improvement

Feature/unreal engine projection fix

examples/example_glfw3/example_glfw3.cpp

@@ -318,22 +318,22 @@ int main()
         glfwPollEvents();
         omath::Vector3<float> move_dir;
         if (glfwGetKey(window, GLFW_KEY_W))
-            move_dir += camera.get_forward();
+            move_dir += camera.get_abs_forward();
 
         if (glfwGetKey(window, GLFW_KEY_A))
-            move_dir -= camera.get_right();
+            move_dir -= camera.get_abs_right();
 
         if (glfwGetKey(window, GLFW_KEY_S))
-            move_dir -= camera.get_forward();
+            move_dir -= camera.get_abs_forward();
 
         if (glfwGetKey(window, GLFW_KEY_D))
-            move_dir += camera.get_right();
+            move_dir += camera.get_abs_right();
 
         if (glfwGetKey(window, GLFW_KEY_SPACE))
-            move_dir += camera.get_up();
+            move_dir += camera.get_abs_up();
 
         if (glfwGetKey(window, GLFW_KEY_LEFT_CONTROL))
-            move_dir -= camera.get_up();
+            move_dir -= camera.get_abs_up();
 
 
         auto delta = glfwGetTime() - old_mouse_time;

include/omath/3d_primitives/aabb.hpp

@@ -7,6 +7,8 @@
 
 namespace omath::primitives
 {
+    enum class UpAxis { X, Y, Z };
+
     template<class Type>
     struct Aabb final
     {
@@ -24,5 +26,42 @@ namespace omath::primitives
         {
             return (max - min) / static_cast<Type>(2);
         }
+
+        template<UpAxis Up = UpAxis::Y>
+        [[nodiscard]]
+        constexpr Vector3<Type> top() const noexcept
+        {
+            const auto aabb_center = center();
+            if constexpr (Up == UpAxis::Z)
+                return {aabb_center.x, aabb_center.y, max.z};
+            else if constexpr (Up == UpAxis::X)
+                return {max.x, aabb_center.y, aabb_center.z};
+            else if constexpr (Up == UpAxis::Y)
+                return {aabb_center.x, max.y, aabb_center.z};
+            else
+                std::unreachable();
+        }
+
+        template<UpAxis Up = UpAxis::Y>
+        [[nodiscard]]
+        constexpr Vector3<Type> bottom() const noexcept
+        {
+            const auto aabb_center = center();
+            if constexpr (Up == UpAxis::Z)
+                return {aabb_center.x, aabb_center.y, min.z};
+            else if constexpr (Up == UpAxis::X)
+                return {min.x, aabb_center.y, aabb_center.z};
+            else if constexpr (Up == UpAxis::Y)
+                return {aabb_center.x, min.y, aabb_center.z};
+            else
+                std::unreachable();
+        }
+
+        [[nodiscard]]
+        constexpr bool is_collide(const Aabb& other) const noexcept
+        {
+            return min.x <= other.max.x && max.x >= other.min.x &&
+                min.y <= other.max.y && max.y >= other.min.y &&min.z <= other.max.z && max.z >= other.min.z;
+        }
     };
 } // namespace omath::primitives

include/omath/engines/cry_engine/camera.hpp

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

include/omath/engines/iw_engine/camera.hpp

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

include/omath/engines/unreal_engine/constants.hpp

@@ -11,16 +11,16 @@
 
 namespace omath::unreal_engine
 {
-    constexpr Vector3<float> k_abs_up = {0, 0, 1};
+    constexpr Vector3<double> k_abs_up = {0, 0, 1};
-    constexpr Vector3<float> k_abs_right = {0, 1, 0};
+    constexpr Vector3<double> k_abs_right = {0, 1, 0};
-    constexpr Vector3<float> k_abs_forward = {1, 0, 0};
+    constexpr Vector3<double> k_abs_forward = {1, 0, 0};
 
-    using Mat4X4 = Mat<4, 4, float, MatStoreType::ROW_MAJOR>;
+    using Mat4X4 = Mat<4, 4, double, MatStoreType::ROW_MAJOR>;
-    using Mat3X3 = Mat<4, 4, float, MatStoreType::ROW_MAJOR>;
+    using Mat3X3 = Mat<4, 4, double, MatStoreType::ROW_MAJOR>;
-    using Mat1X3 = Mat<1, 3, float, MatStoreType::ROW_MAJOR>;
+    using Mat1X3 = Mat<1, 3, double, MatStoreType::ROW_MAJOR>;
-    using PitchAngle = Angle<float, -90.f, 90.f, AngleFlags::Clamped>;
+    using PitchAngle = Angle<double, -90., 90., AngleFlags::Clamped>;
-    using YawAngle = Angle<float, -180.f, 180.f, AngleFlags::Normalized>;
+    using YawAngle = Angle<double, -180., 180., AngleFlags::Normalized>;
-    using RollAngle = Angle<float, -180.f, 180.f, AngleFlags::Normalized>;
+    using RollAngle = Angle<double, -180., 180., AngleFlags::Normalized>;
 
     using ViewAngles = omath::ViewAngles<PitchAngle, YawAngle, RollAngle>;
 } // namespace omath::unreal_engine

include/omath/engines/unreal_engine/formulas.hpp

@@ -8,21 +8,21 @@
 namespace omath::unreal_engine
 {
     [[nodiscard]]
-    Vector3<float> forward_vector(const ViewAngles& angles) noexcept;
+    Vector3<double> forward_vector(const ViewAngles& angles) noexcept;
 
     [[nodiscard]]
-    Vector3<float> right_vector(const ViewAngles& angles) noexcept;
+    Vector3<double> right_vector(const ViewAngles& angles) noexcept;
 
     [[nodiscard]]
-    Vector3<float> up_vector(const ViewAngles& angles) noexcept;
+    Vector3<double> up_vector(const ViewAngles& angles) noexcept;
 
-    [[nodiscard]] Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept;
+    [[nodiscard]] Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<double>& cam_origin) noexcept;
 
     [[nodiscard]]
     Mat4X4 rotation_matrix(const ViewAngles& angles) noexcept;
 
     [[nodiscard]]
-    Mat4X4 calc_perspective_projection_matrix(float field_of_view, float aspect_ratio, float near, float far,
+    Mat4X4 calc_perspective_projection_matrix(double field_of_view, double aspect_ratio, double near, double far,
                                              NDCDepthRange ndc_depth_range = NDCDepthRange::NEGATIVE_ONE_TO_ONE) noexcept;
 
     template<class FloatingType>

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

@@ -12,13 +12,13 @@ namespace omath::unreal_engine
     {
     public:
         [[nodiscard]]
-        static ViewAngles calc_look_at_angle(const Vector3<float>& cam_origin, const Vector3<float>& look_at) noexcept;
+        static ViewAngles calc_look_at_angle(const Vector3<double>& cam_origin, const Vector3<double>& look_at) noexcept;
 
         [[nodiscard]]
-        static Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept;
+        static Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<double>& cam_origin) noexcept;
         [[nodiscard]]
         static Mat4X4 calc_projection_matrix(const projection::FieldOfView& fov, const projection::ViewPort& view_port,
-                                             float near, float far, NDCDepthRange ndc_depth_range) noexcept;
+                                             double near, double far, NDCDepthRange ndc_depth_range) noexcept;
     };
 
 } // namespace omath::unreal_engine

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

@@ -17,9 +17,11 @@ namespace omath::unreal_engine
                                                                     const float time, const float gravity) noexcept
         {
             const auto launch_pos = projectile.m_origin + projectile.m_launch_offset;
+            const auto fwd_d = forward_vector({PitchAngle::from_degrees(-pitch), YawAngle::from_degrees(yaw),
+                                               RollAngle::from_degrees(0)});
             auto current_pos = launch_pos
-                               + forward_vector({PitchAngle::from_degrees(-pitch), YawAngle::from_degrees(yaw),
+                               + Vector3<float>{static_cast<float>(fwd_d.x), static_cast<float>(fwd_d.y),
-                                                 RollAngle::from_degrees(0)})
+                                                static_cast<float>(fwd_d.z)}
                                          * projectile.m_launch_speed * time;
             current_pos.y -= (gravity * projectile.m_gravity_scale) * (time * time) * 0.5f;
 

include/omath/linear_algebra/mat.hpp

@@ -667,21 +667,21 @@ namespace omath
     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,
+    Mat<4, 4, Type, St> mat_perspective_left_handed(const Type field_of_view, const Type aspect_ratio,
-                                                    const float near, const float far) noexcept
+                                                    const Type near, const Type far) noexcept
     {
-        const float fov_half_tan = std::tan(angles::degrees_to_radians(field_of_view) / 2.f);
+        const auto fov_half_tan = std::tan(angles::degrees_to_radians(field_of_view) / Type{2});
 
