- Added more euler rotation orders support.

- Fixed floating point issue on the old one.
- Fixed the equation on the get_euler_yxz function.
- Added unit tests.

This work has been kindly sponsored by IMVU.

(cherry picked from commit 233130098941c384240a0b7109890e0222f96735)

core/math/basis.cpp

@@ -427,12 +427,9 @@ Vector3 Basis::get_euler_xyz() const {
 	//       -cx*cz*sy+sx*sz  cz*sx+cx*sy*sz  cx*cy
 
 	Vector3 euler;
-#ifdef MATH_CHECKS
-	ERR_FAIL_COND_V(!is_rotation(), euler);
-#endif
 	real_t sy = elements[0][2];
-	if (sy < 1.0) {
-		if (sy > -1.0) {
+	if (sy < (1.0 - CMP_EPSILON)) {
+		if (sy > -(1.0 - CMP_EPSILON)) {
 			// is this a pure Y rotation?
 			if (elements[1][0] == 0.0 && elements[0][1] == 0.0 && elements[1][2] == 0 && elements[2][1] == 0 && elements[1][1] == 1) {
 				// return the simplest form (human friendlier in editor and scripts)
@@ -445,12 +442,12 @@ Vector3 Basis::get_euler_xyz() const {
 				euler.z = Math::atan2(-elements[0][1], elements[0][0]);
 			}
 		} else {
-			euler.x = -Math::atan2(elements[0][1], elements[1][1]);
+			euler.x = Math::atan2(elements[2][1], elements[1][1]);
 			euler.y = -Math_PI / 2.0;
 			euler.z = 0.0;
 		}
 	} else {
-		euler.x = Math::atan2(elements[0][1], elements[1][1]);
+		euler.x = Math::atan2(elements[2][1], elements[1][1]);
 		euler.y = Math_PI / 2.0;
 		euler.z = 0.0;
 	}
@@ -481,16 +478,106 @@ void Basis::set_euler_xyz(const Vector3 &p_euler) {
 	*this = xmat * (ymat * zmat);
 }
 
