- 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.

3 files changed, 371 insertions, 0 deletions

diff --git a/main/tests/test_basis.cpp b/main/tests/test_basis.cpp
new file mode 100644
index 0000000000..ac25151fd8
--- /dev/null
+++ b/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
diff --git a/main/tests/test_basis.h b/main/tests/test_basis.h
new file mode 100644
index 0000000000..67c9db8877
--- /dev/null
+++ b/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
diff --git a/main/tests/test_main.cpp b/main/tests/test_main.cpp
index 0bb8367240..5ebdaf1741 100644
--- a/main/tests/test_main.cpp
+++ b/main/tests/test_main.cpp
@@ -35,6 +35,7 @@
 #ifdef DEBUG_ENABLED
 
 #include "test_astar.h"
+#include "test_basis.h"
 #include "test_class_db.h"
 #include "test_gdscript.h"
 #include "test_gui.h"
@@ -51,6 +52,7 @@ const char **tests_get_names() {
 	static const char *test_names[] = {
 		"string",
 		"math",
+		"basis",
 		"physics_2d",
 		"physics_3d",
 		"render",
@@ -79,6 +81,10 @@ 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_2d") {
 		return TestPhysics2D::test();
 	}