Merge pull request #178 from orange-cpp/feature/imrovements

Feature/imrovements

include/omath/engines/cry_engine/camera.hpp

@@ -9,5 +9,5 @@
 
 namespace omath::cry_engine
 {
-    using Camera = projection::Camera<Mat4X4, ViewAngles, CameraTrait>;
+    using Camera = projection::Camera<Mat4X4, ViewAngles, CameraTrait, false, NDCDepthRange::ZERO_TO_ONE>;
 } // namespace omath::cry_engine

include/omath/engines/cry_engine/formulas.hpp

@@ -22,7 +22,8 @@ namespace omath::cry_engine
     Mat4X4 rotation_matrix(const ViewAngles& angles) noexcept;
 
     [[nodiscard]]
-    Mat4X4 calc_perspective_projection_matrix(float field_of_view, float aspect_ratio, float near, float far) noexcept;
+    Mat4X4 calc_perspective_projection_matrix(float field_of_view, float aspect_ratio, float near, float far,
+                                             NDCDepthRange ndc_depth_range = NDCDepthRange::NEGATIVE_ONE_TO_ONE) noexcept;
 
     template<class FloatingType>
     requires std::is_floating_point_v<FloatingType>

include/omath/engines/cry_engine/traits/camera_trait.hpp

@@ -18,7 +18,7 @@ namespace omath::cry_engine
         static Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept;
         [[nodiscard]]
         static Mat4X4 calc_projection_matrix(const projection::FieldOfView& fov, const projection::ViewPort& view_port,
-                                             float near, float far) noexcept;
+                                             float near, float far, NDCDepthRange ndc_depth_range) noexcept;
     };
 
 } // namespace omath::cry_engine

include/omath/engines/frostbite_engine/camera.hpp

@@ -9,5 +9,5 @@
 
 namespace omath::frostbite_engine
 {
-    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait>;
+    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait, false, NDCDepthRange::ZERO_TO_ONE>;
 } // namespace omath::unity_engine

include/omath/engines/frostbite_engine/formulas.hpp

@@ -22,7 +22,8 @@ namespace omath::frostbite_engine
     Mat4X4 rotation_matrix(const ViewAngles& angles) noexcept;
 
     [[nodiscard]]
-    Mat4X4 calc_perspective_projection_matrix(float field_of_view, float aspect_ratio, float near, float far) noexcept;
+    Mat4X4 calc_perspective_projection_matrix(float field_of_view, float aspect_ratio, float near, float far,
+                                             NDCDepthRange ndc_depth_range = NDCDepthRange::NEGATIVE_ONE_TO_ONE) noexcept;
 
     template<class FloatingType>
     requires std::is_floating_point_v<FloatingType>

include/omath/engines/frostbite_engine/traits/camera_trait.hpp

@@ -18,7 +18,7 @@ namespace omath::frostbite_engine
         static Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept;
         [[nodiscard]]
         static Mat4X4 calc_projection_matrix(const projection::FieldOfView& fov, const projection::ViewPort& view_port,
-                                             float near, float far) noexcept;
+                                             float near, float far, NDCDepthRange ndc_depth_range) noexcept;
     };
 
 } // namespace omath::unreal_engine

include/omath/engines/iw_engine/camera.hpp

@@ -9,5 +9,5 @@
 
 namespace omath::iw_engine
 {
-    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait>;
+    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait, false, NDCDepthRange::ZERO_TO_ONE>;
 } // namespace omath::iw_engine

include/omath/engines/iw_engine/formulas.hpp

@@ -22,7 +22,8 @@ namespace omath::iw_engine
     [[nodiscard]] Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept;
 
     [[nodiscard]]
-    Mat4X4 calc_perspective_projection_matrix(float field_of_view, float aspect_ratio, float near, float far) noexcept;
+    Mat4X4 calc_perspective_projection_matrix(float field_of_view, float aspect_ratio, float near, float far,
+                                             NDCDepthRange ndc_depth_range = NDCDepthRange::NEGATIVE_ONE_TO_ONE) noexcept;
 
     template<class FloatingType>
     requires std::is_floating_point_v<FloatingType>

include/omath/engines/iw_engine/traits/camera_trait.hpp

@@ -18,7 +18,7 @@ namespace omath::iw_engine
         static Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept;
         [[nodiscard]]
         static Mat4X4 calc_projection_matrix(const projection::FieldOfView& fov, const projection::ViewPort& view_port,
-                                             float near, float far) noexcept;
+                                             float near, float far, NDCDepthRange ndc_depth_range) noexcept;
     };
 
 } // namespace omath::iw_engine

include/omath/engines/opengl_engine/camera.hpp

@@ -8,5 +8,5 @@
 
 namespace omath::opengl_engine
 {
-    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait, true>;
+    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait, true, NDCDepthRange::NEGATIVE_ONE_TO_ONE>;
 } // namespace omath::opengl_engine

include/omath/engines/opengl_engine/formulas.hpp

@@ -21,7 +21,8 @@ namespace omath::opengl_engine
     Mat4X4 rotation_matrix(const ViewAngles& angles) noexcept;
 
     [[nodiscard]]
-    Mat4X4 calc_perspective_projection_matrix(float field_of_view, float aspect_ratio, float near, float far) noexcept;
+    Mat4X4 calc_perspective_projection_matrix(float field_of_view, float aspect_ratio, float near, float far,
+                                             NDCDepthRange ndc_depth_range = NDCDepthRange::NEGATIVE_ONE_TO_ONE) noexcept;
 
     template<class FloatingType>
     requires std::is_floating_point_v<FloatingType>

include/omath/engines/opengl_engine/traits/camera_trait.hpp

@@ -18,7 +18,7 @@ namespace omath::opengl_engine
         static Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept;
         [[nodiscard]]
         static Mat4X4 calc_projection_matrix(const projection::FieldOfView& fov, const projection::ViewPort& view_port,
-                                             float near, float far) noexcept;
+                                             float near, float far, NDCDepthRange ndc_depth_range) noexcept;
     };
 
 } // namespace omath::opengl_engine

include/omath/engines/source_engine/camera.hpp

@@ -7,5 +7,5 @@
 #include "traits/camera_trait.hpp"
 namespace omath::source_engine
 {
-    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait>;
+    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait, false, NDCDepthRange::ZERO_TO_ONE>;
 } // namespace omath::source_engine

include/omath/engines/source_engine/formulas.hpp

@@ -21,7 +21,8 @@ namespace omath::source_engine
     [[nodiscard]] Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept;
 
     [[nodiscard]]
-    Mat4X4 calc_perspective_projection_matrix(float field_of_view, float aspect_ratio, float near, float far) noexcept;
+    Mat4X4 calc_perspective_projection_matrix(float field_of_view, float aspect_ratio, float near, float far,
+                                             NDCDepthRange ndc_depth_range = NDCDepthRange::NEGATIVE_ONE_TO_ONE) noexcept;
 
     template<class FloatingType>
     requires std::is_floating_point_v<FloatingType>

include/omath/engines/source_engine/traits/camera_trait.hpp

@@ -18,7 +18,7 @@ namespace omath::source_engine
         static Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept;
         [[nodiscard]]
         static Mat4X4 calc_projection_matrix(const projection::FieldOfView& fov, const projection::ViewPort& view_port,
-                                             float near, float far) noexcept;
+                                             float near, float far, NDCDepthRange ndc_depth_range) noexcept;
     };
 
 } // namespace omath::source_engine

include/omath/engines/unity_engine/camera.hpp

@@ -9,5 +9,5 @@
 
 namespace omath::unity_engine
 {
-    using Camera = projection::Camera<Mat4X4, ViewAngles, CameraTrait>;
+    using Camera = projection::Camera<Mat4X4, ViewAngles, CameraTrait, false, NDCDepthRange::ZERO_TO_ONE>;
 } // namespace omath::unity_engine

include/omath/engines/unity_engine/formulas.hpp

@@ -22,7 +22,8 @@ namespace omath::unity_engine
     Mat4X4 rotation_matrix(const ViewAngles& angles) noexcept;
 
