -155,7 +155,7 @@ void test_rotation(Vector3 deg_original_euler, RotOrder rot_order) {
 	// are correct.
 
 	// Euler to rotation
-	const Vector3 original_euler = deg2rad(deg_original_euler);
+	const Vector3 original_euler = deg_to_rad(deg_original_euler);
 	const Basis to_rotation = EulerToBasis(rot_order, original_euler);
 
 	// Euler from rotation
@@ -281,6 +281,59 @@ TEST_CASE("[Stress][Basis] Euler conversions") {
 		}
 	}
 }
+
+TEST_CASE("[Basis] Set axis angle") {
+	Vector3 axis;
+	real_t angle;
+	real_t pi = (real_t)Math_PI;
+
+	// Testing the singularity when the angle is 0°.
+	Basis identity(1, 0, 0, 0, 1, 0, 0, 0, 1);
+	identity.get_axis_angle(axis, angle);
+	CHECK(angle == 0);
+
+	// Testing the singularity when the angle is 180°.
+	Basis singularityPi(-1, 0, 0, 0, 1, 0, 0, 0, -1);
+	singularityPi.get_axis_angle(axis, angle);
+	CHECK(Math::is_equal_approx(angle, pi));
+
+	// Testing reversing the an axis (of an 30° angle).
+	float cos30deg = Math::cos(Math::deg_to_rad((real_t)30.0));
+	Basis z_positive(cos30deg, -0.5, 0, 0.5, cos30deg, 0, 0, 0, 1);
+	Basis z_negative(cos30deg, 0.5, 0, -0.5, cos30deg, 0, 0, 0, 1);
+
+	z_positive.get_axis_angle(axis, angle);
+	CHECK(Math::is_equal_approx(angle, Math::deg_to_rad((real_t)30.0)));
+	CHECK(axis == Vector3(0, 0, 1));
+
+	z_negative.get_axis_angle(axis, angle);
+	CHECK(Math::is_equal_approx(angle, Math::deg_to_rad((real_t)30.0)));
+	CHECK(axis == Vector3(0, 0, -1));
+
+	// Testing a rotation of 90° on x-y-z.
+	Basis x90deg(1, 0, 0, 0, 0, -1, 0, 1, 0);
+	x90deg.get_axis_angle(axis, angle);
+	CHECK(Math::is_equal_approx(angle, pi / (real_t)2));
+	CHECK(axis == Vector3(1, 0, 0));
+
+	Basis y90deg(0, 0, 1, 0, 1, 0, -1, 0, 0);
+	y90deg.get_axis_angle(axis, angle);
+	CHECK(axis == Vector3(0, 1, 0));
+
+	Basis z90deg(0, -1, 0, 1, 0, 0, 0, 0, 1);
+	z90deg.get_axis_angle(axis, angle);
+	CHECK(axis == Vector3(0, 0, 1));
+
+	// Regression test: checks that the method returns a small angle (not 0).
+	Basis tiny(1, 0, 0, 0, 0.9999995, -0.001, 0, 001, 0.9999995); // The min angle possible with float is 0.001rad.
+	tiny.get_axis_angle(axis, angle);
+	CHECK(Math::is_equal_approx(angle, (real_t)0.001, (real_t)0.0001));
+
+	// Regression test: checks that the method returns an angle which is a number (not NaN)
+	Basis bugNan(1.00000024, 0, 0.000100001693, 0, 1, 0, -0.000100009143, 0, 1.00000024);
+	bugNan.get_axis_angle(axis, angle);
+	CHECK(!Math::is_nan(angle));
+}
 } // namespace TestBasis
 
 #endif // TEST_BASIS_H