         if constexpr (DepthRange == NDCDepthRange::ZERO_TO_ONE)
-            return {{1.f / (aspect_ratio * fov_half_tan), 0.f, 0.f, 0.f},
+            return {{Type{1} / (aspect_ratio * fov_half_tan), Type{0},                Type{0},             Type{0}},
-                    {0.f, 1.f / fov_half_tan, 0.f, 0.f},
+                    {Type{0},                                 Type{1} / fov_half_tan, Type{0},             Type{0}},
-                    {0.f, 0.f, far / (far - near), -(near * far) / (far - near)},
+                    {Type{0},                                 Type{0},                far / (far - near), -(near * far) / (far - near)},
-                    {0.f, 0.f, 1.f, 0.f}};
+                    {Type{0},                                 Type{0},                Type{1},            Type{0}}};
         else if constexpr (DepthRange == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
-            return {{1.f / (aspect_ratio * fov_half_tan), 0.f, 0.f, 0.f},
+            return {{Type{1} / (aspect_ratio * fov_half_tan), Type{0},                Type{0},                      Type{0}},
-                    {0.f, 1.f / fov_half_tan, 0.f, 0.f},
+                    {Type{0},                                 Type{1} / fov_half_tan, Type{0},                      Type{0}},
-                    {0.f, 0.f, (far + near) / (far - near), -(2.f * near * far) / (far - near)},
+                    {Type{0},                                 Type{0},                (far + near) / (far - near), -(Type{2} * near * far) / (far - near)},
-                    {0.f, 0.f, 1.f, 0.f}};
+                    {Type{0},                                 Type{0},                Type{1},                     Type{0}}};
         else
             std::unreachable();
     }
@@ -689,21 +689,74 @@ namespace omath
     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,
+    Mat<4, 4, Type, St> mat_perspective_right_handed(const Type field_of_view, const Type aspect_ratio,
-                                                     const float near, const float far) noexcept
+                                                     const Type near, const Type far) noexcept
     {
-        const float fov_half_tan = std::tan(angles::degrees_to_radians(field_of_view) / 2.f);
+        const auto fov_half_tan = std::tan(angles::degrees_to_radians(field_of_view) / Type{2});
 
         if constexpr (DepthRange == NDCDepthRange::ZERO_TO_ONE)
-            return {{1.f / (aspect_ratio * fov_half_tan), 0.f, 0.f, 0.f},
+            return {{Type{1} / (aspect_ratio * fov_half_tan), Type{0},                Type{0},             Type{0}},
-                    {0.f, 1.f / fov_half_tan, 0.f, 0.f},
+                    {Type{0},                                 Type{1} / fov_half_tan, Type{0},             Type{0}},
-                    {0.f, 0.f, -far / (far - near), -(near * far) / (far - near)},
+                    {Type{0},                                 Type{0},                -far / (far - near), -(near * far) / (far - near)},
-                    {0.f, 0.f, -1.f, 0.f}};
+                    {Type{0},                                 Type{0},                -Type{1},            Type{0}}};
         else if constexpr (DepthRange == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
-            return {{1.f / (aspect_ratio * fov_half_tan), 0.f, 0.f, 0.f},
+            return {{Type{1} / (aspect_ratio * fov_half_tan), Type{0},                Type{0},                      Type{0}},
-                    {0.f, 1.f / fov_half_tan, 0.f, 0.f},
+                    {Type{0},                                 Type{1} / fov_half_tan, Type{0},                      Type{0}},
-                    {0.f, 0.f, -(far + near) / (far - near), -(2.f * near * far) / (far - near)},
+                    {Type{0},                                 Type{0},                -(far + near) / (far - near), -(Type{2} * near * far) / (far - near)},
-                    {0.f, 0.f, -1.f, 0.f}};
+                    {Type{0},                                 Type{0},                -Type{1},                     Type{0}}};
+        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 Type horizontal_fov,
+                                                                   const Type aspect_ratio, const Type near,
+                                                                   const Type far) noexcept
+    {
+        const auto inv_tan_half_hfov = Type{1} / std::tan(angles::degrees_to_radians(horizontal_fov) / Type{2});
+        const auto x_axis = inv_tan_half_hfov;
+        const auto y_axis = inv_tan_half_hfov * aspect_ratio;
+
+        if constexpr (DepthRange == NDCDepthRange::ZERO_TO_ONE)
+            return {{x_axis,     Type{0},    Type{0},             Type{0}},
+                    {Type{0},    y_axis,     Type{0},             Type{0}},
+                    {Type{0},    Type{0},    far / (far - near),  -(near * far) / (far - near)},
+                    {Type{0},    Type{0},    Type{1},             Type{0}}};
+        else if constexpr (DepthRange == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
+            return {{x_axis,  Type{0}, Type{0},                     Type{0}},
+                    {Type{0}, y_axis,  Type{0},                     Type{0}},
+                    {Type{0}, Type{0}, (far + near) / (far - near), -(2.f * near * far) / (far - near)},
+                    {Type{0}, Type{0}, Type{1},                     Type{0}}};
+        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 Type horizontal_fov,
+                                                                    const Type aspect_ratio, const Type near,
+                                                                    const Type far) noexcept
+    {
+        const auto inv_tan_half_hfov = Type{1} / std::tan(angles::degrees_to_radians(horizontal_fov) / Type{2});
+        const auto x_axis = inv_tan_half_hfov;
+        const auto y_axis = inv_tan_half_hfov * aspect_ratio;
+
+        if constexpr (DepthRange == NDCDepthRange::ZERO_TO_ONE)
+            return {{x_axis,  Type{0}, Type{0},             Type{0}},
+                    {Type{0}, y_axis,  Type{0},             Type{0}},
+                    {Type{0}, Type{0}, -far / (far - near), -(near * far) / (far - near)},
+                    {Type{0}, Type{0}, -Type{1},            Type{0}}};
+        else if constexpr (DepthRange == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
+            return {{x_axis,  Type{0}, Type{0},                      Type{0}},
+                    {Type{0}, y_axis,  Type{0},                      Type{0}},
+                    {Type{0}, Type{0}, -(far + near) / (far - near), -(2.f * near * far) / (far - near)},
+                    {Type{0}, Type{0}, -Type{1},                     Type{0}}};
         else
             std::unreachable();
     }

include/omath/projection/camera.hpp

@@ -42,25 +42,32 @@ namespace omath::projection
         AUTO,
         MANUAL,
     };
-    template<class T, class MatType, class ViewAnglesType>
+    struct CameraAxes
+    {
+        bool inverted_forward = false;
+        bool inverted_right = false;
+    };
+
+    template<class T, class MatType, class ViewAnglesType, class NumericType>
     concept CameraEngineConcept =
-            requires(const Vector3<float>& cam_origin, const Vector3<float>& look_at, const ViewAnglesType& angles,
+            requires(const Vector3<NumericType>& cam_origin, const Vector3<NumericType>& look_at,
-                     const FieldOfView& fov, const ViewPort& viewport, float znear, float zfar,
+                     const ViewAnglesType& angles, const FieldOfView& fov, const ViewPort& viewport, NumericType z_near,
-                     NDCDepthRange ndc_depth_range) {
+                     NumericType z_far, 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, ndc_depth_range) } -> std::same_as<MatType>;
+                { T::calc_projection_matrix(fov, viewport, z_near, z_far, ndc_depth_range) } -> std::same_as<MatType>;
-
+                requires std::is_floating_point_v<NumericType>;
                 // 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, ndc_depth_range));
+                requires noexcept(T::calc_projection_matrix(fov, viewport, z_near, z_far, ndc_depth_range));
             };
 
-    template<class Mat4X4Type, class ViewAnglesType, class TraitClass, bool inverted_z = false,
+    template<class Mat4X4Type, class ViewAnglesType, class TraitClass,
-             NDCDepthRange depth_range = NDCDepthRange::NEGATIVE_ONE_TO_ONE>
+             NDCDepthRange depth_range = NDCDepthRange::NEGATIVE_ONE_TO_ONE, CameraAxes axes = {},
-    requires CameraEngineConcept<TraitClass, Mat4X4Type, ViewAnglesType>
+             class NumericType = float>
+    requires CameraEngineConcept<TraitClass, Mat4X4Type, ViewAnglesType, NumericType>
     class Camera final
     {
 #ifdef OMATH_BUILD_TESTS
@@ -76,48 +83,110 @@ namespace omath::projection
         };
 
         ~Camera() = default;
-        Camera(const Vector3<float>& position, const ViewAnglesType& view_angles, const ViewPort& view_port,
+        Camera(const Vector3<NumericType>& position, const ViewAnglesType& view_angles, const ViewPort& view_port,
-               const FieldOfView& fov, const float near, const float far) noexcept
+               const FieldOfView& fov, const NumericType near, const NumericType far) noexcept
             : m_view_port(view_port), m_field_of_view(fov), m_far_plane_distance(far), m_near_plane_distance(near),
               m_view_angles(view_angles), m_origin(position)
         {
         }
 
-        void look_at(const Vector3<float>& target)
+        struct ProjectionParams final
+        {
+            FieldOfView fov;
+            NumericType aspect_ratio{};
+        };
+
+        // Recovers vertical FOV and aspect ratio from a perspective projection matrix
+        // built by any of the engine traits.  Both variants (ZERO_TO_ONE and
+        // NEGATIVE_ONE_TO_ONE) share the same m[0,0]/m[1,1] layout, so this works
+        // regardless of the NDC depth range.
+        [[nodiscard]]
+        static ProjectionParams extract_projection_params(const Mat4X4Type& proj_matrix) noexcept
+        {
+            // m[1,1] == 1 / tan(fov/2)  =>  fov = 2 * atan(1 / m[1,1])
+            const auto f = proj_matrix.at(1, 1);
+            // m[0,0] == m[1,1] / aspect_ratio  =>  aspect = m[1,1] / m[0,0]
+            return {FieldOfView::from_radians(NumericType{2} * std::atan(NumericType{1} / f)),
+                    f / proj_matrix.at(0, 0)};
+        }
+
+        [[nodiscard]]
+        static ViewAnglesType calc_view_angles_from_view_matrix(const Mat4X4Type& view_matrix) noexcept
+        {
+            Vector3<NumericType> forward_vector = {view_matrix[2, 0], view_matrix[2, 1], view_matrix[2, 2]};
+            if constexpr (axes.inverted_forward)
+                forward_vector = -forward_vector;
+            return TraitClass::calc_look_at_angle({}, forward_vector);
+        }
+
+        [[nodiscard]]
+        static Vector3<NumericType> calc_origin_from_view_matrix(const Mat4X4Type& view_matrix) noexcept
+        {
+            // The view matrix is R * T(-origin), so the last column stores t = -R * origin.
+            // Recovering origin: origin = -R^T * t
+            return {
+                    -(view_matrix[0, 0] * view_matrix[0, 3] + view_matrix[1, 0] * view_matrix[1, 3]
+                      + view_matrix[2, 0] * view_matrix[2, 3]),
+                    -(view_matrix[0, 1] * view_matrix[0, 3] + view_matrix[1, 1] * view_matrix[1, 3]
+                      + view_matrix[2, 1] * view_matrix[2, 3]),
+                    -(view_matrix[0, 2] * view_matrix[0, 3] + view_matrix[1, 2] * view_matrix[1, 3]
+                      + view_matrix[2, 2] * view_matrix[2, 3]),
+            };
+        }
+
+        void look_at(const Vector3<NumericType>& target)
         {
             m_view_angles = TraitClass::calc_look_at_angle(m_origin, target);
             m_view_projection_matrix = std::nullopt;
             m_view_matrix = std::nullopt;
         }
         [[nodiscard]]
-        ViewAnglesType calc_look_at_angles(const Vector3<float>& look_to) const
+        ViewAnglesType calc_look_at_angles(const Vector3<NumericType>& look_to) const
         {
             return TraitClass::calc_look_at_angle(m_origin, look_to);
         }
 