     [[nodiscard]]
-    Mat4X4 calc_perspective_projection_matrix(float field_of_view, float aspect_ratio, float near, float far) noexcept;
+    Mat4X4 calc_perspective_projection_matrix(float field_of_view, float aspect_ratio, float near, float far,
+                                             NDCDepthRange ndc_depth_range = NDCDepthRange::NEGATIVE_ONE_TO_ONE) noexcept;
 
     template<class FloatingType>
     requires std::is_floating_point_v<FloatingType>

include/omath/engines/unity_engine/traits/camera_trait.hpp

@@ -18,7 +18,7 @@ namespace omath::unity_engine
         static Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept;
         [[nodiscard]]
         static Mat4X4 calc_projection_matrix(const projection::FieldOfView& fov, const projection::ViewPort& view_port,
-                                             float near, float far) noexcept;
+                                             float near, float far, NDCDepthRange ndc_depth_range) noexcept;
     };
 
 } // namespace omath::unity_engine

include/omath/engines/unreal_engine/camera.hpp

@@ -9,5 +9,5 @@
 
 namespace omath::unreal_engine
 {
-    using Camera = projection::Camera<Mat4X4, ViewAngles, CameraTrait>;
+    using Camera = projection::Camera<Mat4X4, ViewAngles, CameraTrait, false, NDCDepthRange::ZERO_TO_ONE>;
 } // namespace omath::unreal_engine

include/omath/engines/unreal_engine/formulas.hpp

@@ -22,7 +22,8 @@ namespace omath::unreal_engine
     Mat4X4 rotation_matrix(const ViewAngles& angles) noexcept;
 
     [[nodiscard]]
-    Mat4X4 calc_perspective_projection_matrix(float field_of_view, float aspect_ratio, float near, float far) noexcept;
+    Mat4X4 calc_perspective_projection_matrix(float field_of_view, float aspect_ratio, float near, float far,
+                                             NDCDepthRange ndc_depth_range = NDCDepthRange::NEGATIVE_ONE_TO_ONE) noexcept;
 
     template<class FloatingType>
     requires std::is_floating_point_v<FloatingType>

include/omath/engines/unreal_engine/traits/camera_trait.hpp

@@ -18,7 +18,7 @@ namespace omath::unreal_engine
         static Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept;
         [[nodiscard]]
         static Mat4X4 calc_projection_matrix(const projection::FieldOfView& fov, const projection::ViewPort& view_port,
-                                             float near, float far) noexcept;
+                                             float near, float far, NDCDepthRange ndc_depth_range) noexcept;
     };
 
 } // namespace omath::unreal_engine

include/omath/linear_algebra/mat.hpp

@@ -37,6 +37,12 @@ namespace omath
         COLUMN_MAJOR
     };
 
+    enum class NDCDepthRange : uint8_t
+    {
+        NEGATIVE_ONE_TO_ONE = 0, // OpenGL: [-1.0, 1.0]
+        ZERO_TO_ONE              // DirectX / Vulkan: [0.0, 1.0]
+    };
+
     template<typename M1, typename M2> concept MatTemplateEqual
             = (M1::rows == M2::rows) && (M1::columns == M2::columns)
               && std::is_same_v<typename M1::value_type, typename M2::value_type> && (M1::store_type == M2::store_type);
@@ -658,56 +664,98 @@ namespace omath
         } * mat_translation<Type, St>(-camera_origin);
     }
 
-    template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR>
+    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(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 {{1.f / (aspect_ratio * fov_half_tan), 0.f, 0.f, 0.f},
+        if constexpr (DepthRange == NDCDepthRange::ZERO_TO_ONE)
-                {0.f, 1.f / fov_half_tan, 0.f, 0.f},
+            return {{1.f / (aspect_ratio * fov_half_tan), 0.f, 0.f, 0.f},
-                {0.f, 0.f, (far + near) / (far - near), -(2.f * near * far) / (far - near)},
+                    {0.f, 1.f / fov_half_tan, 0.f, 0.f},
-                {0.f, 0.f, 1.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 {{1.f / (aspect_ratio * fov_half_tan), 0.f, 0.f, 0.f},
+                    {0.f, 1.f / fov_half_tan, 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>
+    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(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 {{1.f / (aspect_ratio * fov_half_tan), 0.f, 0.f, 0.f},
+        if constexpr (DepthRange == NDCDepthRange::ZERO_TO_ONE)
-                {0.f, 1.f / fov_half_tan, 0.f, 0.f},
+            return {{1.f / (aspect_ratio * fov_half_tan), 0.f, 0.f, 0.f},
-                {0.f, 0.f, -(far + near) / (far - near), -(2.f * near * far) / (far - near)},
+                    {0.f, 1.f / fov_half_tan, 0.f, 0.f},
-                {0.f, 0.f, -1.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 {{1.f / (aspect_ratio * fov_half_tan), 0.f, 0.f, 0.f},
+                    {0.f, 1.f / fov_half_tan, 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>
+    template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR,
+             NDCDepthRange DepthRange = NDCDepthRange::NEGATIVE_ONE_TO_ONE>
     [[nodiscard]]
     Mat<4, 4, Type, St> mat_ortho_left_handed(const Type left, const Type right, const Type bottom, const Type top,
                                               const Type near, const Type far) noexcept
     {
-        return
+        if constexpr (DepthRange == NDCDepthRange::ZERO_TO_ONE)
-        {
+            return
-            { static_cast<Type>(2) / (right - left), 0.f,       0.f,    -(right + left) / (right - left)},
+            {
-            { 0.f,      static_cast<Type>(2) / (top - bottom),  0.f,    -(top + bottom) / (top - bottom)},
+                { static_cast<Type>(2) / (right - left), 0.f,       0.f,    -(right + left) / (right - left)},
-            { 0.f,      0.f,       static_cast<Type>(2) / (far - near), -(far + near) / (far - near)    },
+                { 0.f,      static_cast<Type>(2) / (top - bottom),  0.f,    -(top + bottom) / (top - bottom)},
-            { 0.f,      0.f,       0.f,                                 1.f                             }
+                { 0.f,      0.f,       static_cast<Type>(1) / (far - near), -near / (far - near)            },
-        };
+                { 0.f,      0.f,       0.f,                                 1.f                             }
+            };
+        else if constexpr (DepthRange == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
+            return
+            {
+                { static_cast<Type>(2) / (right - left), 0.f,       0.f,    -(right + left) / (right - left)},
+                { 0.f,      static_cast<Type>(2) / (top - bottom),  0.f,    -(top + bottom) / (top - bottom)},
+                { 0.f,      0.f,       static_cast<Type>(2) / (far - near), -(far + near) / (far - near)    },
+                { 0.f,      0.f,       0.f,                                 1.f                             }
+            };
+        else
+            std::unreachable();
     }
-    template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR>
+    template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR,
+             NDCDepthRange DepthRange = NDCDepthRange::NEGATIVE_ONE_TO_ONE>
     [[nodiscard]]
     Mat<4, 4, Type, St> mat_ortho_right_handed(const Type left, const Type right, const Type bottom, const Type top,
                                                const Type near, const Type far) noexcept
     {
-        return
+        if constexpr (DepthRange == NDCDepthRange::ZERO_TO_ONE)
-        {
+            return
-                { static_cast<Type>(2) / (right - left), 0.f,       0.f,     -(right + left) / (right - left)},
+            {
-                { 0.f,      static_cast<Type>(2) / (top - bottom),  0.f,     -(top + bottom) / (top - bottom)},
+                    { static_cast<Type>(2) / (right - left), 0.f,       0.f,     -(right + left) / (right - left)},
-                { 0.f,      0.f,       -static_cast<Type>(2) / (far - near), -(far + near) / (far - near)    },
+                    { 0.f,      static_cast<Type>(2) / (top - bottom),  0.f,     -(top + bottom) / (top - bottom)},
-                { 0.f,      0.f,       0.f,                                  1.f                             }
+                    { 0.f,      0.f,       -static_cast<Type>(1) / (far - near), -near / (far - near)            },
-        };
+                    { 0.f,      0.f,       0.f,                                  1.f                             }
+            };
+        else if constexpr (DepthRange == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
+            return
+            {
+                    { static_cast<Type>(2) / (right - left), 0.f,       0.f,     -(right + left) / (right - left)},
+                    { 0.f,      static_cast<Type>(2) / (top - bottom),  0.f,     -(top + bottom) / (top - bottom)},
+                    { 0.f,      0.f,       -static_cast<Type>(2) / (far - near), -(far + near) / (far - near)    },
+                    { 0.f,      0.f,       0.f,                                  1.f                             }
+            };
+        else
+            std::unreachable();
     }
     template<class T = float, MatStoreType St = MatStoreType::COLUMN_MAJOR>
    Mat<4, 4, T, St> mat_look_at_left_handed(const Vector3<T>& eye, const Vector3<T>& center, const Vector3<T>& up)