+Vector3 Basis::get_euler_xzy() const {
+	// Euler angles in XZY convention.
+	// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
+	//
+	// rot =  cz*cy             -sz             cz*sy
+	//        sx*sy+cx*cy*sz    cx*cz           cx*sz*sy-cy*sx
+	//        cy*sx*sz          cz*sx           cx*cy+sx*sz*sy
+
+	Vector3 euler;
+	real_t sz = elements[0][1];
+	if (sz < (1.0 - CMP_EPSILON)) {
+		if (sz > -(1.0 - CMP_EPSILON)) {
+			euler.x = Math::atan2(elements[2][1], elements[1][1]);
+			euler.y = Math::atan2(elements[0][2], elements[0][0]);
+			euler.z = Math::asin(-sz);
+		} else {
+			// It's -1
+			euler.x = -Math::atan2(elements[1][2], elements[2][2]);
+			euler.y = 0.0;
+			euler.z = Math_PI / 2.0;
+		}
+	} else {
+		// It's 1
+		euler.x = -Math::atan2(elements[1][2], elements[2][2]);
+		euler.y = 0.0;
+		euler.z = -Math_PI / 2.0;
+	}
+	return euler;
+}
+
+void Basis::set_euler_xzy(const Vector3 &p_euler) {
+	real_t c, s;
+
+	c = Math::cos(p_euler.x);
+	s = Math::sin(p_euler.x);
+	Basis xmat(1.0, 0.0, 0.0, 0.0, c, -s, 0.0, s, c);
+
+	c = Math::cos(p_euler.y);
+	s = Math::sin(p_euler.y);
+	Basis ymat(c, 0.0, s, 0.0, 1.0, 0.0, -s, 0.0, c);
+
+	c = Math::cos(p_euler.z);
+	s = Math::sin(p_euler.z);
+	Basis zmat(c, -s, 0.0, s, c, 0.0, 0.0, 0.0, 1.0);
+
+	*this = xmat * zmat * ymat;
+}
+
+Vector3 Basis::get_euler_yzx() const {
+	// Euler angles in YZX convention.
+	// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
+	//
+	// rot =  cy*cz             sy*sx-cy*cx*sz     cx*sy+cy*sz*sx
+	//        sz                cz*cx              -cz*sx
+	//        -cz*sy            cy*sx+cx*sy*sz     cy*cx-sy*sz*sx
+
+	Vector3 euler;
+	real_t sz = elements[1][0];
+	if (sz < (1.0 - CMP_EPSILON)) {
+		if (sz > -(1.0 - CMP_EPSILON)) {
+			euler.x = Math::atan2(-elements[1][2], elements[1][1]);
+			euler.y = Math::atan2(-elements[2][0], elements[0][0]);
+			euler.z = Math::asin(sz);
+		} else {
+			// It's -1
+			euler.x = Math::atan2(elements[2][1], elements[2][2]);
+			euler.y = 0.0;
+			euler.z = -Math_PI / 2.0;
+		}
+	} else {
+		// It's 1
+		euler.x = Math::atan2(elements[2][1], elements[2][2]);
+		euler.y = 0.0;
+		euler.z = Math_PI / 2.0;
+	}
+	return euler;
+}
+
+void Basis::set_euler_yzx(const Vector3 &p_euler) {
+	real_t c, s;
+
+	c = Math::cos(p_euler.x);
+	s = Math::sin(p_euler.x);
+	Basis xmat(1.0, 0.0, 0.0, 0.0, c, -s, 0.0, s, c);
+
+	c = Math::cos(p_euler.y);
+	s = Math::sin(p_euler.y);
+	Basis ymat(c, 0.0, s, 0.0, 1.0, 0.0, -s, 0.0, c);
+
+	c = Math::cos(p_euler.z);
+	s = Math::sin(p_euler.z);
+	Basis zmat(c, -s, 0.0, s, c, 0.0, 0.0, 0.0, 1.0);
+
+	*this = ymat * zmat * xmat;
+}
+
 // get_euler_yxz returns a vector containing the Euler angles in the YXZ convention,
 // as in first-Z, then-X, last-Y. The angles for X, Y, and Z rotations are returned
 // as the x, y, and z components of a Vector3 respectively.
 Vector3 Basis::get_euler_yxz() const {
-
-	/* checking this is a bad idea, because obtaining from scaled transform is a valid use case
-#ifdef MATH_CHECKS
-	ERR_FAIL_COND(!is_rotation());
-#endif
-*/
 	// Euler angles in YXZ convention.
 	// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
 	//
@@ -502,8 +589,8 @@ Vector3 Basis::get_euler_yxz() const {
 
 	real_t m12 = elements[1][2];
 
-	if (m12 < 1) {
-		if (m12 > -1) {
+	if (m12 < (1 - CMP_EPSILON)) {
+		if (m12 > -(1 - CMP_EPSILON)) {
 			// is this a pure X rotation?
 			if (elements[1][0] == 0 && elements[0][1] == 0 && elements[0][2] == 0 && elements[2][0] == 0 && elements[0][0] == 1) {
 				// return the simplest form (human friendlier in editor and scripts)
@@ -517,12 +604,12 @@ Vector3 Basis::get_euler_yxz() const {
 			}
 		} else { // m12 == -1
 			euler.x = Math_PI * 0.5;
-			euler.y = -atan2(-elements[0][1], elements[0][0]);
+			euler.y = atan2(elements[0][1], elements[0][0]);
 			euler.z = 0;
 		}
 	} else { // m12 == 1
 		euler.x = -Math_PI * 0.5;
-		euler.y = -atan2(-elements[0][1], elements[0][0]);
+		euler.y = -atan2(elements[0][1], elements[0][0]);
 		euler.z = 0;
 	}
 
@@ -553,6 +640,100 @@ void Basis::set_euler_yxz(const Vector3 &p_euler) {
 	*this = ymat * xmat * zmat;
 }
 
