Fix `Projection::invert` on orthogonal projections and others.

Relates to godotengine/godot#68878, specially when using orthographic projection.

Also adds some tests.

Adapted from godotengine/godot#95303

1 files changed, 89 insertions, 0 deletions

diff --git a/tests/core/math/test_projection.h b/tests/core/math/test_projection.h
new file mode 100644
index 0000000000..2cd6198cba
--- /dev/null
+++ b/tests/core/math/test_projection.h
@@ -0,0 +1,89 @@
+/**************************************************************************/
+/*  test_projection.h                                                     */
+/**************************************************************************/
+/*                         This file is part of:                          */
+/*                             GODOT ENGINE                               */
+/*                        https://godotengine.org                         */
+/**************************************************************************/
+/* Copyright (c) 2024-present Redot Engine contributors                   */
+/*                                          (see REDOT_AUTHORS.md)        */
+/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
+/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur.                  */
+/*                                                                        */
+/* 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_PROJECTION_H
+#define TEST_PROJECTION_H
+
+#include "core/math/projection.h"
+
+#include "core/string/print_string.h"
+#include "tests/test_macros.h"
+
+namespace TestProjection {
+
+TEST_CASE("[Projection] Default construct") {
+	Projection p;
+	CHECK(p.columns[0][0] == 1.0);
+	CHECK(p.columns[0][1] == 0.0);
+	CHECK(p.columns[0][2] == 0.0);
+	CHECK(p.columns[0][3] == 0.0);
+
+	CHECK(p.columns[1][0] == 0.0);
+	CHECK(p.columns[1][1] == 1.0);
+	CHECK(p.columns[1][2] == 0.0);
+	CHECK(p.columns[1][3] == 0.0);
+
+	CHECK(p.columns[2][0] == 0.0);
+	CHECK(p.columns[2][1] == 0.0);
+	CHECK(p.columns[2][2] == 1.0);
+	CHECK(p.columns[2][3] == 0.0);
+
+	CHECK(p.columns[3][0] == 0.0);
+	CHECK(p.columns[3][1] == 0.0);
+	CHECK(p.columns[3][2] == 0.0);
+	CHECK(p.columns[3][3] == 1.0);
+}
+
+bool projection_is_equal_approx(const Projection &p_a, const Projection &p_b) {
+	for (int i = 0; i < 4; i++) {
+		for (int j = 0; j < 4; j++) {
+			if (!Math::is_equal_approx(p_a.columns[i][j], p_b.columns[i][j])) {
+				return false;
+			}
+		}
+	}
+	return true;
+}
+
+TEST_CASE("[Projection] Orthogonal projection matrix inversion") {
+	Projection p = Projection::create_orthogonal(-125.0f, 125.0f, -125.0f, 125.0f, 0.01f, 25.0f);
+	CHECK(projection_is_equal_approx(p.inverse() * p, Projection()));
+}
+
+TEST_CASE("[Projection] Perspective projection matrix inversion") {
+	Projection p = Projection::create_perspective(90.0f, 1.77777f, 0.05f, 4000.0f);
+	CHECK(projection_is_equal_approx(p.inverse() * p, Projection()));
+}
+
+} //namespace TestProjection
+
+#endif // TEST_PROJECTION_H