include/omath/projection/camera.hpp

@@ -44,19 +44,21 @@ namespace omath::projection
     template<class T, class MatType, class ViewAnglesType>
     concept CameraEngineConcept =
             requires(const Vector3<float>& cam_origin, const Vector3<float>& look_at, const ViewAnglesType& angles,
-                     const FieldOfView& fov, const ViewPort& viewport, float znear, float zfar) {
+                     const FieldOfView& fov, const ViewPort& viewport, float znear, float zfar,
+                     NDCDepthRange ndc_depth_range) {
                 // Presence + return types
                 { T::calc_look_at_angle(cam_origin, look_at) } -> std::same_as<ViewAnglesType>;
                 { T::calc_view_matrix(angles, cam_origin) } -> std::same_as<MatType>;
-                { T::calc_projection_matrix(fov, viewport, znear, zfar) } -> std::same_as<MatType>;
+                { T::calc_projection_matrix(fov, viewport, znear, zfar, ndc_depth_range) } -> std::same_as<MatType>;
 
                 // Enforce noexcept as in the trait declaration
                 requires noexcept(T::calc_look_at_angle(cam_origin, look_at));
                 requires noexcept(T::calc_view_matrix(angles, cam_origin));
-                requires noexcept(T::calc_projection_matrix(fov, viewport, znear, zfar));
+                requires noexcept(T::calc_projection_matrix(fov, viewport, znear, zfar, ndc_depth_range));
             };
 
-    template<class Mat4X4Type, class ViewAnglesType, class TraitClass, bool inverted_z = false>
+    template<class Mat4X4Type, class ViewAnglesType, class TraitClass, bool inverted_z = false,
+             NDCDepthRange depth_range = NDCDepthRange::NEGATIVE_ONE_TO_ONE>
     requires CameraEngineConcept<TraitClass, Mat4X4Type, ViewAnglesType>
     class Camera final
     {
@@ -135,7 +137,8 @@ namespace omath::projection
         {
             if (!m_projection_matrix.has_value())
                 m_projection_matrix = TraitClass::calc_projection_matrix(m_field_of_view, m_view_port,
-                                                                         m_near_plane_distance, m_far_plane_distance);
+                                                                         m_near_plane_distance, m_far_plane_distance,
+                                                                         depth_range);
 
             return m_projection_matrix.value();
         }
@@ -271,17 +274,36 @@ namespace omath::projection
                 return a[axis] < -a[3] && b[axis] < -b[3] && c[axis] < -c[3];
             };
 
-            // Clip volume in clip space (OpenGL-style):
+            // Clip volume in clip space:
             // -w <= x <= w
             // -w <= y <= w
-            // -w <= z <= w
+            // z_min <= z <= w  (z_min = -w for [-1,1], 0 for [0,1])
 
-            for (int i = 0; i < 3; i++)
+            // x and y planes
+            for (int i = 0; i < 2; i++)
             {
                 if (all_outside_plane(i, c0, c1, c2, false))
-                    return true; // x < -w (left)
+                    return true;
                 if (all_outside_plane(i, c0, c1, c2, true))
-                    return true; // x >  w (right)
+                    return true;
+            }
+
+            // z far plane: z > w
+            if (all_outside_plane(2, c0, c1, c2, true))
+                return true;
+
+            // z near plane
+            if constexpr (depth_range == NDCDepthRange::ZERO_TO_ONE)
+            {
+                // 0 <= z, so reject if z < 0 for all vertices
+                if (c0[2] < 0.f && c1[2] < 0.f && c2[2] < 0.f)
+                    return true;
+            }
+            else
+            {
+                // -w <= z
+                if (all_outside_plane(2, c0, c1, c2, false))
+                    return true;
             }
             return false;
         }
@@ -306,7 +328,8 @@ namespace omath::projection
                 return std::unexpected(Error::WORLD_POSITION_IS_OUT_OF_SCREEN_BOUNDS);
 
             // ReSharper disable once CppTooWideScope
-            const auto clipped_manually = clipping == ViewPortClipping::MANUAL && (projected.at(2, 0) < 0.0f - eps
+            constexpr auto z_min = depth_range == NDCDepthRange::ZERO_TO_ONE ? 0.0f : -1.0f;
+            const auto clipped_manually = clipping == ViewPortClipping::MANUAL && (projected.at(2, 0) < z_min - eps
                                           || projected.at(2, 0) > 1.0f + eps);
             if (clipped_manually)
                 return std::unexpected(Error::WORLD_POSITION_IS_OUT_OF_SCREEN_BOUNDS);
@@ -368,8 +391,27 @@ namespace omath::projection
         [[nodiscard]] constexpr static bool is_ndc_out_of_bounds(const Type& ndc) noexcept
         {
             constexpr auto eps = std::numeric_limits<float>::epsilon();
-            return std::ranges::any_of(ndc.raw_array(),
+
-                                       [](const auto& val) { return val < -1.0f - eps || val > 1.0f + eps; });
+            const auto& data = ndc.raw_array();
+            // x and y are always in [-1, 1]
+            if (data[0] < -1.0f - eps || data[0] > 1.0f + eps)
+                return true;
+            if (data[1] < -1.0f - eps || data[1] > 1.0f + eps)
+                return true;
+
+            // z range depends on the NDC depth convention
+            if constexpr (depth_range == NDCDepthRange::ZERO_TO_ONE)
+            {
+                if (data[2] < 0.0f - eps || data[2] > 1.0f + eps)
+                    return true;
+            }
+            else
+            {
+                if (data[2] < -1.0f - eps || data[2] > 1.0f + eps)
+                    return true;
+            }
+
+            return false;
         }
 
         // NDC REPRESENTATION:

source/engines/cry_engine/formulas.cpp

@@ -35,8 +35,15 @@ namespace omath::cry_engine
                * mat_rotation_axis_x<float, MatStoreType::ROW_MAJOR>(angles.pitch);
     }
     Mat4X4 calc_perspective_projection_matrix(const float field_of_view, const float aspect_ratio, const float near,
-                                              const float far) noexcept
+                                              const float far, const NDCDepthRange ndc_depth_range) noexcept
     {
-        return mat_perspective_left_handed(field_of_view, aspect_ratio, near, far);
+        if (ndc_depth_range == NDCDepthRange::ZERO_TO_ONE)
+            return mat_perspective_left_handed<float, MatStoreType::ROW_MAJOR, NDCDepthRange::ZERO_TO_ONE>(
+                    field_of_view, aspect_ratio, near, far);
+
+        if (ndc_depth_range == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
+            return mat_perspective_left_handed<float, MatStoreType::ROW_MAJOR, NDCDepthRange::NEGATIVE_ONE_TO_ONE>(
+                    field_of_view, aspect_ratio, near, far);
+        std::unreachable();
     }
 } // namespace omath::unity_engine

source/engines/cry_engine/traits/camera_trait.cpp

@@ -19,8 +19,9 @@ namespace omath::cry_engine
     }
     Mat4X4 CameraTrait::calc_projection_matrix(const projection::FieldOfView& fov,
                                                const projection::ViewPort& view_port, const float near,
-                                               const float far) noexcept
+                                               const float far, const NDCDepthRange ndc_depth_range) noexcept
     {
-        return calc_perspective_projection_matrix(fov.as_degrees(), view_port.aspect_ratio(), near, far);
+        return calc_perspective_projection_matrix(fov.as_degrees(), view_port.aspect_ratio(), near, far,
+                                                  ndc_depth_range);
     }
 } // namespace omath::unity_engine