         [[nodiscard]]
-        Vector3<float> get_forward() const noexcept
+        Vector3<NumericType> get_forward() const noexcept
         {
             const auto& view_matrix = get_view_matrix();
-
-            if constexpr (inverted_z)
-                return -Vector3<float>{view_matrix[2, 0], view_matrix[2, 1], view_matrix[2, 2]};
             return {view_matrix[2, 0], view_matrix[2, 1], view_matrix[2, 2]};
         }
 
         [[nodiscard]]
-        Vector3<float> get_right() const noexcept
+        Vector3<NumericType> get_right() const noexcept
         {
             const auto& view_matrix = get_view_matrix();
             return {view_matrix[0, 0], view_matrix[0, 1], view_matrix[0, 2]};
         }
 
         [[nodiscard]]
-        Vector3<float> get_up() const noexcept
+        Vector3<NumericType> get_up() const noexcept
         {
             const auto& view_matrix = get_view_matrix();
             return {view_matrix[1, 0], view_matrix[1, 1], view_matrix[1, 2]};
         }
+        [[nodiscard]]
+        Vector3<NumericType> get_abs_forward() const noexcept
+        {
+            if constexpr (axes.inverted_forward)
+                return -get_forward();
+            return get_forward();
+        }
+
+        [[nodiscard]]
+        Vector3<NumericType> get_abs_right() const noexcept
+        {
+            if constexpr (axes.inverted_right)
+                return -get_right();
+            return get_right();
+        }
+
+        [[nodiscard]]
+        Vector3<NumericType> get_abs_up() const noexcept
+        {
+            return get_up();
+        }
 
         [[nodiscard]] const Mat4X4Type& get_view_projection_matrix() const noexcept
         {
@@ -137,9 +206,8 @@ namespace omath::projection
         [[nodiscard]] const Mat4X4Type& get_projection_matrix() const noexcept
         {
             if (!m_projection_matrix.has_value())
-                m_projection_matrix = TraitClass::calc_projection_matrix(m_field_of_view, m_view_port,
+                m_projection_matrix = TraitClass::calc_projection_matrix(
-                                                                         m_near_plane_distance, m_far_plane_distance,
+                        m_field_of_view, m_view_port, m_near_plane_distance, m_far_plane_distance, depth_range);
-                                                                         depth_range);
 
             return m_projection_matrix.value();
         }
@@ -151,14 +219,14 @@ namespace omath::projection
             m_projection_matrix = std::nullopt;
         }
 
-        void set_near_plane(const float near_plane) noexcept
+        void set_near_plane(const NumericType near_plane) noexcept
         {
             m_near_plane_distance = near_plane;
             m_view_projection_matrix = std::nullopt;
             m_projection_matrix = std::nullopt;
         }
 
-        void set_far_plane(const float far_plane) noexcept
+        void set_far_plane(const NumericType far_plane) noexcept
         {
             m_far_plane_distance = far_plane;
             m_view_projection_matrix = std::nullopt;
@@ -172,7 +240,7 @@ namespace omath::projection
             m_view_matrix = std::nullopt;
         }
 
-        void set_origin(const Vector3<float>& origin) noexcept
+        void set_origin(const Vector3<NumericType>& origin) noexcept
         {
             m_origin = origin;
             m_view_projection_matrix = std::nullopt;
@@ -190,12 +258,12 @@ namespace omath::projection
             return m_field_of_view;
         }
 
-        [[nodiscard]] const float& get_near_plane() const noexcept
+        [[nodiscard]] const NumericType& get_near_plane() const noexcept
         {
             return m_near_plane_distance;
         }
 
-        [[nodiscard]] const float& get_far_plane() const noexcept
+        [[nodiscard]] const NumericType& get_far_plane() const noexcept
         {
             return m_far_plane_distance;
         }
@@ -205,14 +273,14 @@ namespace omath::projection
             return m_view_angles;
         }
 
-        [[nodiscard]] const Vector3<float>& get_origin() const noexcept
+        [[nodiscard]] const Vector3<NumericType>& get_origin() const noexcept
         {
             return m_origin;
         }
 
         template<ScreenStart screen_start = ScreenStart::TOP_LEFT_CORNER>
-        [[nodiscard]] std::expected<Vector3<float>, Error>
+        [[nodiscard]] std::expected<Vector3<NumericType>, Error>
-        world_to_screen(const Vector3<float>& world_position) const noexcept
+        world_to_screen(const Vector3<NumericType>& world_position) const noexcept
         {
             const auto normalized_cords = world_to_view_port(world_position);
 
@@ -227,8 +295,8 @@ namespace omath::projection
                 std::unreachable();
         }
         template<ScreenStart screen_start = ScreenStart::TOP_LEFT_CORNER>
-        [[nodiscard]] std::expected<Vector3<float>, Error>
+        [[nodiscard]] std::expected<Vector3<NumericType>, Error>
-        world_to_screen_unclipped(const Vector3<float>& world_position) const noexcept
+        world_to_screen_unclipped(const Vector3<NumericType>& world_position) const noexcept
         {
             const auto normalized_cords = world_to_view_port(world_position, ViewPortClipping::MANUAL);
 
@@ -243,14 +311,14 @@ namespace omath::projection
                 std::unreachable();
         }
 
-        [[nodiscard]] bool is_culled_by_frustum(const Triangle<Vector3<float>>& triangle) const noexcept
+        [[nodiscard]] bool is_culled_by_frustum(const Triangle<Vector3<NumericType>>& triangle) const noexcept
         {
             // Transform to clip space (before perspective divide)
-            auto to_clip = [this](const Vector3<float>& point)
+            auto to_clip = [this](const Vector3<NumericType>& point)
             {
                 auto clip = get_view_projection_matrix()
-                            * mat_column_from_vector<float, Mat4X4Type::get_store_ordering()>(point);
+                            * mat_column_from_vector<NumericType, Mat4X4Type::get_store_ordering()>(point);
-                return std::array<float, 4>{
+                return std::array<NumericType, 4>{
                         clip.at(0, 0), // x
                         clip.at(1, 0), // y
                         clip.at(2, 0), // z
@@ -263,12 +331,13 @@ namespace omath::projection
             const auto c2 = to_clip(triangle.m_vertex3);
 
             // If all vertices are behind the camera (w <= 0), trivially reject
-            if (c0[3] <= 0.f && c1[3] <= 0.f && c2[3] <= 0.f)
+            if (c0[3] <= NumericType{0} && c1[3] <= NumericType{0} && c2[3] <= NumericType{0})
                 return true;
 
             // Helper: all three vertices outside the same clip plane
-            auto all_outside_plane = [](const int axis, const std::array<float, 4>& a, const std::array<float, 4>& b,
+            auto all_outside_plane = [](const int axis, const std::array<NumericType, 4>& a,
-                                        const std::array<float, 4>& c, const bool positive_side)
+                                        const std::array<NumericType, 4>& b, const std::array<NumericType, 4>& c,
+                                        const bool positive_side)
             {
                 if (positive_side)
                     return a[axis] > a[3] && b[axis] > b[3] && c[axis] > c[3];
@@ -309,7 +378,7 @@ namespace omath::projection
             return false;
         }
 
-        [[nodiscard]] bool is_aabb_culled_by_frustum(const primitives::Aabb<float>& aabb) const noexcept
+        [[nodiscard]] bool is_aabb_culled_by_frustum(const primitives::Aabb<NumericType>& aabb) const noexcept
         {
             const auto& m = get_view_projection_matrix();
 
@@ -324,16 +393,16 @@ namespace omath::projection
             //   Far    = r3 - r2
             struct Plane final
             {
-                float a, b, c, d;
+                NumericType a, b, c, d;
             };
 
             const auto extract_plane = [&m](const int sign, const int row) -> Plane
             {
                 return {
-                        m.at(3, 0) + static_cast<float>(sign) * m.at(row, 0),
+                        m.at(3, 0) + static_cast<NumericType>(sign) * m.at(row, 0),
-                        m.at(3, 1) + static_cast<float>(sign) * m.at(row, 1),
+                        m.at(3, 1) + static_cast<NumericType>(sign) * m.at(row, 1),
-                        m.at(3, 2) + static_cast<float>(sign) * m.at(row, 2),
+                        m.at(3, 2) + static_cast<NumericType>(sign) * m.at(row, 2),
-                        m.at(3, 3) + static_cast<float>(sign) * m.at(row, 3),
+                        m.at(3, 3) + static_cast<NumericType>(sign) * m.at(row, 3),
                 };
             };
 
