updated formulas

include/omath/linear_algebra/mat.hpp

@@ -707,6 +707,59 @@ namespace omath
         else
             std::unreachable();
     }
+
+    // Horizontal-FOV variants — use these when the engine reports FOV as
+    // horizontal (UE's FMinimalViewInfo::FOV, Quake-family fov_x, etc.).
+    // X and Y scales derived as: X = 1 / tan(hfov/2), Y = aspect / tan(hfov/2).
+    template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR,
+             NDCDepthRange DepthRange = NDCDepthRange::NEGATIVE_ONE_TO_ONE>
+    [[nodiscard]]
+    Mat<4, 4, Type, St> mat_perspective_left_handed_horizontal_fov(const float horizontal_fov,
+                                                                   const float aspect_ratio, const float near,
+                                                                   const float far) noexcept
+    {
+        const float inv_tan_half_hfov = 1.f / std::tan(angles::degrees_to_radians(horizontal_fov) / 2.f);
+        const float x_axis = inv_tan_half_hfov;
+        const float y_axis = inv_tan_half_hfov * aspect_ratio;
+
+        if constexpr (DepthRange == NDCDepthRange::ZERO_TO_ONE)
+            return {{x_axis, 0.f,    0.f,                          0.f},
+                    {0.f,    y_axis, 0.f,                          0.f},
+                    {0.f,    0.f,    far / (far - near),          -(near * far) / (far - near)},
+                    {0.f,    0.f,    1.f,                          0.f}};
+        else if constexpr (DepthRange == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
+            return {{x_axis, 0.f,    0.f,                                  0.f},
+                    {0.f,    y_axis, 0.f,                                  0.f},
+                    {0.f,    0.f,    (far + near) / (far - near),         -(2.f * near * far) / (far - near)},
+                    {0.f,    0.f,    1.f,                                  0.f}};
+        else
+            std::unreachable();
+    }
+
+    template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR,
+             NDCDepthRange DepthRange = NDCDepthRange::NEGATIVE_ONE_TO_ONE>
+    [[nodiscard]]
+    Mat<4, 4, Type, St> mat_perspective_right_handed_horizontal_fov(const float horizontal_fov,
+                                                                    const float aspect_ratio, const float near,
+                                                                    const float far) noexcept
+    {
+        const float inv_tan_half_hfov = 1.f / std::tan(angles::degrees_to_radians(horizontal_fov) / 2.f);
+        const float x_axis = inv_tan_half_hfov;
+        const float y_axis = inv_tan_half_hfov * aspect_ratio;
+
+        if constexpr (DepthRange == NDCDepthRange::ZERO_TO_ONE)
+            return {{x_axis, 0.f,    0.f,                          0.f},
+                    {0.f,    y_axis, 0.f,                          0.f},
+                    {0.f,    0.f,   -far / (far - near),          -(near * far) / (far - near)},
+                    {0.f,    0.f,   -1.f,                          0.f}};
+        else if constexpr (DepthRange == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
+            return {{x_axis, 0.f,    0.f,                                  0.f},
+                    {0.f,    y_axis, 0.f,                                  0.f},
+                    {0.f,    0.f,   -(far + near) / (far - near),         -(2.f * near * far) / (far - near)},
+                    {0.f,    0.f,   -1.f,                                  0.f}};
+        else
+            std::unreachable();
+    }
     template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR,
              NDCDepthRange DepthRange = NDCDepthRange::NEGATIVE_ONE_TO_ONE>
     [[nodiscard]]