source/engines/frostbite_engine/formulas.cpp

@@ -35,8 +35,16 @@ namespace omath::frostbite_engine
                * mat_rotation_axis_x<float, MatStoreType::ROW_MAJOR>(angles.pitch);
     }
     Mat4X4 calc_perspective_projection_matrix(const float field_of_view, const float aspect_ratio, const float near,
-                                              const float far) noexcept
+                                              const float far, const NDCDepthRange ndc_depth_range) noexcept
     {
-        return mat_perspective_left_handed(field_of_view, aspect_ratio, near, far);
+        if (ndc_depth_range == NDCDepthRange::ZERO_TO_ONE)
+            return mat_perspective_left_handed<float, MatStoreType::ROW_MAJOR, NDCDepthRange::ZERO_TO_ONE>(
+                    field_of_view, aspect_ratio, near, far);
+
+        if (ndc_depth_range == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
+            return mat_perspective_left_handed<float, MatStoreType::ROW_MAJOR, NDCDepthRange::NEGATIVE_ONE_TO_ONE>(
+                    field_of_view, aspect_ratio, near, far);
+
+        std::unreachable();
     }
 } // namespace omath::unity_engine

source/engines/frostbite_engine/traits/camera_trait.cpp

@@ -19,8 +19,9 @@ namespace omath::frostbite_engine
     }
     Mat4X4 CameraTrait::calc_projection_matrix(const projection::FieldOfView& fov,
                                                const projection::ViewPort& view_port, const float near,
-                                               const float far) noexcept
+                                               const float far, const NDCDepthRange ndc_depth_range) noexcept
     {
-        return calc_perspective_projection_matrix(fov.as_degrees(), view_port.aspect_ratio(), near, far);
+        return calc_perspective_projection_matrix(fov.as_degrees(), view_port.aspect_ratio(), near, far,
+                                                  ndc_depth_range);
     }
 } // namespace omath::unity_engine

source/engines/iw_engine/formulas.cpp

@@ -36,18 +36,27 @@ namespace omath::iw_engine
     }
 
     Mat4X4 calc_perspective_projection_matrix(const float field_of_view, const float aspect_ratio, const float near,
-                                              const float far) noexcept
+                                              const float far, const NDCDepthRange ndc_depth_range) noexcept
     {
         // NOTE: Need magic number to fix fov calculation, since IW engine inherit Quake proj matrix calculation
         constexpr auto k_multiply_factor = 0.75f;
 
         const float fov_half_tan = std::tan(angles::degrees_to_radians(field_of_view) / 2.f) * k_multiply_factor;
 
-        return {
+        if (ndc_depth_range == NDCDepthRange::ZERO_TO_ONE)
-                {1.f / (aspect_ratio * fov_half_tan), 0, 0, 0},
+            return {
-                {0, 1.f / (fov_half_tan), 0, 0},
+                    {1.f / (aspect_ratio * fov_half_tan), 0, 0, 0},
-                {0, 0, (far + near) / (far - near), -(2.f * far * near) / (far - near)},
+                    {0, 1.f / (fov_half_tan), 0, 0},
-                {0, 0, 1, 0},
+                    {0, 0, far / (far - near), -(near * far) / (far - near)},
-        };
+                    {0, 0, 1, 0},
+            };
+        if (ndc_depth_range == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
+            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, 0},
+            };
+        std::unreachable();
     };
 } // namespace omath::iw_engine

source/engines/iw_engine/traits/camera_trait.cpp

@@ -19,8 +19,9 @@ namespace omath::iw_engine
     }
     Mat4X4 CameraTrait::calc_projection_matrix(const projection::FieldOfView& fov,
                                                const projection::ViewPort& view_port, const float near,
-                                               const float far) noexcept
+                                               const float far, const NDCDepthRange ndc_depth_range) noexcept
     {
-        return calc_perspective_projection_matrix(fov.as_degrees(), view_port.aspect_ratio(), near, far);
+        return calc_perspective_projection_matrix(fov.as_degrees(), view_port.aspect_ratio(), near, far,
+                                                  ndc_depth_range);
     }
 } // namespace omath::iw_engine

source/engines/opengl_engine/formulas.cpp

@@ -8,15 +8,15 @@ namespace omath::opengl_engine
 
     Vector3<float> forward_vector(const ViewAngles& angles) noexcept
     {
-        const auto vec
+        const auto vec =
-                = rotation_matrix(angles) * mat_column_from_vector<float, MatStoreType::COLUMN_MAJOR>(k_abs_forward);
+                rotation_matrix(angles) * mat_column_from_vector<float, MatStoreType::COLUMN_MAJOR>(k_abs_forward);
 
         return {vec.at(0, 0), vec.at(1, 0), vec.at(2, 0)};
     }
     Vector3<float> right_vector(const ViewAngles& angles) noexcept
     {
-        const auto vec
+        const auto vec =
-                = rotation_matrix(angles) * mat_column_from_vector<float, MatStoreType::COLUMN_MAJOR>(k_abs_right);
+                rotation_matrix(angles) * mat_column_from_vector<float, MatStoreType::COLUMN_MAJOR>(k_abs_right);
 
         return {vec.at(0, 0), vec.at(1, 0), vec.at(2, 0)};
     }
@@ -28,7 +28,7 @@ namespace omath::opengl_engine
     }
     Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept
     {
-        return mat_look_at_right_handed(cam_origin, cam_origin+forward_vector(angles), up_vector(angles));
+        return mat_look_at_right_handed(cam_origin, cam_origin + forward_vector(angles), up_vector(angles));
     }
     Mat4X4 rotation_matrix(const ViewAngles& angles) noexcept
     {
@@ -37,15 +37,16 @@ namespace omath::opengl_engine
                * mat_rotation_axis_x<float, MatStoreType::COLUMN_MAJOR>(angles.pitch);
     }
     Mat4X4 calc_perspective_projection_matrix(const float field_of_view, const float aspect_ratio, const float near,
-                                              const float far) noexcept
+                                              const float far, const NDCDepthRange ndc_depth_range) noexcept
     {
-        const float fov_half_tan = std::tan(angles::degrees_to_radians(field_of_view) / 2.f);
+        if (ndc_depth_range == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
+            return mat_perspective_right_handed<float, MatStoreType::COLUMN_MAJOR, NDCDepthRange::NEGATIVE_ONE_TO_ONE>(
+                    field_of_view, aspect_ratio, near, far);
 
-        return {
+        if (ndc_depth_range == NDCDepthRange::ZERO_TO_ONE)
-                {1.f / (aspect_ratio * fov_half_tan), 0, 0, 0},
+            return mat_perspective_right_handed<float, MatStoreType::COLUMN_MAJOR, NDCDepthRange::ZERO_TO_ONE>(
-                {0, 1.f / (fov_half_tan), 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::opengl_engine

source/engines/opengl_engine/traits/camera_trait.cpp

@@ -20,8 +20,9 @@ namespace omath::opengl_engine
     }
     Mat4X4 CameraTrait::calc_projection_matrix(const projection::FieldOfView& fov,
                                                const projection::ViewPort& view_port, const float near,
-                                               const float far) noexcept
+                                               const float far, const NDCDepthRange ndc_depth_range) noexcept
     {
-        return calc_perspective_projection_matrix(fov.as_degrees(), view_port.aspect_ratio(), near, far);
+        return calc_perspective_projection_matrix(fov.as_degrees(), view_port.aspect_ratio(), near, far,
+                                                  ndc_depth_range);
     }
 } // namespace omath::opengl_engine

source/engines/source_engine/formulas.cpp

@@ -36,18 +36,27 @@ namespace omath::source_engine
     }
 
     Mat4X4 calc_perspective_projection_matrix(const float field_of_view, const float aspect_ratio, const float near,
-                                              const float far) noexcept
+                                              const float far, const NDCDepthRange ndc_depth_range) noexcept
     {
         // NOTE: Need magic number to fix fov calculation, since source inherit Quake proj matrix calculation
         constexpr auto k_multiply_factor = 0.75f;
 
         const float fov_half_tan = std::tan(angles::degrees_to_radians(field_of_view) / 2.f) * k_multiply_factor;
 