@@ -355,26 +424,26 @@ namespace omath::projection
             // (the "positive vertex"). If it's outside, the entire AABB is outside.
             for (const auto& [a, b, c, d] : planes)
             {
-                const float px = a >= 0.f ? aabb.max.x : aabb.min.x;
+                const auto px = a >= NumericType{0} ? aabb.max.x : aabb.min.x;
-                const float py = b >= 0.f ? aabb.max.y : aabb.min.y;
+                const auto py = b >= NumericType{0} ? aabb.max.y : aabb.min.y;
-                const float pz = c >= 0.f ? aabb.max.z : aabb.min.z;
+                const auto pz = c >= NumericType{0} ? aabb.max.z : aabb.min.z;
 
-                if (a * px + b * py + c * pz + d < 0.f)
+                if (a * px + b * py + c * pz + d < NumericType{0})
                     return true;
             }
 
             return false;
         }
 
-        [[nodiscard]] std::expected<Vector3<float>, Error>
+        [[nodiscard]] std::expected<Vector3<NumericType>, Error>
-        world_to_view_port(const Vector3<float>& world_position,
+        world_to_view_port(const Vector3<NumericType>& world_position,
                            const ViewPortClipping& clipping = ViewPortClipping::AUTO) const noexcept
         {
             auto projected = get_view_projection_matrix()
-                             * mat_column_from_vector<float, Mat4X4Type::get_store_ordering()>(world_position);
+                             * mat_column_from_vector<NumericType, Mat4X4Type::get_store_ordering()>(world_position);
 
             const auto& w = projected.at(3, 0);
-            constexpr auto eps = std::numeric_limits<float>::epsilon();
+            constexpr auto eps = std::numeric_limits<NumericType>::epsilon();
             if (w <= eps)
                 return std::unexpected(Error::PERSPECTIVE_DIVIDER_LESS_EQ_ZERO);
 
@@ -386,16 +455,17 @@ namespace omath::projection
                 return std::unexpected(Error::WORLD_POSITION_IS_OUT_OF_SCREEN_BOUNDS);
 
             // ReSharper disable once CppTooWideScope
-            constexpr auto z_min = depth_range == NDCDepthRange::ZERO_TO_ONE ? 0.0f : -1.0f;
+            constexpr auto z_min = depth_range == NDCDepthRange::ZERO_TO_ONE ? NumericType{0} : -NumericType{1};
-            const auto clipped_manually = clipping == ViewPortClipping::MANUAL && (projected.at(2, 0) < z_min - eps
+            const auto clipped_manually =
-                                          || projected.at(2, 0) > 1.0f + eps);
+                    clipping == ViewPortClipping::MANUAL
+                    && (projected.at(2, 0) < z_min - eps || projected.at(2, 0) > NumericType{1} + eps);
             if (clipped_manually)
                 return std::unexpected(Error::WORLD_POSITION_IS_OUT_OF_SCREEN_BOUNDS);
 
-            return Vector3<float>{projected.at(0, 0), projected.at(1, 0), projected.at(2, 0)};
+            return Vector3<NumericType>{projected.at(0, 0), projected.at(1, 0), projected.at(2, 0)};
         }
         [[nodiscard]]
-        std::expected<Vector3<float>, Error> view_port_to_world(const Vector3<float>& ndc) const noexcept
+        std::expected<Vector3<NumericType>, Error> view_port_to_world(const Vector3<NumericType>& ndc) const noexcept
         {
             const auto inv_view_proj = get_view_projection_matrix().inverted();
 
@@ -403,58 +473,60 @@ namespace omath::projection
                 return std::unexpected(Error::INV_VIEW_PROJ_MAT_DET_EQ_ZERO);
 
             auto inverted_projection =
-                    inv_view_proj.value() * mat_column_from_vector<float, Mat4X4Type::get_store_ordering()>(ndc);
+                    inv_view_proj.value() * mat_column_from_vector<NumericType, Mat4X4Type::get_store_ordering()>(ndc);
 
             const auto& w = inverted_projection.at(3, 0);
 
-            if (std::abs(w) < std::numeric_limits<float>::epsilon())
+            if (std::abs(w) < std::numeric_limits<NumericType>::epsilon())
                 return std::unexpected(Error::WORLD_POSITION_IS_OUT_OF_SCREEN_BOUNDS);
 
             inverted_projection /= w;
 
-            return Vector3<float>{inverted_projection.at(0, 0), inverted_projection.at(1, 0),
+            return Vector3<NumericType>{inverted_projection.at(0, 0), inverted_projection.at(1, 0),
                                         inverted_projection.at(2, 0)};
         }
 
         template<ScreenStart screen_start = ScreenStart::TOP_LEFT_CORNER>
         [[nodiscard]]
-        std::expected<Vector3<float>, Error> screen_to_world(const Vector3<float>& screen_pos) const noexcept
+        std::expected<Vector3<NumericType>, Error>
+        screen_to_world(const Vector3<NumericType>& screen_pos) const noexcept
         {
             return view_port_to_world(screen_to_ndc<screen_start>(screen_pos));
         }
 
         template<ScreenStart screen_start = ScreenStart::TOP_LEFT_CORNER>
         [[nodiscard]]
-        std::expected<Vector3<float>, Error> screen_to_world(const Vector2<float>& screen_pos) const noexcept
+        std::expected<Vector3<NumericType>, Error>
+        screen_to_world(const Vector2<NumericType>& screen_pos) const noexcept
         {
             const auto& [x, y] = screen_pos;
-            return screen_to_world<screen_start>({x, y, 1.f});
+            return screen_to_world<screen_start>({x, y, 1});
         }
 
     protected:
         ViewPort m_view_port{};
-        Angle<float, 0.f, 180.f, AngleFlags::Clamped> m_field_of_view;
+        FieldOfView m_field_of_view;
 
         mutable std::optional<Mat4X4Type> m_view_projection_matrix;
         mutable std::optional<Mat4X4Type> m_projection_matrix;
         mutable std::optional<Mat4X4Type> m_view_matrix;
-        float m_far_plane_distance;
+        NumericType m_far_plane_distance;
-        float m_near_plane_distance;
+        NumericType m_near_plane_distance;
 
         ViewAnglesType m_view_angles;
-        Vector3<float> m_origin;
+        Vector3<NumericType> m_origin;
 
     private:
         template<class Type>
         [[nodiscard]] constexpr static bool is_ndc_out_of_bounds(const Type& ndc) noexcept
         {
-            constexpr auto eps = std::numeric_limits<float>::epsilon();
+            constexpr auto eps = std::numeric_limits<NumericType>::epsilon();
 
             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)
+            if (data[0] < -NumericType{1} - eps || data[0] > NumericType{1} + eps)
                 return true;
-            if (data[1] < -1.0f - eps || data[1] > 1.0f + eps)
+            if (data[1] < -NumericType{1} - eps || data[1] > NumericType{1} + eps)
                 return true;
             return is_ndc_z_value_out_of_bounds(data[2]);
         }
@@ -462,11 +534,11 @@ namespace omath::projection
         [[nodiscard]]
         constexpr static bool is_ndc_z_value_out_of_bounds(const ZType& z_ndc) noexcept
         {
-            constexpr auto eps = std::numeric_limits<float>::epsilon();
+            constexpr auto eps = std::numeric_limits<NumericType>::epsilon();
             if constexpr (depth_range == NDCDepthRange::NEGATIVE_ONE_TO_ONE)
-                return z_ndc < -1.0f - eps || z_ndc > 1.0f + eps;
+                return z_ndc < -NumericType{1} - eps || z_ndc > NumericType{1} + eps;
             if constexpr (depth_range == NDCDepthRange::ZERO_TO_ONE)
-                return z_ndc < 0.0f - eps || z_ndc > 1.0f + eps;
+                return z_ndc < NumericType{0} - eps || z_ndc > NumericType{1} + eps;
 
             std::unreachable();
         }
@@ -485,8 +557,8 @@ namespace omath::projection
                                 v
             */
 
-        [[nodiscard]] Vector3<float>
+        [[nodiscard]] Vector3<NumericType>
-        ndc_to_screen_position_from_top_left_corner(const Vector3<float>& ndc) const noexcept
+        ndc_to_screen_position_from_top_left_corner(const Vector3<NumericType>& ndc) const noexcept
         {
             /*
             +------------------------>
@@ -499,11 +571,12 @@ namespace omath::projection
             |
             ⌄
             */
-            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};
+            return {(ndc.x + NumericType{1}) / NumericType{2} * m_view_port.m_width,
+                    (ndc.y / -NumericType{2} + NumericType{0.5}) * m_view_port.m_height, ndc.z};
         }
 