+Vector3 Basis::get_euler_zxy() const {
+	// Euler angles in ZXY convention.
+	// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
+	//
+	// rot =  cz*cy-sz*sx*sy    -cx*sz                cz*sy+cy*sz*sx
+	//        cy*sz+cz*sx*sy    cz*cx                 sz*sy-cz*cy*sx
+	//        -cx*sy            sx                    cx*cy
+	Vector3 euler;
+	real_t sx = elements[2][1];
+	if (sx < (1.0 - CMP_EPSILON)) {
+		if (sx > -(1.0 - CMP_EPSILON)) {
+			euler.x = Math::asin(sx);
+			euler.y = Math::atan2(-elements[2][0], elements[2][2]);
+			euler.z = Math::atan2(-elements[0][1], elements[1][1]);
+		} else {
+			// It's -1
+			euler.x = -Math_PI / 2.0;
+			euler.y = Math::atan2(elements[0][2], elements[0][0]);
+			euler.z = 0;
+		}
+	} else {
+		// It's 1
+		euler.x = Math_PI / 2.0;
+		euler.y = Math::atan2(elements[0][2], elements[0][0]);
+		euler.z = 0;
+	}
+	return euler;
+}
+
+void Basis::set_euler_zxy(const Vector3 &p_euler) {
+	real_t c, s;
+
+	c = Math::cos(p_euler.x);
+	s = Math::sin(p_euler.x);
+	Basis xmat(1.0, 0.0, 0.0, 0.0, c, -s, 0.0, s, c);
+
+	c = Math::cos(p_euler.y);
+	s = Math::sin(p_euler.y);
+	Basis ymat(c, 0.0, s, 0.0, 1.0, 0.0, -s, 0.0, c);
+
+	c = Math::cos(p_euler.z);
+	s = Math::sin(p_euler.z);
+	Basis zmat(c, -s, 0.0, s, c, 0.0, 0.0, 0.0, 1.0);
+
+	*this = zmat * xmat * ymat;
+}
+
+Vector3 Basis::get_euler_zyx() const {
+	// Euler angles in ZYX convention.
+	// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
+	//
+	// rot =  cz*cy             cz*sy*sx-cx*sz        sz*sx+cz*cx*cy
+	//        cy*sz             cz*cx+sz*sy*sx        cx*sz*sy-cz*sx
+	//        -sy               cy*sx                 cy*cx
+	Vector3 euler;
+	real_t sy = elements[2][0];
+	if (sy < (1.0 - CMP_EPSILON)) {
+		if (sy > -(1.0 - CMP_EPSILON)) {
+			euler.x = Math::atan2(elements[2][1], elements[2][2]);
+			euler.y = Math::asin(-sy);
+			euler.z = Math::atan2(elements[1][0], elements[0][0]);
+		} else {
+			// It's -1
+			euler.x = 0;
+			euler.y = Math_PI / 2.0;
+			euler.z = -Math::atan2(elements[0][1], elements[1][1]);
+		}
+	} else {
+		// It's 1
+		euler.x = 0;
+		euler.y = -Math_PI / 2.0;
+		euler.z = -Math::atan2(elements[0][1], elements[1][1]);
+	}
+	return euler;
+}
+
+void Basis::set_euler_zyx(const Vector3 &p_euler) {
+	real_t c, s;
+
+	c = Math::cos(p_euler.x);
+	s = Math::sin(p_euler.x);
+	Basis xmat(1.0, 0.0, 0.0, 0.0, c, -s, 0.0, s, c);
+
+	c = Math::cos(p_euler.y);
+	s = Math::sin(p_euler.y);
+	Basis ymat(c, 0.0, s, 0.0, 1.0, 0.0, -s, 0.0, c);
+
+	c = Math::cos(p_euler.z);
+	s = Math::sin(p_euler.z);
+	Basis zmat(c, -s, 0.0, s, c, 0.0, 0.0, 0.0, 1.0);
+
+	*this = zmat * ymat * xmat;
+}
+
 bool Basis::is_equal_approx(const Basis &p_basis) const {
 
 	return elements[0].is_equal_approx(p_basis.elements[0]) && elements[1].is_equal_approx(p_basis.elements[1]) && elements[2].is_equal_approx(p_basis.elements[2]);

core/math/basis.h

@@ -90,9 +90,22 @@ public:
 
 	Vector3 get_euler_xyz() const;
 	void set_euler_xyz(const Vector3 &p_euler);
+
+	Vector3 get_euler_xzy() const;
+	void set_euler_xzy(const Vector3 &p_euler);
+
+	Vector3 get_euler_yzx() const;
+	void set_euler_yzx(const Vector3 &p_euler);
+
 	Vector3 get_euler_yxz() const;
 	void set_euler_yxz(const Vector3 &p_euler);
 
