Fix `Basis::get_euler` incorrectly simplifying rotations in some cases.

core/math/basis.cpp

@@ -455,6 +455,11 @@ void Basis::get_rotation_axis_angle_local(Vector3 &p_axis, real_t &p_angle) cons
 }
 
 Vector3 Basis::get_euler(EulerOrder p_order) const {
+	// This epsilon value results in angles within a +/- 0.04 degree range being simplified/truncated.
+	// Based on testing, this is the largest the epsilon can be without the angle truncation becoming
+	// visually noticeable.
+	const real_t epsilon = 0.00000025;
+
 	switch (p_order) {
 		case EulerOrder::XYZ: {
 			// Euler angles in XYZ convention.
@@ -466,8 +471,8 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 
 			Vector3 euler;
 			real_t sy = rows[0][2];
-			if (sy < (1.0f - (real_t)CMP_EPSILON)) {
-				if (sy > -(1.0f - (real_t)CMP_EPSILON)) {
+			if (sy < (1.0f - epsilon)) {
+				if (sy > -(1.0f - epsilon)) {
 					// is this a pure Y rotation?
 					if (rows[1][0] == 0 && rows[0][1] == 0 && rows[1][2] == 0 && rows[2][1] == 0 && rows[1][1] == 1) {
 						// return the simplest form (human friendlier in editor and scripts)
@@ -501,8 +506,8 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 
 			Vector3 euler;
 			real_t sz = rows[0][1];
-			if (sz < (1.0f - (real_t)CMP_EPSILON)) {
-				if (sz > -(1.0f - (real_t)CMP_EPSILON)) {
+			if (sz < (1.0f - epsilon)) {
+				if (sz > -(1.0f - epsilon)) {
 					euler.x = Math::atan2(rows[2][1], rows[1][1]);
 					euler.y = Math::atan2(rows[0][2], rows[0][0]);
 					euler.z = Math::asin(-sz);
@@ -532,8 +537,8 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 
 			real_t m12 = rows[1][2];
 
-			if (m12 < (1 - (real_t)CMP_EPSILON)) {
-				if (m12 > -(1 - (real_t)CMP_EPSILON)) {
+			if (m12 < (1 - epsilon)) {
+				if (m12 > -(1 - epsilon)) {
 					// is this a pure X rotation?
 					if (rows[1][0] == 0 && rows[0][1] == 0 && rows[0][2] == 0 && rows[2][0] == 0 && rows[0][0] == 1) {
 						// return the simplest form (human friendlier in editor and scripts)
@@ -568,8 +573,8 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 
 			Vector3 euler;
 			real_t sz = rows[1][0];
-			if (sz < (1.0f - (real_t)CMP_EPSILON)) {
-				if (sz > -(1.0f - (real_t)CMP_EPSILON)) {
+			if (sz < (1.0f - epsilon)) {
+				if (sz > -(1.0f - epsilon)) {
 					euler.x = Math::atan2(-rows[1][2], rows[1][1]);
 					euler.y = Math::atan2(-rows[2][0], rows[0][0]);
 					euler.z = Math::asin(sz);
@@ -596,8 +601,8 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 			//        -cx*sy            sx                    cx*cy
 			Vector3 euler;
 			real_t sx = rows[2][1];
-			if (sx < (1.0f - (real_t)CMP_EPSILON)) {
-				if (sx > -(1.0f - (real_t)CMP_EPSILON)) {
+			if (sx < (1.0f - epsilon)) {
+				if (sx > -(1.0f - epsilon)) {
 					euler.x = Math::asin(sx);
 					euler.y = Math::atan2(-rows[2][0], rows[2][2]);
 					euler.z = Math::atan2(-rows[0][1], rows[1][1]);
@@ -624,8 +629,8 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 			//        -sy               cy*sx                 cy*cx
 			Vector3 euler;
 			real_t sy = rows[2][0];
-			if (sy < (1.0f - (real_t)CMP_EPSILON)) {
-				if (sy > -(1.0f - (real_t)CMP_EPSILON)) {
+			if (sy < (1.0f - epsilon)) {
+				if (sy > -(1.0f - epsilon)) {
 					euler.x = Math::atan2(rows[2][1], rows[2][2]);
 					euler.y = Math::asin(-sy);
 					euler.z = Math::atan2(rows[1][0], rows[0][0]);

tests/core/math/test_basis.h

@@ -93,9 +93,9 @@ void test_rotation(Vector3 deg_original_euler, EulerOrder rot_order) {
 