-        [[nodiscard]] Vector3<float>
+        [[nodiscard]] Vector3<NumericType>
-        ndc_to_screen_position_from_bottom_left_corner(const Vector3<float>& ndc) const noexcept
+        ndc_to_screen_position_from_bottom_left_corner(const Vector3<NumericType>& ndc) const noexcept
         {
             /*
              ^
@@ -516,18 +589,19 @@ namespace omath::projection
              | (0, 0)
              +------------------------>
              */
-            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};
+            return {(ndc.x + NumericType{1}) / NumericType{2} * m_view_port.m_width,
+                    (ndc.y / NumericType{2} + NumericType{0.5}) * m_view_port.m_height, ndc.z};
         }
 
         template<ScreenStart screen_start = ScreenStart::TOP_LEFT_CORNER>
-        [[nodiscard]] Vector3<float> screen_to_ndc(const Vector3<float>& screen_pos) const noexcept
+        [[nodiscard]] Vector3<NumericType> screen_to_ndc(const Vector3<NumericType>& screen_pos) const noexcept
         {
             if constexpr (screen_start == ScreenStart::TOP_LEFT_CORNER)
-                return {screen_pos.x / m_view_port.m_width * 2.f - 1.f, 1.f - screen_pos.y / m_view_port.m_height * 2.f,
+                return {screen_pos.x / m_view_port.m_width * NumericType{2} - NumericType{1},
-                        screen_pos.z};
+                        NumericType{1} - screen_pos.y / m_view_port.m_height * NumericType{2}, screen_pos.z};
             else if constexpr (screen_start == ScreenStart::BOTTOM_LEFT_CORNER)
-                return {screen_pos.x / m_view_port.m_width * 2.f - 1.f,
+                return {screen_pos.x / m_view_port.m_width * NumericType{2} - NumericType{1},
-                        (screen_pos.y / m_view_port.m_height - 0.5f) * 2.f, screen_pos.z};
+                        (screen_pos.y / m_view_port.m_height - NumericType{0.5}) * NumericType{2}, screen_pos.z};
             else
                 std::unreachable();
         }

scripts/gource-timelapse.sh

@@ -0,0 +1,61 @@
+#!/bin/bash
+
+# =============================================================================
+# Gource Timelapse — renders the repository history as a video
+# Requires: gource, ffmpeg
+# =============================================================================
+
+set -euo pipefail
+
+# --- Config (override via env vars) ---
+OUTPUT="${OUTPUT:-gource-timelapse.mp4}"
+SECONDS_PER_DAY="${SECONDS_PER_DAY:-0.1}"
+RESOLUTION="${RESOLUTION:-1920x1080}"
+FPS="${FPS:-60}"
+TITLE="${TITLE:-omath}"
+
+# --- Dependency checks ---
+for cmd in gource ffmpeg; do
+    if ! command -v "$cmd" &>/dev/null; then
+        echo "Error: '$cmd' is not installed."
+        echo "  macOS:  brew install $cmd"
+        echo "  Linux:  sudo apt install $cmd"
+        exit 1
+    fi
+done
+
+echo "----------------------------------------------------"
+echo "Rendering gource timelapse → $OUTPUT"
+echo "  Resolution : $RESOLUTION"
+echo "  FPS        : $FPS"
+echo "  Speed      : ${SECONDS_PER_DAY}s per day"
+echo "----------------------------------------------------"
+
+gource \
+    --title "$TITLE" \
+    --seconds-per-day "$SECONDS_PER_DAY" \
+    --auto-skip-seconds 0.1 \
+    --time-scale 3 \
+    --max-files 0 \
+    --hide filenames \
+    --date-format "%Y-%m-%d" \
+    --multi-sampling \
+    --bloom-multiplier 0.5 \
+    --elasticity 0.05 \
+    --${RESOLUTION%x*}x${RESOLUTION#*x} \
+    --output-framerate "$FPS" \
+    --output-ppm-stream - \
+    | ffmpeg -y \
+        -r "$FPS" \
+        -f image2pipe \
+        -vcodec ppm \
+        -i - \
+        -vcodec libx264 \
+        -preset fast \
+        -pix_fmt yuv420p \
+        -crf 18 \
+        "$OUTPUT"
+
+echo "----------------------------------------------------"
+echo "Done: $OUTPUT"
+echo "----------------------------------------------------"

source/engines/source_engine/formulas.cpp

@@ -38,25 +38,24 @@ namespace omath::source_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
     {
-        // NOTE: Need magic number to fix fov calculation, since source inherit Quake proj matrix calculation
+        // Source (inherited from Quake) stores FOV as horizontal FOV at a 4:3
-        constexpr auto k_multiply_factor = 0.75f;
+        // reference aspect. Convert to true vertical FOV, then delegate to the
-
+        // standard vertical-FOV left-handed builder with the caller's actual
-        const float fov_half_tan = std::tan(angles::degrees_to_radians(field_of_view) / 2.f) * k_multiply_factor;
+        // 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 vfov_deg = angles::radians_to_degrees(
+                2.f * std::atan(std::tan(half_hfov_4_3) / k_source_reference_aspect));
 
         if (ndc_depth_range == NDCDepthRange::ZERO_TO_ONE)
-            return {
+            return mat_perspective_left_handed<
-                    {1.f / (aspect_ratio * fov_half_tan), 0, 0, 0},
+                    float, MatStoreType::ROW_MAJOR, NDCDepthRange::ZERO_TO_ONE>(
-                    {0, 1.f / (fov_half_tan), 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<
-                    {1.f / (aspect_ratio * fov_half_tan), 0, 0, 0},
+                    float, MatStoreType::ROW_MAJOR, NDCDepthRange::NEGATIVE_ONE_TO_ONE>(
-                    {0, 1.f / (fov_half_tan), 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

@@ -2,45 +2,56 @@
 // Created by Vlad on 3/22/2025.
 //
 #include "omath/engines/unreal_engine/formulas.hpp"
-
 namespace omath::unreal_engine
 {
-    Vector3<float> forward_vector(const ViewAngles& angles) noexcept
+    Vector3<double> forward_vector(const ViewAngles& angles) noexcept
     {
         const auto vec = rotation_matrix(angles) * mat_column_from_vector(k_abs_forward);
 
         return {vec.at(0, 0), vec.at(1, 0), vec.at(2, 0)};
     }
-    Vector3<float> right_vector(const ViewAngles& angles) noexcept
+    Vector3<double> right_vector(const ViewAngles& angles) noexcept
     {
         const auto vec = rotation_matrix(angles) * mat_column_from_vector(k_abs_right);
 
         return {vec.at(0, 0), vec.at(1, 0), vec.at(2, 0)};
     }
-    Vector3<float> up_vector(const ViewAngles& angles) noexcept
+    Vector3<double> up_vector(const ViewAngles& angles) noexcept
     {
         const auto vec = rotation_matrix(angles) * mat_column_from_vector(k_abs_up);
 
         return {vec.at(0, 0), vec.at(1, 0), vec.at(2, 0)};
     }
-    Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept
+    Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<double>& cam_origin) noexcept
     {
-        return mat_camera_view<float, MatStoreType::ROW_MAJOR>(forward_vector(angles), -right_vector(angles),
+        return mat_camera_view<double, MatStoreType::ROW_MAJOR>(forward_vector(angles), right_vector(angles),
                                                                up_vector(angles), cam_origin);
     }
     Mat4X4 rotation_matrix(const ViewAngles& angles) noexcept
     {
-        return mat_rotation_axis_x<float, MatStoreType::ROW_MAJOR>(angles.roll)
+        // UE FRotator is intrinsic Z-Y-X (Yaw → Pitch → Roll applied in local
-               * mat_rotation_axis_z<float, MatStoreType::ROW_MAJOR>(angles.yaw)
+        // frame), which for column-vector composition is Rz·Ry·Rx.
-               * mat_rotation_axis_y<float, MatStoreType::ROW_MAJOR>(angles.pitch);
+        // Pitch and roll axes in omath spin opposite to UE's convention, so
+        // both carry a sign flip.
+        return mat_rotation_axis_z<double, MatStoreType::ROW_MAJOR>(angles.yaw)
+               * mat_rotation_axis_y<double, MatStoreType::ROW_MAJOR>(-angles.pitch)
+               * mat_rotation_axis_x<double, MatStoreType::ROW_MAJOR>(-angles.roll);
     }
-    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
-    {
-        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);
+
+    Mat4X4 calc_perspective_projection_matrix(const double field_of_view, const double aspect_ratio, const double near,
+                                              const double far, const NDCDepthRange ndc_depth_range) noexcept
+    {
+        // UE stores horizontal FOV in FMinimalViewInfo — use the left-handed
+        // horizontal-FOV builder directly.
+        if (ndc_depth_range == NDCDepthRange::ZERO_TO_ONE)
+            return mat_perspective_left_handed_horizontal_fov<
+                    double, 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_horizontal_fov<
+                    double, MatStoreType::ROW_MAJOR, NDCDepthRange::NEGATIVE_ONE_TO_ONE>(
+                    field_of_view, aspect_ratio, near, far);
+        std::unreachable();
     }
 } // namespace omath::unreal_engine

source/engines/unreal_engine/traits/camera_trait.cpp

@@ -6,20 +6,20 @@
 namespace omath::unreal_engine
 {
 
-    ViewAngles CameraTrait::calc_look_at_angle(const Vector3<float>& cam_origin, const Vector3<float>& look_at) noexcept
+    ViewAngles CameraTrait::calc_look_at_angle(const Vector3<double>& cam_origin, const Vector3<double>& look_at) noexcept
     {
         const auto direction = (look_at - cam_origin).normalized();
 