+	Vector3 get_euler_zxy() const;
+	void set_euler_zxy(const Vector3 &p_euler);
+
+	Vector3 get_euler_zyx() const;
+	void set_euler_zyx(const Vector3 &p_euler);
+
 	Quat get_quat() const;
 	void set_quat(const Quat &p_quat);
 

core/variant_call.cpp

@@ -824,6 +824,18 @@ struct _VariantCall {
 	VCALL_PTR1R(Basis, scaled);
 	VCALL_PTR0R(Basis, get_scale);
 	VCALL_PTR0R(Basis, get_euler);
+	VCALL_PTR0R(Basis, get_euler_xyz);
+	VCALL_PTR1(Basis, set_euler_xyz);
+	VCALL_PTR0R(Basis, get_euler_xzy);
+	VCALL_PTR1(Basis, set_euler_xzy);
+	VCALL_PTR0R(Basis, get_euler_yzx);
+	VCALL_PTR1(Basis, set_euler_yzx);
+	VCALL_PTR0R(Basis, get_euler_yxz);
+	VCALL_PTR1(Basis, set_euler_yxz);
+	VCALL_PTR0R(Basis, get_euler_zxy);
+	VCALL_PTR1(Basis, set_euler_zxy);
+	VCALL_PTR0R(Basis, get_euler_zyx);
+	VCALL_PTR1(Basis, set_euler_zyx);
 	VCALL_PTR1R(Basis, tdotx);
 	VCALL_PTR1R(Basis, tdoty);
 	VCALL_PTR1R(Basis, tdotz);