source/engines/source_engine/formulas.cpp

@@ -39,30 +39,23 @@ namespace omath::source_engine
                                               const float far, const NDCDepthRange ndc_depth_range) noexcept
     {
         // Source (inherited from Quake) stores FOV as horizontal FOV at a 4:3
-        // reference aspect. Convert to vertical FOV first, then use the
+        // reference aspect. Convert to true vertical FOV, then delegate to the
-        // standard vfov-based projection against the caller's actual aspect.
+        // standard vertical-FOV left-handed builder with the caller's actual
+        // aspect ratio.
         //   vfov = 2 · atan( tan(hfov_4:3 / 2) / (4/3) )
         constexpr float k_source_reference_aspect = 4.f / 3.f;
         const float half_hfov_4_3 = angles::degrees_to_radians(field_of_view) / 2.f;
-        const float tan_half_vfov = std::tan(half_hfov_4_3) / k_source_reference_aspect;
+        const float vfov_deg = angles::radians_to_degrees(
-
+                2.f * std::atan(std::tan(half_hfov_4_3) / k_source_reference_aspect));
-        const float x_axis = 1.f / (aspect_ratio * tan_half_vfov);
-        const float y_axis = 1.f / tan_half_vfov;
 
         if (ndc_depth_range == NDCDepthRange::ZERO_TO_ONE)
-            return {
+            return mat_perspective_left_handed<
-                    {x_axis, 0,      0,                     0},
+                    float, MatStoreType::ROW_MAJOR, NDCDepthRange::ZERO_TO_ONE>(
-                    {0,      y_axis, 0,                     0},
+                    vfov_deg, aspect_ratio, near, far);
-                    {0,      0,      far / (far - near),   -(near * far) / (far - near)},
-                    {0,      0,      1,                     0},
-            };
         if (ndc_depth_range == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
-            return {
+            return mat_perspective_left_handed<
-                    {x_axis, 0,      0,                             0},
+                    float, MatStoreType::ROW_MAJOR, NDCDepthRange::NEGATIVE_ONE_TO_ONE>(
-                    {0,      y_axis, 0,                             0},
+                    vfov_deg, aspect_ratio, near, far);
-                    {0,      0,      (far + near) / (far - near),  -(2.f * far * near) / (far - near)},
-                    {0,      0,      1,                             0},
-            };
         std::unreachable();
     }
 } // namespace omath::source_engine

source/engines/unreal_engine/formulas.cpp

@@ -38,28 +38,16 @@ namespace omath::unreal_engine
     Mat4X4 calc_perspective_projection_matrix(const float field_of_view, const float aspect_ratio, const float near,
                                               const float far, const NDCDepthRange ndc_depth_range) noexcept
     {
-        // UE stores horizontal FOV in FMinimalViewInfo — mirror engine's
+        // UE stores horizontal FOV in FMinimalViewInfo — use the left-handed
-        // FMinimalViewInfo::CalculateProjectionMatrixGivenViewRectangle:
+        // horizontal-FOV builder directly.
-        //   XAxisMultiplier = 1 / tan(hfov/2)
-        //   YAxisMultiplier = aspect / tan(hfov/2)
-        const float inv_tan_half_hfov = 1.f / std::tan(angles::degrees_to_radians(field_of_view) / 2.f);
-        const float x_axis = inv_tan_half_hfov;
-        const float y_axis = inv_tan_half_hfov * aspect_ratio;
-
         if (ndc_depth_range == NDCDepthRange::ZERO_TO_ONE)
-            return {
+            return mat_perspective_left_handed_horizontal_fov<
-                        {x_axis, 0,      0,                     0},
+                    float, MatStoreType::ROW_MAJOR, NDCDepthRange::ZERO_TO_ONE>(
-                        {0,      y_axis, 0,                     0},
+                    field_of_view, aspect_ratio, near, far);
-                        {0,      0,      far / (far - near),   -(near * far) / (far - near)},
-                        {0,      0,      1,                     0},
-                };
         if (ndc_depth_range == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
-            return {
+            return mat_perspective_left_handed_horizontal_fov<
-                        {x_axis, 0,      0,                             0},
+                    float, MatStoreType::ROW_MAJOR, NDCDepthRange::NEGATIVE_ONE_TO_ONE>(
-                        {0,      y_axis, 0,                             0},
+                    field_of_view, aspect_ratio, near, far);
-                        {0,      0,      (far + near) / (far - near),  -(2.f * far * near) / (far - near)},
-                        {0,      0,      1,                             0},
-                };
         std::unreachable();
     }
 } // namespace omath::unreal_engine