-        return {PitchAngle::from_radians(-std::asin(direction.z)),
+        return {PitchAngle::from_radians(std::asin(direction.z)),
                 YawAngle::from_radians(std::atan2(direction.y, direction.x)), RollAngle::from_radians(0.f)};
     }
-    Mat4X4 CameraTrait::calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept
+    Mat4X4 CameraTrait::calc_view_matrix(const ViewAngles& angles, const Vector3<double>& cam_origin) noexcept
     {
         return unreal_engine::calc_view_matrix(angles, cam_origin);
     }
     Mat4X4 CameraTrait::calc_projection_matrix(const projection::FieldOfView& fov,
-                                               const projection::ViewPort& view_port, const float near,
+                                               const projection::ViewPort& view_port, const double near,
-                                               const float far, const NDCDepthRange ndc_depth_range) noexcept
+                                               const double far, const NDCDepthRange ndc_depth_range) noexcept
     {
         return calc_perspective_projection_matrix(fov.as_degrees(), view_port.aspect_ratio(), near, far,
                                                   ndc_depth_range);

source/lua/lua_engines.cpp

@@ -78,7 +78,8 @@ namespace
     }
 
     // Register an engine: alias shared types, register unique Camera
-    template<class EngineTraits>
+    template<class EngineTraits, class ArithmeticType = float>
+    requires std::is_arithmetic_v<ArithmeticType>
     void register_engine(sol::table& omath_table, const char* subtable_name)
     {
         using PitchAngle = typename EngineTraits::PitchAngle;
@@ -92,9 +93,9 @@ namespace
 
         engine_table.new_usertype<Camera>(
                 "Camera",
-                sol::constructors<Camera(const omath::Vector3<float>&, const ViewAngles&,
+                sol::constructors<Camera(const omath::Vector3<ArithmeticType>&, const ViewAngles&,
                                          const omath::projection::ViewPort&, const omath::projection::FieldOfView&,
-                                         float, float)>(),
+                                         ArithmeticType, ArithmeticType)>(),
                 "look_at", &Camera::look_at, "get_forward", &Camera::get_forward, "get_right", &Camera::get_right,
                 "get_up", &Camera::get_up, "get_origin", &Camera::get_origin, "get_view_angles",
                 &Camera::get_view_angles, "get_near_plane", &Camera::get_near_plane, "get_far_plane",
@@ -104,8 +105,8 @@ namespace
                 &Camera::set_near_plane, "set_far_plane", &Camera::set_far_plane,
 
                 "world_to_screen",
-                [](const Camera& cam, const omath::Vector3<float>& pos)
+                [](const Camera& cam, const omath::Vector3<ArithmeticType>& pos)
-                        -> std::tuple<sol::optional<omath::Vector3<float>>, sol::optional<std::string>>
+                        -> std::tuple<sol::optional<omath::Vector3<ArithmeticType>>, sol::optional<std::string>>
                 {
                     auto result = cam.world_to_screen(pos);
                     if (result)
@@ -114,8 +115,8 @@ namespace
                 },
 
                 "screen_to_world",
-                [](const Camera& cam, const omath::Vector3<float>& pos)
+                [](const Camera& cam, const omath::Vector3<ArithmeticType>& pos)
-                        -> std::tuple<sol::optional<omath::Vector3<float>>, sol::optional<std::string>>
+                        -> std::tuple<sol::optional<omath::Vector3<ArithmeticType>>, sol::optional<std::string>>
                 {
                     auto result = cam.screen_to_world(pos);
                     if (result)
@@ -224,7 +225,7 @@ namespace omath::lua
         register_engine<IWEngineTraits>(omath_table, "iw");
         register_engine<SourceEngineTraits>(omath_table, "source");
         register_engine<UnityEngineTraits>(omath_table, "unity");
-        register_engine<UnrealEngineTraits>(omath_table, "unreal");
+        register_engine<UnrealEngineTraits, double>(omath_table, "unreal");
         register_engine<CryEngineTraits>(omath_table, "cry");
     }
 } // namespace omath::lua::detail

tests/engines/unit_test_frostbite_engine.cpp

@@ -453,3 +453,184 @@ TEST(unit_test_frostbite_engine, ViewAnglesAsVector3NormalizedYaw)
 
     EXPECT_NEAR(vec.y, -90.f, 0.01f);
 }
+
+// ---------------------------------------------------------------------------
+// extract_projection_params
+// ---------------------------------------------------------------------------
+
+// Tolerance: tan/atan round-trip in single precision introduces ~1e-5 rad
+// error, which is ~5.7e-4 degrees.
+static constexpr float k_fov_tolerance_deg  = 0.001f;
+static constexpr float k_aspect_tolerance   = 1e-5f;
+
+TEST(unit_test_frostbite_engine, ExtractProjectionParams_BasicRoundTrip)
+{
+    // Build a matrix with known inputs and verify both outputs are recovered.
+    constexpr float fov_deg    = 60.f;
+    constexpr float aspect     = 16.f / 9.f;
+    const auto mat = omath::frostbite_engine::calc_perspective_projection_matrix(
+        fov_deg, aspect, 0.1f, 1000.f, omath::NDCDepthRange::ZERO_TO_ONE);
+
+    const auto [fov, ar] = omath::frostbite_engine::Camera::extract_projection_params(mat);
+
+    EXPECT_NEAR(fov.as_degrees(), fov_deg, k_fov_tolerance_deg);
+    EXPECT_NEAR(ar, aspect, k_aspect_tolerance);
+}
+
+TEST(unit_test_frostbite_engine, ExtractProjectionParams_NegOneToOneDepthRange)
+{
+    // The FOV/aspect encoding in rows 0 and 1 is identical for both NDC
+    // depth ranges, so extraction must work the same way.
+    constexpr float fov_deg = 75.f;
+    constexpr float aspect  = 4.f / 3.f;
+    const auto mat = omath::frostbite_engine::calc_perspective_projection_matrix(
+        fov_deg, aspect, 0.1f, 500.f, omath::NDCDepthRange::NEGATIVE_ONE_TO_ONE);
+
+    const auto [fov, ar] = omath::frostbite_engine::Camera::extract_projection_params(mat);
+
+    EXPECT_NEAR(fov.as_degrees(), fov_deg, k_fov_tolerance_deg);
+    EXPECT_NEAR(ar, aspect, k_aspect_tolerance);
+}
+
+TEST(unit_test_frostbite_engine, ExtractProjectionParams_Fov45)
+{
+    constexpr float fov_deg = 45.f;
+    constexpr float aspect  = 16.f / 9.f;
+    const auto mat = omath::frostbite_engine::calc_perspective_projection_matrix(
+        fov_deg, aspect, 0.01f, 1000.f);
+
+    const auto [fov, ar] = omath::frostbite_engine::Camera::extract_projection_params(mat);
+
+    EXPECT_NEAR(fov.as_degrees(), fov_deg, k_fov_tolerance_deg);
+    EXPECT_NEAR(ar, aspect, k_aspect_tolerance);
+}
+
+TEST(unit_test_frostbite_engine, ExtractProjectionParams_Fov90)
+{
+    constexpr float fov_deg = 90.f;
+    constexpr float aspect  = 16.f / 9.f;
+    const auto mat = omath::frostbite_engine::calc_perspective_projection_matrix(
+        fov_deg, aspect, 0.01f, 1000.f);
+
+    const auto [fov, ar] = omath::frostbite_engine::Camera::extract_projection_params(mat);
+
+    EXPECT_NEAR(fov.as_degrees(), fov_deg, k_fov_tolerance_deg);
+    EXPECT_NEAR(ar, aspect, k_aspect_tolerance);
+}
+
+TEST(unit_test_frostbite_engine, ExtractProjectionParams_Fov120)
+{
+    constexpr float fov_deg = 120.f;
+    constexpr float aspect  = 16.f / 9.f;
+    const auto mat = omath::frostbite_engine::calc_perspective_projection_matrix(
+        fov_deg, aspect, 0.01f, 1000.f);
+
+    const auto [fov, ar] = omath::frostbite_engine::Camera::extract_projection_params(mat);
+
+    EXPECT_NEAR(fov.as_degrees(), fov_deg, k_fov_tolerance_deg);
+    EXPECT_NEAR(ar, aspect, k_aspect_tolerance);
+}
+
+TEST(unit_test_frostbite_engine, ExtractProjectionParams_AspectRatio_4by3)
+{
+    constexpr float fov_deg = 60.f;
+    constexpr float aspect  = 4.f / 3.f;
+    const auto mat = omath::frostbite_engine::calc_perspective_projection_matrix(
+        fov_deg, aspect, 0.1f, 500.f);
+
+    const auto [fov, ar] = omath::frostbite_engine::Camera::extract_projection_params(mat);
+
+    EXPECT_NEAR(fov.as_degrees(), fov_deg, k_fov_tolerance_deg);
+    EXPECT_NEAR(ar, aspect, k_aspect_tolerance);
+}
+
+TEST(unit_test_frostbite_engine, ExtractProjectionParams_AspectRatio_Ultrawide)
+{
+    constexpr float fov_deg = 90.f;
+    constexpr float aspect  = 21.f / 9.f;
+    const auto mat = omath::frostbite_engine::calc_perspective_projection_matrix(
+        fov_deg, aspect, 0.1f, 500.f);
+
+    const auto [fov, ar] = omath::frostbite_engine::Camera::extract_projection_params(mat);
+
+    EXPECT_NEAR(fov.as_degrees(), fov_deg, k_fov_tolerance_deg);
+    EXPECT_NEAR(ar, aspect, k_aspect_tolerance);
+}
+
+TEST(unit_test_frostbite_engine, ExtractProjectionParams_AspectRatio_Square)
+{
+    constexpr float fov_deg = 90.f;
+    constexpr float aspect  = 1.f;
+    const auto mat = omath::frostbite_engine::calc_perspective_projection_matrix(
+        fov_deg, aspect, 0.1f, 500.f);
+
+    const auto [fov, ar] = omath::frostbite_engine::Camera::extract_projection_params(mat);
+
+    EXPECT_NEAR(fov.as_degrees(), fov_deg, k_fov_tolerance_deg);
+    EXPECT_NEAR(ar, aspect, k_aspect_tolerance);
+}
+
+TEST(unit_test_frostbite_engine, ExtractProjectionParams_FovAndAspectAreIndependent)
+{
+    // Changing only FOV must not affect recovered aspect ratio, and vice versa.
+    constexpr float aspect = 16.f / 9.f;
+
+    for (const float fov_deg : {45.f, 60.f, 90.f, 110.f})
+    {
+        const auto mat = omath::frostbite_engine::calc_perspective_projection_matrix(
+            fov_deg, aspect, 0.1f, 1000.f);
+        const auto [fov, ar] = omath::frostbite_engine::Camera::extract_projection_params(mat);
+
+        EXPECT_NEAR(fov.as_degrees(), fov_deg, k_fov_tolerance_deg);
+        EXPECT_NEAR(ar, aspect, k_aspect_tolerance);
+    }
+}
+
+TEST(unit_test_frostbite_engine, ExtractProjectionParams_ViaCamera_RoundTrip)
+{
+    // End-to-end: construct a Camera, retrieve its projection matrix, then
+    // recover the FOV and aspect ratio and compare against the original inputs.
+    constexpr auto fov_in  = omath::projection::FieldOfView::from_degrees(90.f);
+    constexpr float aspect = 1920.f / 1080.f;
+
+    const auto cam = omath::frostbite_engine::Camera(
+        {0.f, 0.f, 0.f}, {}, {1920.f, 1080.f}, fov_in, 0.01f, 1000.f);
+
+    const auto [fov_out, ar_out] =
+        omath::frostbite_engine::Camera::extract_projection_params(cam.get_projection_matrix());
+
+    EXPECT_NEAR(fov_out.as_degrees(), fov_in.as_degrees(), k_fov_tolerance_deg);
+    EXPECT_NEAR(ar_out, aspect, k_aspect_tolerance);
+}
+
+TEST(unit_test_frostbite_engine, ExtractProjectionParams_ViaCamera_AfterFovChange)
+{
+    // Verify that the extracted FOV tracks the camera's FOV after set_field_of_view().
+    auto cam = omath::frostbite_engine::Camera(
+        {0.f, 0.f, 0.f}, {}, {1920.f, 1080.f},
+        omath::projection::FieldOfView::from_degrees(60.f), 0.01f, 1000.f);
+
+    cam.set_field_of_view(omath::projection::FieldOfView::from_degrees(110.f));
+
+    const auto [fov, ar] =
+        omath::frostbite_engine::Camera::extract_projection_params(cam.get_projection_matrix());
+
+    EXPECT_NEAR(fov.as_degrees(), 110.f, k_fov_tolerance_deg);
+    EXPECT_NEAR(ar, 1920.f / 1080.f, k_aspect_tolerance);
+}
+
+TEST(unit_test_frostbite_engine, ExtractProjectionParams_ViaCamera_AfterViewportChange)
+{
+    // Verify that the extracted aspect ratio tracks the viewport after set_view_port().
+    auto cam = omath::frostbite_engine::Camera(
+        {0.f, 0.f, 0.f}, {}, {1920.f, 1080.f},
+        omath::projection::FieldOfView::from_degrees(90.f), 0.01f, 1000.f);
+
+    cam.set_view_port({1280.f, 720.f});
+
+    const auto [fov, ar] =
+        omath::frostbite_engine::Camera::extract_projection_params(cam.get_projection_matrix());
+
+    EXPECT_NEAR(fov.as_degrees(), 90.f, k_fov_tolerance_deg);
+    EXPECT_NEAR(ar, 1280.f / 720.f, k_aspect_tolerance);
+}