main/tests/test_basis.cpp

@@ -0,0 +1,325 @@
+/*************************************************************************/
+/*  test_fbx.cpp                                                         */
+/*************************************************************************/
+/*                       This file is part of:                           */
+/*                           GODOT ENGINE                                */
+/*                      https://godotengine.org                          */
+/*************************************************************************/
+/* Copyright (c) 2007-2020 Juan Linietsky, Ariel Manzur.                 */
+/* Copyright (c) 2014-2020 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_basis.h"
+
+#include "core/math/random_number_generator.h"
+#include "core/os/os.h"
+#include "core/ustring.h"
+
+namespace TestBasis {
+
+enum RotOrder {
+	EulerXYZ,
+	EulerXZY,
+	EulerYZX,
+	EulerYXZ,
+	EulerZXY,
+	EulerZYX
+};
+
+Vector3 deg2rad(const Vector3 &p_rotation) {
+	return p_rotation / 180.0 * Math_PI;
+}
+
+Vector3 rad2deg(const Vector3 &p_rotation) {
+	return p_rotation / Math_PI * 180.0;
+}
+
+Basis EulerToBasis(RotOrder mode, const Vector3 &p_rotation) {
+	Basis ret;
+	switch (mode) {
+		case EulerXYZ:
+			ret.set_euler_xyz(p_rotation);
+			break;
+
+		case EulerXZY:
+			ret.set_euler_xzy(p_rotation);
+			break;
+
+		case EulerYZX:
+			ret.set_euler_yzx(p_rotation);
+			break;
+
+		case EulerYXZ:
+			ret.set_euler_yxz(p_rotation);
+			break;
+
+		case EulerZXY:
+			ret.set_euler_zxy(p_rotation);
+			break;
+
+		case EulerZYX:
+			ret.set_euler_zyx(p_rotation);
+			break;
+
+		default:
+			// If you land here, Please integrate all rotation orders.
+			CRASH_NOW_MSG("This is not unreachable.");
+	}
+
+	return ret;
+}
+
+Vector3 BasisToEuler(RotOrder mode, const Basis &p_rotation) {
+	switch (mode) {
+		case EulerXYZ:
+			return p_rotation.get_euler_xyz();
+
+		case EulerXZY:
+			return p_rotation.get_euler_xzy();
+
+		case EulerYZX:
+			return p_rotation.get_euler_yzx();
+
+		case EulerYXZ:
+			return p_rotation.get_euler_yxz();
+
+		case EulerZXY:
+			return p_rotation.get_euler_zxy();
+
+		case EulerZYX:
+			return p_rotation.get_euler_zyx();
+
+		default:
+			// If you land here, Please integrate all rotation orders.
+			CRASH_NOW_MSG("This is not unreachable.");
+			return Vector3();
+	}
+}
+
+String get_rot_order_name(RotOrder ro) {
+	switch (ro) {
+		case EulerXYZ:
+			return "XYZ";
+		case EulerXZY:
+			return "XZY";
+		case EulerYZX:
+			return "YZX";
+		case EulerYXZ:
+			return "YXZ";
+		case EulerZXY:
+			return "ZXY";
+		case EulerZYX:
+			return "ZYX";
+		default:
+			return "[Not supported]";
+	}
+}
+
+bool test_rotation(Vector3 deg_original_euler, RotOrder rot_order) {
+	// This test:
+	// 1. Converts the rotation vector from deg to rad.
+	// 2. Converts euler to basis.
+	// 3. Converts the above basis back into euler.
+	// 4. Converts the above euler into basis again.
+	// 5. Compares the basis obtained in step 2 with the basis of step 4
+	//
+	// The conversion "basis to euler", done in the step 3, may be different from
+	// the original euler, even if the final rotation are the same.
+	// This happens because there are more ways to represents the same rotation,
+	// both valid, using eulers.
+	// For this reason is necessary to convert that euler back to basis and finally
+	// compares it.
+	//
+	// In this way we can assert that both functions: basis to euler / euler to basis
+	// are correct.
+
+	bool pass = true;
+
+	// Euler to rotation
+	const Vector3 original_euler = deg2rad(deg_original_euler);
+	const Basis to_rotation = EulerToBasis(rot_order, original_euler);
+
+	// Euler from rotation
+	const Vector3 euler_from_rotation = BasisToEuler(rot_order, to_rotation);
+	const Basis rotation_from_computed_euler = EulerToBasis(rot_order, euler_from_rotation);
+
+	Basis res = to_rotation.inverse() * rotation_from_computed_euler;
+
+	if ((res.get_axis(0) - Vector3(1.0, 0.0, 0.0)).length() > 0.1) {
+		OS::get_singleton()->print("Fail due to X %ls\n", String(res.get_axis(0)).c_str());
+		pass = false;
+	}
+	if ((res.get_axis(1) - Vector3(0.0, 1.0, 0.0)).length() > 0.1) {
+		OS::get_singleton()->print("Fail due to Y %ls\n", String(res.get_axis(1)).c_str());
+		pass = false;
+	}
+	if ((res.get_axis(2) - Vector3(0.0, 0.0, 1.0)).length() > 0.1) {
+		OS::get_singleton()->print("Fail due to Z %ls\n", String(res.get_axis(2)).c_str());
+		pass = false;
+	}
+
+	if (pass) {
+		// Double check `to_rotation` decomposing with XYZ rotation order.
+		const Vector3 euler_xyz_from_rotation = to_rotation.get_euler_xyz();
+		Basis rotation_from_xyz_computed_euler;
+		rotation_from_xyz_computed_euler.set_euler_xyz(euler_xyz_from_rotation);
+
+		res = to_rotation.inverse() * rotation_from_xyz_computed_euler;
+
+		if ((res.get_axis(0) - Vector3(1.0, 0.0, 0.0)).length() > 0.1) {
+			OS::get_singleton()->print("Double check with XYZ rot order failed, due to X %ls\n", String(res.get_axis(0)).c_str());
+			pass = false;
+		}
+		if ((res.get_axis(1) - Vector3(0.0, 1.0, 0.0)).length() > 0.1) {
+			OS::get_singleton()->print("Double check with XYZ rot order failed, due to Y %ls\n", String(res.get_axis(1)).c_str());
+			pass = false;
+		}