-        return {
+        if (ndc_depth_range == NDCDepthRange::ZERO_TO_ONE)
-                {1.f / (aspect_ratio * fov_half_tan), 0, 0, 0},
+            return {
-                {0, 1.f / (fov_half_tan), 0, 0},
+                    {1.f / (aspect_ratio * fov_half_tan), 0, 0, 0},
-                {0, 0, (far + near) / (far - near), -(2.f * far * near) / (far - near)},
+                    {0, 1.f / (fov_half_tan), 0, 0},
-                {0, 0, 1, 0},
+                    {0, 0, far / (far - near), -(near * far) / (far - near)},
-        };
+                    {0, 0, 1, 0},
+            };
+        if (ndc_depth_range == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
+            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, 0},
+            };
+        std::unreachable();
     }
 } // namespace omath::source_engine

source/engines/source_engine/traits/camera_trait.cpp

@@ -20,8 +20,9 @@ namespace omath::source_engine
     }
     Mat4X4 CameraTrait::calc_projection_matrix(const projection::FieldOfView& fov,
                                                const projection::ViewPort& view_port, const float near,
-                                               const float far) noexcept
+                                               const float far, const NDCDepthRange ndc_depth_range) noexcept
     {
-        return calc_perspective_projection_matrix(fov.as_degrees(), view_port.aspect_ratio(), near, far);
+        return calc_perspective_projection_matrix(fov.as_degrees(), view_port.aspect_ratio(), near, far,
+                                                  ndc_depth_range);
     }
 } // namespace omath::source_engine

source/engines/unity_engine/formulas.cpp

@@ -35,8 +35,15 @@ namespace omath::unity_engine
                * mat_rotation_axis_x<float, MatStoreType::ROW_MAJOR>(angles.pitch);
     }
     Mat4X4 calc_perspective_projection_matrix(const float field_of_view, const float aspect_ratio, const float near,
-                                              const float far) noexcept
+                                              const float far, const NDCDepthRange ndc_depth_range) noexcept
     {
-        return omath::mat_perspective_right_handed(field_of_view, aspect_ratio, near, far);
+        if (ndc_depth_range == NDCDepthRange::ZERO_TO_ONE)
+            return omath::mat_perspective_right_handed<float, MatStoreType::ROW_MAJOR, NDCDepthRange::ZERO_TO_ONE>(
+                    field_of_view, aspect_ratio, near, far);
+        if (ndc_depth_range == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
+            return omath::mat_perspective_right_handed<float, MatStoreType::ROW_MAJOR,
+                                                       NDCDepthRange::NEGATIVE_ONE_TO_ONE>(field_of_view, aspect_ratio,
+                                                                                           near, far);
+        std::unreachable();
     }
 } // namespace omath::unity_engine

source/engines/unity_engine/traits/camera_trait.cpp

@@ -19,8 +19,9 @@ namespace omath::unity_engine
     }
     Mat4X4 CameraTrait::calc_projection_matrix(const projection::FieldOfView& fov,
                                                const projection::ViewPort& view_port, const float near,
-                                               const float far) noexcept
+                                               const float far, const NDCDepthRange ndc_depth_range) noexcept
     {
-        return calc_perspective_projection_matrix(fov.as_degrees(), view_port.aspect_ratio(), near, far);
+        return calc_perspective_projection_matrix(fov.as_degrees(), view_port.aspect_ratio(), near, far,
+                                                  ndc_depth_range);
     }
 } // namespace omath::unity_engine

source/engines/unreal_engine/formulas.cpp

@@ -35,8 +35,12 @@ namespace omath::unreal_engine
                * mat_rotation_axis_y<float, MatStoreType::ROW_MAJOR>(angles.pitch);
     }
     Mat4X4 calc_perspective_projection_matrix(const float field_of_view, const float aspect_ratio, const float near,
-                                              const float far) noexcept
+                                              const float far, const NDCDepthRange ndc_depth_range) noexcept
     {
+        if (ndc_depth_range == NDCDepthRange::ZERO_TO_ONE)
+            return mat_perspective_left_handed<float, MatStoreType::ROW_MAJOR, NDCDepthRange::ZERO_TO_ONE>(
+                    field_of_view, aspect_ratio, near, far);
+
         return mat_perspective_left_handed(field_of_view, aspect_ratio, near, far);
     }
 } // namespace omath::unreal_engine

source/engines/unreal_engine/traits/camera_trait.cpp

@@ -19,8 +19,9 @@ namespace omath::unreal_engine
     }
     Mat4X4 CameraTrait::calc_projection_matrix(const projection::FieldOfView& fov,
                                                const projection::ViewPort& view_port, const float near,
-                                               const float far) noexcept
+                                               const float far, const NDCDepthRange ndc_depth_range) noexcept
     {
-        return calc_perspective_projection_matrix(fov.as_degrees(), view_port.aspect_ratio(), near, far);
+        return calc_perspective_projection_matrix(fov.as_degrees(), view_port.aspect_ratio(), near, far,
+                                                  ndc_depth_range);
     }
 } // namespace omath::unreal_engine

tests/engines/unit_test_traits_engines.cpp

@@ -21,6 +21,9 @@
 #include <omath/engines/unreal_engine/traits/camera_trait.hpp>
 
 #include <omath/engines/source_engine/traits/pred_engine_trait.hpp>
+#include <omath/engines/source_engine/traits/camera_trait.hpp>
+
+#include <omath/engines/cry_engine/traits/camera_trait.hpp>
 
 #include <omath/projectile_prediction/projectile.hpp>
 #include <omath/projectile_prediction/target.hpp>
@@ -218,9 +221,14 @@ TEST(TraitTests, Frostbite_Pred_And_Mesh_And_Camera)
     // CameraTrait look at should be callable
     const auto angles = e::CameraTrait::calc_look_at_angle({0, 0, 0}, {0, 1, 1});
     (void)angles;
-    const auto proj = e::CameraTrait::calc_projection_matrix(projection::FieldOfView::from_degrees(60.f), {1280.f, 720.f}, 0.1f, 1000.f);
+    const auto proj = e::CameraTrait::calc_projection_matrix(projection::FieldOfView::from_degrees(60.f), {1280.f, 720.f}, 0.1f, 1000.f, NDCDepthRange::NEGATIVE_ONE_TO_ONE);
     const auto expected = e::calc_perspective_projection_matrix(60.f, 1280.f / 720.f, 0.1f, 1000.f);
     expect_matrix_near(proj, expected);
+
+    const auto proj_zo = e::CameraTrait::calc_projection_matrix(projection::FieldOfView::from_degrees(60.f), {1280.f, 720.f}, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+    const auto expected_zo = e::calc_perspective_projection_matrix(60.f, 1280.f / 720.f, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+    expect_matrix_near(proj_zo, expected_zo);
+    EXPECT_NE(proj, proj_zo);
 }
 
 TEST(TraitTests, IW_Pred_And_Mesh_And_Camera)
@@ -264,10 +272,15 @@ TEST(TraitTests, IW_Pred_And_Mesh_And_Camera)
     e::ViewAngles va;
     expect_matrix_near(e::MeshTrait::rotation_matrix(va), e::rotation_matrix(va));
 
-    const auto proj = e::CameraTrait::calc_projection_matrix(projection::FieldOfView::from_degrees(45.f), {1920.f, 1080.f}, 0.1f, 1000.f);
+    const auto proj = e::CameraTrait::calc_projection_matrix(projection::FieldOfView::from_degrees(45.f), {1920.f, 1080.f}, 0.1f, 1000.f, NDCDepthRange::NEGATIVE_ONE_TO_ONE);
     const auto expected = e::calc_perspective_projection_matrix(45.f, 1920.f / 1080.f, 0.1f, 1000.f);
     expect_matrix_near(proj, expected);
 