tests/engines/unit_test_traits_engines.cpp

@@ -499,10 +499,11 @@ TEST(NDCDepthRangeTests, CryEngine_BothDepthRanges)
 // ── 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)
+template<class Type = float, MatStoreType Store = MatStoreType::ROW_MAJOR>
+static float project_z_lh(const Mat<4, 4, Type, Store>& proj, float z)
 {
-    auto clip = proj * mat_column_from_vector<float>({0, 0, z});
+    auto clip = proj * mat_column_from_vector<Type, Store>({0, 0, static_cast<Type>(z)});
-    return clip.at(2, 0) / clip.at(3, 0);
+    return static_cast<float>(clip.at(2, 0) / clip.at(3, 0));
 }
 
 TEST(NDCDepthRangeTests, Source_ZeroToOne_ZRange)

tests/engines/unit_test_unreal_engine.cpp

@@ -32,7 +32,7 @@ TEST(unit_test_unreal_engine, ForwardVectorRotationPitch)
 {
     omath::unreal_engine::ViewAngles angles;
 
-    angles.pitch = omath::unreal_engine::PitchAngle::from_degrees(-90.f);
+    angles.pitch = omath::unreal_engine::PitchAngle::from_degrees(90.f);
 
     const auto forward = omath::unreal_engine::forward_vector(angles);
     EXPECT_NEAR(forward.x, omath::unreal_engine::k_abs_up.x, 0.00001f);
@@ -44,7 +44,7 @@ TEST(unit_test_unreal_engine, ForwardVectorRotationRoll)
 {
     omath::unreal_engine::ViewAngles angles;
 
-    angles.roll = omath::unreal_engine::RollAngle::from_degrees(-90.f);
+    angles.roll = omath::unreal_engine::RollAngle::from_degrees(90.f);
 
     const auto forward = omath::unreal_engine::up_vector(angles);
     EXPECT_NEAR(forward.x, omath::unreal_engine::k_abs_right.x, 0.00001f);
@@ -111,7 +111,7 @@ TEST(unit_test_unreal_engine, CameraSetAndGetOrigin)
 {
     auto cam = omath::unreal_engine::Camera({0, 0, 0}, {}, {1920.f, 1080.f}, {}, 0.01f, 1000.f);
 
-    EXPECT_EQ(cam.get_origin(), omath::Vector3<float>{});
+    EXPECT_EQ(cam.get_origin(), omath::Vector3<double>{});
     cam.set_field_of_view(omath::projection::FieldOfView::from_degrees(50.f));
 
     EXPECT_EQ(cam.get_field_of_view().as_degrees(), 50.f);
@@ -129,7 +129,7 @@ TEST(unit_test_unreal_engine, loook_at_random_all_axis)
     std::size_t failed_points = 0;
     for (int i = 0; i < 100; i++)
     {
-        const auto position_to_look = omath::Vector3<float>{dist(gen), dist(gen), dist(gen)};
+        const auto position_to_look = omath::Vector3<double>{dist(gen), dist(gen), dist(gen)};
 
         if (cam.get_origin().distance_to(position_to_look) < 10)
             continue;
@@ -151,7 +151,7 @@ TEST(unit_test_unreal_engine, loook_at_random_all_axis)
 TEST(unit_test_unreal_engine, loook_at_random_x_axis)
 {
     std::mt19937 gen(std::random_device{}()); // Seed with a non-deterministic source
-    std::uniform_real_distribution<float> dist(-1000.f, 1000.f);
+    std::uniform_real_distribution<double> dist(-1000.f, 1000.f);
 
     constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
     auto cam = omath::unreal_engine::Camera({0, 0, 0}, {}, {1920.f, 1080.f}, fov, 0.001f, 10000.f);
@@ -159,7 +159,7 @@ TEST(unit_test_unreal_engine, loook_at_random_x_axis)
     std::size_t failed_points = 0;
     for (int i = 0; i < 1000; i++)
     {
-        const auto position_to_look = omath::Vector3<float>{dist(gen), dist(gen), dist(gen)};
+        const auto position_to_look = omath::Vector3<double>{dist(gen), dist(gen), dist(gen)};
 
         if (cam.get_origin().distance_to(position_to_look) < 10)
             continue;
@@ -190,7 +190,7 @@ TEST(unit_test_unreal_engine, loook_at_random_y_axis)
     std::size_t failed_points = 0;
     for (int i = 0; i < 1000; i++)
     {
-        const auto position_to_look = omath::Vector3<float>{0.f, dist(gen), 0.f};
+        const auto position_to_look = omath::Vector3<double>{0.f, dist(gen), 0.f};
 
         if (cam.get_origin().distance_to(position_to_look) < 10)
             continue;
@@ -221,7 +221,7 @@ TEST(unit_test_unreal_engine, loook_at_random_z_axis)
     std::size_t failed_points = 0;
     for (int i = 0; i < 1000; i++)
     {
-        const auto position_to_look = omath::Vector3<float>{0.f, 0.f, dist(gen)};
+        const auto position_to_look = omath::Vector3<double>{0.f, 0.f, dist(gen)};
 
         if (cam.get_origin().distance_to(position_to_look) < 10)
             continue;

tests/general/mem_fd_helper.hpp

@@ -20,19 +20,19 @@
 #include <vector>
 
 #if defined(__linux__)
-#  include <unistd.h>
+#include <fcntl.h>
-#  include <fcntl.h>
+#include <unistd.h>
-#  if defined(__ANDROID__)
+#if defined(__ANDROID__)
-#    if __ANDROID_API__ >= 30
+#if __ANDROID_API__ >= 30
-#      include <sys/mman.h>
+#include <sys/mman.h>
-#      define OMATH_TEST_USE_MEMFD 1
+#define OMATH_TEST_USE_MEMFD 1
-#    endif
+#endif
 // Android < 30: fall through to tmpfile() path below
-#  else
+#else
 // Desktop Linux: memfd_create available since glibc 2.27 / kernel 3.17
-#    include <sys/mman.h>
+#include <sys/mman.h>
-#    define OMATH_TEST_USE_MEMFD 1
+#define OMATH_TEST_USE_MEMFD 1
-#  endif
+#endif
 #endif
 
 class MemFdFile
@@ -57,9 +57,11 @@ public:
     MemFdFile(MemFdFile&& o) noexcept
         : m_path(std::move(o.m_path))
 #if defined(OMATH_TEST_USE_MEMFD)
-        , m_fd(o.m_fd)
+          ,
+          m_fd(o.m_fd)
 #else
-        , m_temp_path(std::move(o.m_temp_path))
+          ,
+          m_temp_path(std::move(o.m_temp_path))
 #endif
     {
 #if defined(OMATH_TEST_USE_MEMFD)
@@ -69,9 +71,15 @@ public:
 #endif
     }
 