+		if ((res.get_axis(2) - Vector3(0.0, 0.0, 1.0)).length() > 0.1) {
+			OS::get_singleton()->print("Double check with XYZ rot order failed, due to Z %ls\n", String(res.get_axis(2)).c_str());
+			pass = false;
+		}
+	}
+
+	if (pass == false) {
+		// Print phase only if not pass.
+		OS *os = OS::get_singleton();
+		os->print("Rotation order: %ls\n.", get_rot_order_name(rot_order).c_str());
+		os->print("Original Rotation: %ls\n", String(deg_original_euler).c_str());
+		os->print("Quaternion to rotation order: %ls\n", String(rad2deg(euler_from_rotation)).c_str());
+	}
+
+	return pass;
+}
+
+void test_euler_conversion() {
+	Vector<RotOrder> rotorder_to_test;
+	rotorder_to_test.push_back(EulerXYZ);
+	rotorder_to_test.push_back(EulerXZY);
+	rotorder_to_test.push_back(EulerYZX);
+	rotorder_to_test.push_back(EulerYXZ);
+	rotorder_to_test.push_back(EulerZXY);
+	rotorder_to_test.push_back(EulerZYX);
+
+	Vector<Vector3> vectors_to_test;
+
+	// Test the special cases.
+	vectors_to_test.push_back(Vector3(0.0, 0.0, 0.0));
+	vectors_to_test.push_back(Vector3(0.5, 0.5, 0.5));
+	vectors_to_test.push_back(Vector3(-0.5, -0.5, -0.5));
+	vectors_to_test.push_back(Vector3(40.0, 40.0, 40.0));
+	vectors_to_test.push_back(Vector3(-40.0, -40.0, -40.0));
+	vectors_to_test.push_back(Vector3(0.0, 0.0, -90.0));
+	vectors_to_test.push_back(Vector3(0.0, -90.0, 0.0));
+	vectors_to_test.push_back(Vector3(-90.0, 0.0, 0.0));
+	vectors_to_test.push_back(Vector3(0.0, 0.0, 90.0));
+	vectors_to_test.push_back(Vector3(0.0, 90.0, 0.0));
+	vectors_to_test.push_back(Vector3(90.0, 0.0, 0.0));
+	vectors_to_test.push_back(Vector3(0.0, 0.0, -30.0));
+	vectors_to_test.push_back(Vector3(0.0, -30.0, 0.0));
+	vectors_to_test.push_back(Vector3(-30.0, 0.0, 0.0));
+	vectors_to_test.push_back(Vector3(0.0, 0.0, 30.0));
+	vectors_to_test.push_back(Vector3(0.0, 30.0, 0.0));
+	vectors_to_test.push_back(Vector3(30.0, 0.0, 0.0));
+	vectors_to_test.push_back(Vector3(0.5, 50.0, 20.0));
+	vectors_to_test.push_back(Vector3(-0.5, -50.0, -20.0));
+	vectors_to_test.push_back(Vector3(0.5, 0.0, 90.0));
+	vectors_to_test.push_back(Vector3(0.5, 0.0, -90.0));
+	vectors_to_test.push_back(Vector3(360.0, 360.0, 360.0));
+	vectors_to_test.push_back(Vector3(-360.0, -360.0, -360.0));
+	vectors_to_test.push_back(Vector3(-90.0, 60.0, -90.0));
+	vectors_to_test.push_back(Vector3(90.0, 60.0, -90.0));
+	vectors_to_test.push_back(Vector3(90.0, -60.0, -90.0));
+	vectors_to_test.push_back(Vector3(-90.0, -60.0, -90.0));
+	vectors_to_test.push_back(Vector3(-90.0, 60.0, 90.0));
+	vectors_to_test.push_back(Vector3(90.0, 60.0, 90.0));
+	vectors_to_test.push_back(Vector3(90.0, -60.0, 90.0));
+	vectors_to_test.push_back(Vector3(-90.0, -60.0, 90.0));
+	vectors_to_test.push_back(Vector3(60.0, 90.0, -40.0));
+	vectors_to_test.push_back(Vector3(60.0, -90.0, -40.0));
+	vectors_to_test.push_back(Vector3(-60.0, -90.0, -40.0));
+	vectors_to_test.push_back(Vector3(-60.0, 90.0, 40.0));
+	vectors_to_test.push_back(Vector3(60.0, 90.0, 40.0));
+	vectors_to_test.push_back(Vector3(60.0, -90.0, 40.0));
+	vectors_to_test.push_back(Vector3(-60.0, -90.0, 40.0));
+	vectors_to_test.push_back(Vector3(-90.0, 90.0, -90.0));
+	vectors_to_test.push_back(Vector3(90.0, 90.0, -90.0));
+	vectors_to_test.push_back(Vector3(90.0, -90.0, -90.0));
+	vectors_to_test.push_back(Vector3(-90.0, -90.0, -90.0));
+	vectors_to_test.push_back(Vector3(-90.0, 90.0, 90.0));
+	vectors_to_test.push_back(Vector3(90.0, 90.0, 90.0));
+	vectors_to_test.push_back(Vector3(90.0, -90.0, 90.0));
+	vectors_to_test.push_back(Vector3(20.0, 150.0, 30.0));
+	vectors_to_test.push_back(Vector3(20.0, -150.0, 30.0));
+	vectors_to_test.push_back(Vector3(-120.0, -150.0, 30.0));
+	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(120.0, 150.0, -130.0));
+	vectors_to_test.push_back(Vector3(120.0, 150.0, 130.0));
+
+	// Add 1000 random vectors with weirds numbers.
+	RandomNumberGenerator rng;
+	for (int _ = 0; _ < 1000; _ += 1) {
+		vectors_to_test.push_back(Vector3(
+				rng.randf_range(-1800, 1800),
+				rng.randf_range(-1800, 1800),
+				rng.randf_range(-1800, 1800)));
+	}
+
+	bool success = true;
+	for (int h = 0; h < rotorder_to_test.size(); h += 1) {
+		int passed = 0;
+		int failed = 0;
+		for (int i = 0; i < vectors_to_test.size(); i += 1) {
+			if (test_rotation(vectors_to_test[i], rotorder_to_test[h])) {
+				//OS::get_singleton()->print("Success. \n\n");
+				passed += 1;
+			} else {
+				OS::get_singleton()->print("FAILED                   FAILED                        FAILED. \n\n");
+				OS::get_singleton()->print("------------>\n");
+				OS::get_singleton()->print("------------>\n");
+				failed += 1;
+				success = false;
+			}
+		}
+
+		if (failed == 0) {
+			OS::get_singleton()->print("%i passed tests for rotation order: %ls.\n", passed, get_rot_order_name(rotorder_to_test[h]).c_str());
+		} else {
+			OS::get_singleton()->print("%i FAILED tests for rotation order: %ls.\n", failed, get_rot_order_name(rotorder_to_test[h]).c_str());
+		}
+	}
+
+	if (success) {
+		OS::get_singleton()->print("Euler conversion checks passed.\n");
+	} else {
+		OS::get_singleton()->print("Euler conversion checks FAILED.\n");
+	}
+}
+
+MainLoop *test() {
+	OS::get_singleton()->print("Start euler conversion checks.\n");
+	test_euler_conversion();
+
+	return NULL;
+}
+
+} // namespace TestBasis

