Fixes incorrect NDC calculation and updates formulas

Corrects the NDC calculation in `world_to_screen` to improve accuracy.
Replaces custom perspective projection matrix calculation with `omath::mat_perspective_right_handed` for correctness and consistency.
Updates test cases and provides debugging information by printing view and projection matrices.
Addresses an issue in the feature/ndc_invalid_calc_fix branch.

include/omath/projection/camera.hpp

@@ -239,7 +239,8 @@ namespace omath::projection
                            -1   |
                                 v
             */
-            return {(ndc.x + 1.f) / 2.f * m_view_port.m_width, (1.f - ndc.y) / 2.f * m_view_port.m_height, ndc.z};
+
+            return {(ndc.x + 1.f) / 2.f * m_view_port.m_width, (ndc.y / 2.f + 0.5f) * m_view_port.m_height, ndc.z};
         }
 
         [[nodiscard]] Vector3<float> screen_to_ndc(const Vector3<float>& screen_pos) const noexcept

source/engines/unity_engine/formulas.cpp

@@ -25,7 +25,7 @@ namespace omath::unity_engine
     }
     Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept
     {
-        return mat_camera_view<float, MatStoreType::ROW_MAJOR>(forward_vector(angles), -right_vector(angles),
+        return mat_camera_view<float, MatStoreType::ROW_MAJOR>(-forward_vector(angles), right_vector(angles),
                                                                up_vector(angles), cam_origin);
     }
     Mat4X4 rotation_matrix(const ViewAngles& angles) noexcept
@@ -37,13 +37,6 @@ namespace omath::unity_engine
     Mat4X4 calc_perspective_projection_matrix(const float field_of_view, const float aspect_ratio, const float near,
                                               const float far) noexcept
     {
-        const float fov_half_tan = std::tan(angles::degrees_to_radians(field_of_view) / 2.f);
+        return omath::mat_perspective_right_handed(field_of_view, aspect_ratio, near, far);
-
-        return {
-                {1.f / (aspect_ratio * fov_half_tan), 0, 0, 0},
-                {0, 1.f / (fov_half_tan), 0, 0},
-                {0, 0, (far + near) / (far - near), -(2.f * far * near) / (far - near)},
-                {0, 0, -1.f, 0},
-        };
     }
 } // namespace omath::unity_engine

tests/engines/unit_test_unity_engine.cpp

@@ -87,9 +87,9 @@ TEST(unit_test_unity_engine, Project)
     constexpr auto fov = omath::projection::FieldOfView::from_degrees(60.f);
 
     const auto cam = omath::unity_engine::Camera({0, 0, 0}, {}, {1280.f, 720.f}, fov, 0.03f, 1000.f);
-    const auto proj = cam.world_to_screen({5.f, 3, 10.f});
+    const auto proj = cam.world_to_screen({10.f, 3, 10.f});
 
-    EXPECT_NEAR(proj->x, 951.769f, 0.001f);
+    EXPECT_NEAR(proj->x, 1263.538, 0.001f);
     EXPECT_NEAR(proj->y, 547.061f, 0.001f);
 }
 
@@ -234,3 +234,18 @@ TEST(unit_test_unity_engine, loook_at_random_z_axis)
     }
     EXPECT_LE(failed_points, 100);
 }
+
+TEST(unit_test_unity_engine, to_camera_coordiante_syste)
+{
+    omath::Vector3<float> point = {10, 3, 10};
+    auto result = omath::unity_engine::calc_view_matrix({}, {}) * omath::mat_column_from_vector(point);
+    auto perspective = omath::unity_engine::calc_perspective_projection_matrix(60, 1280 / 720.f, 0.3, 1000);
+
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(60.f);
+
+    const auto cam = omath::unity_engine::Camera({0, 0, 0}, {}, {1280.f, 720.f}, fov, 0.03f, 1000.f);
+
+    std::println("View matrix: \n{}", cam.get_view_matrix());
+    std::println("Projection: \n{}", cam.get_projection_matrix());
+    std::print("NDC: projection {} -> {}", point, cam.world_to_screen(point).value());
+}