+    const auto proj_zo = e::CameraTrait::calc_projection_matrix(projection::FieldOfView::from_degrees(45.f), {1920.f, 1080.f}, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+    const auto expected_zo = e::calc_perspective_projection_matrix(45.f, 1920.f / 1080.f, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+    expect_matrix_near(proj_zo, expected_zo);
+    EXPECT_NE(proj, proj_zo);
+
     // non-airborne
     t.m_is_airborne = false;
     const auto pred_ground_iw = e::PredEngineTrait::predict_target_position(t, 2.f, 9.81f);
@@ -314,10 +327,15 @@ TEST(TraitTests, OpenGL_Pred_And_Mesh_And_Camera)
     e::ViewAngles va;
     expect_matrix_near(e::MeshTrait::rotation_matrix(va), e::rotation_matrix(va));
 
-    const auto proj = e::CameraTrait::calc_projection_matrix(projection::FieldOfView::from_degrees(60.f), {1280.f, 720.f}, 0.1f, 1000.f);
+    const auto proj = e::CameraTrait::calc_projection_matrix(projection::FieldOfView::from_degrees(60.f), {1280.f, 720.f}, 0.1f, 1000.f, NDCDepthRange::NEGATIVE_ONE_TO_ONE);
     const auto expected = e::calc_perspective_projection_matrix(60.f, 1280.f / 720.f, 0.1f, 1000.f);
     expect_matrix_near(proj, expected);
 
+    const auto proj_zo = e::CameraTrait::calc_projection_matrix(projection::FieldOfView::from_degrees(60.f), {1280.f, 720.f}, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+    const auto expected_zo = e::calc_perspective_projection_matrix(60.f, 1280.f / 720.f, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+    expect_matrix_near(proj_zo, expected_zo);
+    EXPECT_NE(proj, proj_zo);
+
     // non-airborne
     t.m_is_airborne = false;
     const auto pred_ground_gl = e::PredEngineTrait::predict_target_position(t, 2.f, 9.81f);
@@ -364,10 +382,15 @@ TEST(TraitTests, Unity_Pred_And_Mesh_And_Camera)
     e::ViewAngles va;
     expect_matrix_near(e::MeshTrait::rotation_matrix(va), e::rotation_matrix(va));
 
-    const auto proj = e::CameraTrait::calc_projection_matrix(projection::FieldOfView::from_degrees(60.f), {1280.f, 720.f}, 0.1f, 1000.f);
+    const auto proj = e::CameraTrait::calc_projection_matrix(projection::FieldOfView::from_degrees(60.f), {1280.f, 720.f}, 0.1f, 1000.f, NDCDepthRange::NEGATIVE_ONE_TO_ONE);
     const auto expected = e::calc_perspective_projection_matrix(60.f, 1280.f / 720.f, 0.1f, 1000.f);
     expect_matrix_near(proj, expected);
 
+    const auto proj_zo = e::CameraTrait::calc_projection_matrix(projection::FieldOfView::from_degrees(60.f), {1280.f, 720.f}, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+    const auto expected_zo = e::calc_perspective_projection_matrix(60.f, 1280.f / 720.f, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+    expect_matrix_near(proj_zo, expected_zo);
+    EXPECT_NE(proj, proj_zo);
+
     // non-airborne
     t.m_is_airborne = false;
     const auto pred_ground_unity = e::PredEngineTrait::predict_target_position(t, 2.f, 9.81f);
@@ -414,12 +437,237 @@ TEST(TraitTests, Unreal_Pred_And_Mesh_And_Camera)
     e::ViewAngles va;
     expect_matrix_near(e::MeshTrait::rotation_matrix(va), e::rotation_matrix(va));
 
-    const auto proj = e::CameraTrait::calc_projection_matrix(projection::FieldOfView::from_degrees(60.f), {1280.f, 720.f}, 0.1f, 1000.f);
+    const auto proj = e::CameraTrait::calc_projection_matrix(projection::FieldOfView::from_degrees(60.f), {1280.f, 720.f}, 0.1f, 1000.f, NDCDepthRange::NEGATIVE_ONE_TO_ONE);
     const auto expected = e::calc_perspective_projection_matrix(60.f, 1280.f / 720.f, 0.1f, 1000.f);
     expect_matrix_near(proj, expected);
 