main/tests/test_basis.h

@@ -0,0 +1,40 @@
+/*************************************************************************/
+/*  test_fbx.h                                                        */
+/*************************************************************************/
+/*                       This file is part of:                           */
+/*                           GODOT ENGINE                                */
+/*                      https://godotengine.org                          */
+/*************************************************************************/
+/* Copyright (c) 2007-2020 Juan Linietsky, Ariel Manzur.                 */
+/* Copyright (c) 2014-2020 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_BASIS_H
+#define TEST_BASIS_H
+
+#include "core/os/main_loop.h"
+
+namespace TestBasis {
+MainLoop *test();
+}
+
+#endif

main/tests/test_main.cpp

@@ -35,6 +35,7 @@
 #ifdef DEBUG_ENABLED
 
 #include "test_astar.h"
+#include "test_basis.h"
 #include "test_gdscript.h"
 #include "test_gui.h"
 #include "test_math.h"
@@ -51,6 +52,7 @@ const char **tests_get_names() {
 	static const char *test_names[] = {
 		"string",
 		"math",
+		"basis",
 		"physics",
 		"physics_2d",
 		"render",
@@ -81,6 +83,11 @@ MainLoop *test_main(String p_test, const List<String> &p_args) {
 		return TestMath::test();
 	}
 
+	if (p_test == "basis") {
+
+		return TestBasis::test();
+	}
+
 	if (p_test == "physics") {
 
 		return TestPhysics::test();