 	Basis res = to_rotation.inverse() * rotation_from_computed_euler;
 
-	CHECK_MESSAGE((res.get_column(0) - Vector3(1.0, 0.0, 0.0)).length() <= 0.1, vformat("Fail due to X %s\n", String(res.get_column(0))));
-	CHECK_MESSAGE((res.get_column(1) - Vector3(0.0, 1.0, 0.0)).length() <= 0.1, vformat("Fail due to Y %s\n", String(res.get_column(1))));
-	CHECK_MESSAGE((res.get_column(2) - Vector3(0.0, 0.0, 1.0)).length() <= 0.1, vformat("Fail due to Z %s\n", String(res.get_column(2))));
+	CHECK_MESSAGE((res.get_column(0) - Vector3(1.0, 0.0, 0.0)).length() <= 0.001, vformat("Fail due to X %s\n", String(res.get_column(0))));
+	CHECK_MESSAGE((res.get_column(1) - Vector3(0.0, 1.0, 0.0)).length() <= 0.001, vformat("Fail due to Y %s\n", String(res.get_column(1))));
+	CHECK_MESSAGE((res.get_column(2) - Vector3(0.0, 0.0, 1.0)).length() <= 0.001, vformat("Fail due to Z %s\n", String(res.get_column(2))));
 
 	// Double check `to_rotation` decomposing with XYZ rotation order.
 	const Vector3 euler_xyz_from_rotation = to_rotation.get_euler(EulerOrder::XYZ);
@@ -103,9 +103,9 @@ void test_rotation(Vector3 deg_original_euler, EulerOrder rot_order) {
 
 	res = to_rotation.inverse() * rotation_from_xyz_computed_euler;
 
-	CHECK_MESSAGE((res.get_column(0) - Vector3(1.0, 0.0, 0.0)).length() <= 0.1, vformat("Double check with XYZ rot order failed, due to X %s\n", String(res.get_column(0))));
-	CHECK_MESSAGE((res.get_column(1) - Vector3(0.0, 1.0, 0.0)).length() <= 0.1, vformat("Double check with XYZ rot order failed, due to Y %s\n", String(res.get_column(1))));
-	CHECK_MESSAGE((res.get_column(2) - Vector3(0.0, 0.0, 1.0)).length() <= 0.1, vformat("Double check with XYZ rot order failed, due to Z %s\n", String(res.get_column(2))));
+	CHECK_MESSAGE((res.get_column(0) - Vector3(1.0, 0.0, 0.0)).length() <= 0.001, vformat("Double check with XYZ rot order failed, due to X %s\n", String(res.get_column(0))));
+	CHECK_MESSAGE((res.get_column(1) - Vector3(0.0, 1.0, 0.0)).length() <= 0.001, vformat("Double check with XYZ rot order failed, due to Y %s\n", String(res.get_column(1))));
+	CHECK_MESSAGE((res.get_column(2) - Vector3(0.0, 0.0, 1.0)).length() <= 0.001, vformat("Double check with XYZ rot order failed, due to Z %s\n", String(res.get_column(2))));
 
 	INFO(vformat("Rotation order: %s\n.", get_rot_order_name(rot_order)));
 	INFO(vformat("Original Rotation: %s\n", String(deg_original_euler)));
@@ -176,6 +176,12 @@ TEST_CASE("[Basis] Euler conversions") {
 	vectors_to_test.push_back(Vector3(120.0, -150.0, -130.0));
 	vectors_to_test.push_back(Vector3(120.0, 150.0, -130.0));
 	vectors_to_test.push_back(Vector3(120.0, 150.0, 130.0));
+	vectors_to_test.push_back(Vector3(89.9, 0.0, 0.0));
+	vectors_to_test.push_back(Vector3(-89.9, 0.0, 0.0));
+	vectors_to_test.push_back(Vector3(0.0, 89.9, 0.0));
+	vectors_to_test.push_back(Vector3(0.0, -89.9, 0.0));
+	vectors_to_test.push_back(Vector3(0.0, 0.0, 89.9));
+	vectors_to_test.push_back(Vector3(0.0, 0.0, -89.9));
 
 	for (int h = 0; h < euler_order_to_test.size(); h += 1) {
 		for (int i = 0; i < vectors_to_test.size(); i += 1) {