+    const auto proj_zo = e::CameraTrait::calc_projection_matrix(projection::FieldOfView::from_degrees(60.f), {1280.f, 720.f}, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+    const auto expected_zo = e::calc_perspective_projection_matrix(60.f, 1280.f / 720.f, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+    expect_matrix_near(proj_zo, expected_zo);
+    EXPECT_NE(proj, proj_zo);
+
     // non-airborne
     t.m_is_airborne = false;
     const auto pred_ground_unreal = e::PredEngineTrait::predict_target_position(t, 2.f, 9.81f);
     EXPECT_NEAR(pred_ground_unreal.x, 4.f, 1e-6f);
 }
+
+// ── NDC Depth Range tests for Source and CryEngine camera traits ────────────
+
+TEST(NDCDepthRangeTests, Source_BothDepthRanges)
+{
+    namespace e = omath::source_engine;
+
+    const auto proj_no = e::CameraTrait::calc_projection_matrix(
+            projection::FieldOfView::from_degrees(90.f), {1920.f, 1080.f}, 0.1f, 1000.f,
+            NDCDepthRange::NEGATIVE_ONE_TO_ONE);
+    const auto expected_no = e::calc_perspective_projection_matrix(
+            90.f, 1920.f / 1080.f, 0.1f, 1000.f, NDCDepthRange::NEGATIVE_ONE_TO_ONE);
+    expect_matrix_near(proj_no, expected_no);
+
+    const auto proj_zo = e::CameraTrait::calc_projection_matrix(
+            projection::FieldOfView::from_degrees(90.f), {1920.f, 1080.f}, 0.1f, 1000.f,
+            NDCDepthRange::ZERO_TO_ONE);
+    const auto expected_zo = e::calc_perspective_projection_matrix(
+            90.f, 1920.f / 1080.f, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+    expect_matrix_near(proj_zo, expected_zo);
+
+    EXPECT_NE(proj_no, proj_zo);
+}
+
+TEST(NDCDepthRangeTests, CryEngine_BothDepthRanges)
+{
+    namespace e = omath::cry_engine;
+
+    const auto proj_no = e::CameraTrait::calc_projection_matrix(
+            projection::FieldOfView::from_degrees(90.f), {1920.f, 1080.f}, 0.1f, 1000.f,
+            NDCDepthRange::NEGATIVE_ONE_TO_ONE);
+    const auto expected_no = e::calc_perspective_projection_matrix(
+            90.f, 1920.f / 1080.f, 0.1f, 1000.f, NDCDepthRange::NEGATIVE_ONE_TO_ONE);
+    expect_matrix_near(proj_no, expected_no);
+
+    const auto proj_zo = e::CameraTrait::calc_projection_matrix(
+            projection::FieldOfView::from_degrees(90.f), {1920.f, 1080.f}, 0.1f, 1000.f,
+            NDCDepthRange::ZERO_TO_ONE);
+    const auto expected_zo = e::calc_perspective_projection_matrix(
+            90.f, 1920.f / 1080.f, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+    expect_matrix_near(proj_zo, expected_zo);
+
+    EXPECT_NE(proj_no, proj_zo);
+}
+
+// ── Verify Z mapping for ZERO_TO_ONE across all engines ─────────────────────
+
+// Helper: projects a point at given z through a left-handed projection matrix and returns NDC z
+static float project_z_lh(const Mat<4, 4>& proj, float z)
+{
+    auto clip = proj * mat_column_from_vector<float>({0, 0, z});
+    return clip.at(2, 0) / clip.at(3, 0);
+}
+
+TEST(NDCDepthRangeTests, Source_ZeroToOne_ZRange)
+{
+    namespace e = omath::source_engine;
+    // Source is left-handed
+    const auto proj = e::calc_perspective_projection_matrix(90.f, 16.f / 9.f, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+
+    EXPECT_NEAR(project_z_lh(proj, 0.1f), 0.0f, 1e-4f);
+    EXPECT_NEAR(project_z_lh(proj, 1000.f), 1.0f, 1e-4f);
+    EXPECT_GT(project_z_lh(proj, 500.f), 0.0f);
+    EXPECT_LT(project_z_lh(proj, 500.f), 1.0f);
+}
+
+TEST(NDCDepthRangeTests, IW_ZeroToOne_ZRange)
+{
+    namespace e = omath::iw_engine;
+    // IW is left-handed
+    const auto proj = e::calc_perspective_projection_matrix(90.f, 16.f / 9.f, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+
+    EXPECT_NEAR(project_z_lh(proj, 0.1f), 0.0f, 1e-4f);
+    EXPECT_NEAR(project_z_lh(proj, 1000.f), 1.0f, 1e-4f);
+    EXPECT_GT(project_z_lh(proj, 500.f), 0.0f);
+    EXPECT_LT(project_z_lh(proj, 500.f), 1.0f);
+}
+
+TEST(NDCDepthRangeTests, OpenGL_ZeroToOne_ZRange)
+{
+    namespace e = omath::opengl_engine;
+    // OpenGL is right-handed (negative z forward), column-major
+    const auto proj = e::calc_perspective_projection_matrix(90.f, 16.f / 9.f, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+
+    // OpenGL engine uses column-major matrices, project manually
+    auto proj_z = [&](float z) {
+        auto clip = proj * mat_column_from_vector<float, MatStoreType::COLUMN_MAJOR>({0, 0, z});
+        return clip.at(2, 0) / clip.at(3, 0);
+    };
+
+    EXPECT_NEAR(proj_z(-0.1f), 0.0f, 1e-4f);
+    EXPECT_NEAR(proj_z(-1000.f), 1.0f, 1e-4f);
+    EXPECT_GT(proj_z(-500.f), 0.0f);
+    EXPECT_LT(proj_z(-500.f), 1.0f);
+}
+
+TEST(NDCDepthRangeTests, Frostbite_ZeroToOne_ZRange)
+{
+    namespace e = omath::frostbite_engine;
+    const auto proj = e::calc_perspective_projection_matrix(90.f, 16.f / 9.f, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+
+    EXPECT_NEAR(project_z_lh(proj, 0.1f), 0.0f, 1e-4f);
+    EXPECT_NEAR(project_z_lh(proj, 1000.f), 1.0f, 1e-4f);
+    EXPECT_GT(project_z_lh(proj, 500.f), 0.0f);
+    EXPECT_LT(project_z_lh(proj, 500.f), 1.0f);
+}
+
+TEST(NDCDepthRangeTests, Unity_ZeroToOne_ZRange)
+{
+    namespace e = omath::unity_engine;
+    // Unity is right-handed, row-major
+    const auto proj = e::calc_perspective_projection_matrix(90.f, 16.f / 9.f, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+
+    auto proj_z = [&](float z) {
+        auto clip = proj * mat_column_from_vector<float>({0, 0, z});
+        return clip.at(2, 0) / clip.at(3, 0);
+    };
+
+    EXPECT_NEAR(proj_z(-0.1f), 0.0f, 1e-4f);
+    EXPECT_NEAR(proj_z(-1000.f), 1.0f, 1e-4f);
+    EXPECT_GT(proj_z(-500.f), 0.0f);
+    EXPECT_LT(proj_z(-500.f), 1.0f);
+}
+
+TEST(NDCDepthRangeTests, Unreal_ZeroToOne_ZRange)
+{
+    namespace e = omath::unreal_engine;
+    const auto proj = e::calc_perspective_projection_matrix(90.f, 16.f / 9.f, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+
+    EXPECT_NEAR(project_z_lh(proj, 0.1f), 0.0f, 1e-4f);
+    EXPECT_NEAR(project_z_lh(proj, 1000.f), 1.0f, 1e-4f);
+    EXPECT_GT(project_z_lh(proj, 500.f), 0.0f);
+    EXPECT_LT(project_z_lh(proj, 500.f), 1.0f);
+}
+
+TEST(NDCDepthRangeTests, CryEngine_ZeroToOne_ZRange)
+{
+    namespace e = omath::cry_engine;
+    const auto proj = e::calc_perspective_projection_matrix(90.f, 16.f / 9.f, 0.1f, 1000.f, NDCDepthRange::ZERO_TO_ONE);
+
+    EXPECT_NEAR(project_z_lh(proj, 0.1f), 0.0f, 1e-4f);
+    EXPECT_NEAR(project_z_lh(proj, 1000.f), 1.0f, 1e-4f);
+    EXPECT_GT(project_z_lh(proj, 500.f), 0.0f);
+    EXPECT_LT(project_z_lh(proj, 500.f), 1.0f);
+}
+
+// ── Verify Z mapping for NEGATIVE_ONE_TO_ONE across all engines ─────────────
+
+TEST(NDCDepthRangeTests, Source_NegativeOneToOne_ZRange)
+{
+    namespace e = omath::source_engine;
+    const auto proj = e::calc_perspective_projection_matrix(90.f, 16.f / 9.f, 0.1f, 1000.f, NDCDepthRange::NEGATIVE_ONE_TO_ONE);
+
+    EXPECT_NEAR(project_z_lh(proj, 0.1f), -1.0f, 1e-3f);
+    EXPECT_NEAR(project_z_lh(proj, 1000.f), 1.0f, 1e-3f);
+}
+
+TEST(NDCDepthRangeTests, IW_NegativeOneToOne_ZRange)
+{
+    namespace e = omath::iw_engine;
+    const auto proj = e::calc_perspective_projection_matrix(90.f, 16.f / 9.f, 0.1f, 1000.f, NDCDepthRange::NEGATIVE_ONE_TO_ONE);
+
+    EXPECT_NEAR(project_z_lh(proj, 0.1f), -1.0f, 1e-3f);
+    EXPECT_NEAR(project_z_lh(proj, 1000.f), 1.0f, 1e-3f);
+}
+
+TEST(NDCDepthRangeTests, Frostbite_NegativeOneToOne_ZRange)
+{
+    namespace e = omath::frostbite_engine;
+    const auto proj = e::calc_perspective_projection_matrix(90.f, 16.f / 9.f, 0.1f, 1000.f, NDCDepthRange::NEGATIVE_ONE_TO_ONE);
+
+    EXPECT_NEAR(project_z_lh(proj, 0.1f), -1.0f, 1e-3f);
+    EXPECT_NEAR(project_z_lh(proj, 1000.f), 1.0f, 1e-3f);
+}
+
+TEST(NDCDepthRangeTests, Unreal_NegativeOneToOne_ZRange)
+{
+    namespace e = omath::unreal_engine;
+    const auto proj = e::calc_perspective_projection_matrix(90.f, 16.f / 9.f, 0.1f, 1000.f, NDCDepthRange::NEGATIVE_ONE_TO_ONE);
+
+    EXPECT_NEAR(project_z_lh(proj, 0.1f), -1.0f, 1e-3f);
+    EXPECT_NEAR(project_z_lh(proj, 1000.f), 1.0f, 1e-3f);
+}
+
+TEST(NDCDepthRangeTests, CryEngine_NegativeOneToOne_ZRange)
+{
+    namespace e = omath::cry_engine;
+    const auto proj = e::calc_perspective_projection_matrix(90.f, 16.f / 9.f, 0.1f, 1000.f, NDCDepthRange::NEGATIVE_ONE_TO_ONE);
+
+    EXPECT_NEAR(project_z_lh(proj, 0.1f), -1.0f, 1e-3f);
+    EXPECT_NEAR(project_z_lh(proj, 1000.f), 1.0f, 1e-3f);
+}
+
+TEST(NDCDepthRangeTests, OpenGL_NegativeOneToOne_ZRange)
+{
+    namespace e = omath::opengl_engine;
+    const auto proj = e::calc_perspective_projection_matrix(90.f, 16.f / 9.f, 0.1f, 1000.f, NDCDepthRange::NEGATIVE_ONE_TO_ONE);
+
+    auto proj_z = [&](float z) {
+        auto clip = proj * mat_column_from_vector<float, MatStoreType::COLUMN_MAJOR>({0, 0, z});
+        return clip.at(2, 0) / clip.at(3, 0);
+    };
+
+    EXPECT_NEAR(proj_z(-0.1f), -1.0f, 1e-3f);
+    EXPECT_NEAR(proj_z(-1000.f), 1.0f, 1e-3f);
+}
+
+TEST(NDCDepthRangeTests, Unity_NegativeOneToOne_ZRange)
+{
+    namespace e = omath::unity_engine;
+    const auto proj = e::calc_perspective_projection_matrix(90.f, 16.f / 9.f, 0.1f, 1000.f, NDCDepthRange::NEGATIVE_ONE_TO_ONE);
+
+    auto proj_z = [&](float z) {
+        auto clip = proj * mat_column_from_vector<float>({0, 0, z});
+        return clip.at(2, 0) / clip.at(3, 0);
+    };
+
+    EXPECT_NEAR(proj_z(-0.1f), -1.0f, 1e-3f);
+    EXPECT_NEAR(proj_z(-1000.f), 1.0f, 1e-3f);
+}

tests/general/unit_test_mat.cpp

@@ -240,4 +240,126 @@ TEST(UnitTestMatStandalone, MatPerspectiveLeftHanded)
     projected /= projected.at(3, 0);
 
     EXPECT_TRUE(projected.at(2, 0) > -1.0f && projected.at(2, 0) < 0.f);
+}
+
+TEST(UnitTestMatStandalone, MatPerspectiveLeftHandedZeroToOne)
+{
+    const auto proj = mat_perspective_left_handed<float, MatStoreType::ROW_MAJOR, NDCDepthRange::ZERO_TO_ONE>(
+            90.f, 16.f / 9.f, 0.1f, 1000.f);
+
+    // Near plane point should map to z ~ 0
+    auto near_pt = proj * mat_column_from_vector<float>({0, 0, 0.1f});
+    near_pt /= near_pt.at(3, 0);
+    EXPECT_NEAR(near_pt.at(2, 0), 0.0f, 1e-4f);
+
+    // Far plane point should map to z ~ 1
+    auto far_pt = proj * mat_column_from_vector<float>({0, 0, 1000.f});
+    far_pt /= far_pt.at(3, 0);
+    EXPECT_NEAR(far_pt.at(2, 0), 1.0f, 1e-4f);
+
+    // Mid-range point should be in [0, 1]
+    auto mid_pt = proj * mat_column_from_vector<float>({0, 0, 500.f});
+    mid_pt /= mid_pt.at(3, 0);
+    EXPECT_GT(mid_pt.at(2, 0), 0.0f);
+    EXPECT_LT(mid_pt.at(2, 0), 1.0f);
+}
+
+TEST(UnitTestMatStandalone, MatPerspectiveRightHandedZeroToOne)
+{
+    const auto proj = mat_perspective_right_handed<float, MatStoreType::ROW_MAJOR, NDCDepthRange::ZERO_TO_ONE>(
+            90.f, 16.f / 9.f, 0.1f, 1000.f);
+
+    // Near plane point (negative z for right-handed) should map to z ~ 0
+    auto near_pt = proj * mat_column_from_vector<float>({0, 0, -0.1f});
+    near_pt /= near_pt.at(3, 0);
+    EXPECT_NEAR(near_pt.at(2, 0), 0.0f, 1e-4f);
+
+    // Far plane point should map to z ~ 1
+    auto far_pt = proj * mat_column_from_vector<float>({0, 0, -1000.f});
+    far_pt /= far_pt.at(3, 0);
+    EXPECT_NEAR(far_pt.at(2, 0), 1.0f, 1e-4f);
+
+    // Mid-range point should be in [0, 1]
+    auto mid_pt = proj * mat_column_from_vector<float>({0, 0, -500.f});
+    mid_pt /= mid_pt.at(3, 0);
+    EXPECT_GT(mid_pt.at(2, 0), 0.0f);
+    EXPECT_LT(mid_pt.at(2, 0), 1.0f);
+}
+
+TEST(UnitTestMatStandalone, MatPerspectiveNegativeOneToOneRange)
+{
+    // Verify existing [-1, 1] behavior with explicit template arg matches default
+    const auto proj_default = mat_perspective_left_handed(90.f, 16.f / 9.f, 0.1f, 1000.f);
+    const auto proj_explicit = mat_perspective_left_handed<float, MatStoreType::ROW_MAJOR,
+            NDCDepthRange::NEGATIVE_ONE_TO_ONE>(90.f, 16.f / 9.f, 0.1f, 1000.f);
+
+    EXPECT_EQ(proj_default, proj_explicit);
+
+    // Near plane should map to z ~ -1
+    auto near_pt = proj_default * mat_column_from_vector<float>({0, 0, 0.1f});
+    near_pt /= near_pt.at(3, 0);
+    EXPECT_NEAR(near_pt.at(2, 0), -1.0f, 1e-3f);
+
+    // Far plane should map to z ~ 1
+    auto far_pt = proj_default * mat_column_from_vector<float>({0, 0, 1000.f});
+    far_pt /= far_pt.at(3, 0);
+    EXPECT_NEAR(far_pt.at(2, 0), 1.0f, 1e-3f);
+}
+
+TEST(UnitTestMatStandalone, MatPerspectiveZeroToOneEquanity)
+{
+    // LH and RH should produce same NDC for mirrored z
+    constexpr omath::Vector3<float> left_handed = {0, 2, 10};
+    constexpr omath::Vector3<float> right_handed = {0, 2, -10};
+
+    const auto proj_lh = mat_perspective_left_handed<float, MatStoreType::ROW_MAJOR, NDCDepthRange::ZERO_TO_ONE>(
+            90.f, 16.f / 9.f, 0.1f, 1000.f);
+    const auto proj_rh = mat_perspective_right_handed<float, MatStoreType::ROW_MAJOR, NDCDepthRange::ZERO_TO_ONE>(
+            90.f, 16.f / 9.f, 0.1f, 1000.f);
+
+    auto ndc_lh = proj_lh * mat_column_from_vector(left_handed);
+    auto ndc_rh = proj_rh * mat_column_from_vector(right_handed);
+
+    ndc_lh /= ndc_lh.at(3, 0);
+    ndc_rh /= ndc_rh.at(3, 0);
+
+    EXPECT_EQ(ndc_lh, ndc_rh);
+}
+
+TEST(UnitTestMatStandalone, MatOrthoLeftHandedZeroToOne)
+{
+    const auto ortho = mat_ortho_left_handed<float, MatStoreType::ROW_MAJOR, NDCDepthRange::ZERO_TO_ONE>(
+            -1.f, 1.f, -1.f, 1.f, 0.1f, 100.f);
+
+    // Near plane should map to z ~ 0
+    auto near_pt = ortho * mat_column_from_vector<float>({0, 0, 0.1f});
+    EXPECT_NEAR(near_pt.at(2, 0), 0.0f, 1e-4f);
+
+    // Far plane should map to z ~ 1
+    auto far_pt = ortho * mat_column_from_vector<float>({0, 0, 100.f});
+    EXPECT_NEAR(far_pt.at(2, 0), 1.0f, 1e-4f);
+}
+
+TEST(UnitTestMatStandalone, MatOrthoRightHandedZeroToOne)
+{
+    const auto ortho = mat_ortho_right_handed<float, MatStoreType::ROW_MAJOR, NDCDepthRange::ZERO_TO_ONE>(
+            -1.f, 1.f, -1.f, 1.f, 0.1f, 100.f);
+
+    // Near plane (negative z for RH) should map to z ~ 0
+    auto near_pt = ortho * mat_column_from_vector<float>({0, 0, -0.1f});
+    EXPECT_NEAR(near_pt.at(2, 0), 0.0f, 1e-4f);
+
+    // Far plane should map to z ~ 1
+    auto far_pt = ortho * mat_column_from_vector<float>({0, 0, -100.f});
+    EXPECT_NEAR(far_pt.at(2, 0), 1.0f, 1e-4f);
+}
+
+TEST(UnitTestMatStandalone, MatOrthoNegativeOneToOneDefault)
+{
+    // Verify explicit [-1, 1] matches default
+    const auto ortho_default = mat_ortho_left_handed(-1.f, 1.f, -1.f, 1.f, 0.1f, 100.f);
+    const auto ortho_explicit = mat_ortho_left_handed<float, MatStoreType::ROW_MAJOR,
+            NDCDepthRange::NEGATIVE_ONE_TO_ONE>(-1.f, 1.f, -1.f, 1.f, 0.1f, 100.f);
+
+    EXPECT_EQ(ortho_default, ortho_explicit);
 }