-    [[nodiscard]] bool valid() const { return !m_path.empty(); }
+    [[nodiscard]] bool valid() const
+    {
+        return !m_path.empty();
+    }
 
-    [[nodiscard]] const std::filesystem::path& path() const { return m_path; }
+    [[nodiscard]] const std::filesystem::path& path() const
+    {
+        return m_path;
+    }
 
     static MemFdFile create(const std::vector<std::uint8_t>& data)
     {
@@ -163,25 +171,27 @@ inline std::vector<std::uint8_t> build_minimal_pe(const std::vector<std::uint8_t
 
     std::vector<std::uint8_t> buf(data_off + section_bytes.size(), 0u);
 
-    buf[0] = 'M'; buf[1] = 'Z';
+    buf[0] = 'M';
+    buf[1] = 'Z';
     std::memcpy(buf.data() + 0x3Cu, &e_lfanew, 4);
 
-    buf[nt_off] = 'P'; buf[nt_off + 1] = 'E';
+    buf[nt_off] = 'P';
+    buf[nt_off + 1] = 'E';
 
-    const std::uint16_t machine = 0x8664u, num_sections = 1u;
+    constexpr std::uint16_t machine = 0x8664u, num_sections = 1u;
     std::memcpy(buf.data() + fh_off, &machine, 2);
     std::memcpy(buf.data() + fh_off + 2, &num_sections, 2);
     std::memcpy(buf.data() + fh_off + 16, &size_opt, 2);
 
-    const std::uint16_t magic = 0x20Bu;
+    constexpr std::uint16_t magic = 0x20Bu;
     std::memcpy(buf.data() + oh_off, &magic, 2);
 
-    const char name[8] = {'.','t','e','x','t',0,0,0};
+    constexpr char name[8] = {'.', 't', 'e', 'x', 't', 0, 0, 0};
     std::memcpy(buf.data() + sh_off, name, 8);
 
     const auto vsize = static_cast<std::uint32_t>(section_bytes.size());
-    const std::uint32_t vaddr   = 0x1000u;
+    constexpr std::uint32_t vaddr = 0x1000u;
-    const auto ptr_raw = static_cast<std::uint32_t>(data_off);
+    constexpr auto ptr_raw = static_cast<std::uint32_t>(data_off);
     std::memcpy(buf.data() + sh_off + 8, &vsize, 4);
     std::memcpy(buf.data() + sh_off + 12, &vaddr, 4);
     std::memcpy(buf.data() + sh_off + 16, &vsize, 4);

tests/general/unit_test_aabb.cpp

@@ -0,0 +1,240 @@
+//
+// Created by Vladislav on 19.04.2026.
+//
+#include <gtest/gtest.h>
+#include "omath/3d_primitives/aabb.hpp"
+
+using AABB = omath::primitives::Aabb<float>;
+using Vec3 = omath::Vector3<float>;
+
+// --- center() ---
+
+TEST(AabbTests, CenterOfSymmetricBox)
+{
+    constexpr AABB box{{-1.f, -1.f, -1.f}, {1.f, 1.f, 1.f}};
+    constexpr auto c = box.center();
+    EXPECT_FLOAT_EQ(c.x, 0.f);
+    EXPECT_FLOAT_EQ(c.y, 0.f);
+    EXPECT_FLOAT_EQ(c.z, 0.f);
+}
+
+TEST(AabbTests, CenterOfOffsetBox)
+{
+    constexpr AABB box{{1.f, 2.f, 3.f}, {3.f, 6.f, 7.f}};
+    constexpr auto c = box.center();
+    EXPECT_FLOAT_EQ(c.x, 2.f);
+    EXPECT_FLOAT_EQ(c.y, 4.f);
+    EXPECT_FLOAT_EQ(c.z, 5.f);
+}
+
+TEST(AabbTests, CenterOfDegenerateBox)
+{
+    constexpr AABB box{{5.f, 5.f, 5.f}, {5.f, 5.f, 5.f}};
+    constexpr auto c = box.center();
+    EXPECT_FLOAT_EQ(c.x, 5.f);
+    EXPECT_FLOAT_EQ(c.y, 5.f);
+    EXPECT_FLOAT_EQ(c.z, 5.f);
+}
+
+// --- extents() ---
+
+TEST(AabbTests, ExtentsOfSymmetricBox)
+{
+    constexpr AABB box{{-2.f, -3.f, -4.f}, {2.f, 3.f, 4.f}};
+    constexpr auto e = box.extents();
+    EXPECT_FLOAT_EQ(e.x, 2.f);
+    EXPECT_FLOAT_EQ(e.y, 3.f);
+    EXPECT_FLOAT_EQ(e.z, 4.f);
+}
+
+TEST(AabbTests, ExtentsOfUnitBox)
+{
+    constexpr AABB box{{0.f, 0.f, 0.f}, {2.f, 2.f, 2.f}};
+    constexpr auto e = box.extents();
+    EXPECT_FLOAT_EQ(e.x, 1.f);
+    EXPECT_FLOAT_EQ(e.y, 1.f);
+    EXPECT_FLOAT_EQ(e.z, 1.f);
+}
+
+TEST(AabbTests, ExtentsOfDegenerateBox)
+{
+    constexpr AABB box{{3.f, 3.f, 3.f}, {3.f, 3.f, 3.f}};
+    constexpr auto e = box.extents();
+    EXPECT_FLOAT_EQ(e.x, 0.f);
+    EXPECT_FLOAT_EQ(e.y, 0.f);
+    EXPECT_FLOAT_EQ(e.z, 0.f);
+}
+
+using UpAxis = omath::primitives::UpAxis;
+
+// --- top() ---
+
+TEST(AabbTests, TopYUpSymmetricBox)
+{
+    constexpr AABB box{{-1.f, -2.f, -3.f}, {1.f, 2.f, 3.f}};
+    constexpr auto t = box.top<UpAxis::Y>();
+    EXPECT_FLOAT_EQ(t.x, 0.f);
+    EXPECT_FLOAT_EQ(t.y, 2.f);
+    EXPECT_FLOAT_EQ(t.z, 0.f);
+}
+
+TEST(AabbTests, TopYUpOffsetBox)
+{
+    constexpr AABB box{{1.f, 4.f, 2.f}, {3.f, 10.f, 6.f}};
+    constexpr auto t = box.top<UpAxis::Y>();
+    EXPECT_FLOAT_EQ(t.x, 2.f);
+    EXPECT_FLOAT_EQ(t.y, 10.f);
+    EXPECT_FLOAT_EQ(t.z, 4.f);
+}
+
+TEST(AabbTests, TopZUpSymmetricBox)
+{
+    constexpr AABB box{{-1.f, -2.f, -3.f}, {1.f, 2.f, 3.f}};
+    constexpr auto t = box.top<UpAxis::Z>();
+    EXPECT_FLOAT_EQ(t.x, 0.f);
+    EXPECT_FLOAT_EQ(t.y, 0.f);
+    EXPECT_FLOAT_EQ(t.z, 3.f);
+}
+
+TEST(AabbTests, TopZUpOffsetBox)
+{
+    constexpr AABB box{{1.f, 4.f, 2.f}, {3.f, 10.f, 6.f}};
+    constexpr auto t = box.top<UpAxis::Z>();
+    EXPECT_FLOAT_EQ(t.x, 2.f);
+    EXPECT_FLOAT_EQ(t.y, 7.f);
+    EXPECT_FLOAT_EQ(t.z, 6.f);
+}
+
+TEST(AabbTests, TopDefaultIsYUp)
+{
+    constexpr AABB box{{0.f, 0.f, 0.f}, {2.f, 4.f, 6.f}};
+    EXPECT_EQ(box.top(), box.top<UpAxis::Y>());
+}
+
+// --- bottom() ---
+
+TEST(AabbTests, BottomYUpSymmetricBox)
+{
+    constexpr AABB box{{-1.f, -2.f, -3.f}, {1.f, 2.f, 3.f}};
+    constexpr auto b = box.bottom<UpAxis::Y>();
+    EXPECT_FLOAT_EQ(b.x, 0.f);
+    EXPECT_FLOAT_EQ(b.y, -2.f);
+    EXPECT_FLOAT_EQ(b.z, 0.f);
+}
+
+TEST(AabbTests, BottomYUpOffsetBox)
+{
+    constexpr AABB box{{1.f, 4.f, 2.f}, {3.f, 10.f, 6.f}};
+    constexpr auto b = box.bottom<UpAxis::Y>();
+    EXPECT_FLOAT_EQ(b.x, 2.f);
+    EXPECT_FLOAT_EQ(b.y, 4.f);
+    EXPECT_FLOAT_EQ(b.z, 4.f);
+}
+
+TEST(AabbTests, BottomZUpSymmetricBox)
+{
+    constexpr AABB box{{-1.f, -2.f, -3.f}, {1.f, 2.f, 3.f}};
+    constexpr auto b = box.bottom<UpAxis::Z>();
+    EXPECT_FLOAT_EQ(b.x, 0.f);
+    EXPECT_FLOAT_EQ(b.y, 0.f);
+    EXPECT_FLOAT_EQ(b.z, -3.f);
+}
+
+TEST(AabbTests, BottomZUpOffsetBox)
+{
+    constexpr AABB box{{1.f, 4.f, 2.f}, {3.f, 10.f, 6.f}};
+    constexpr auto b = box.bottom<UpAxis::Z>();
+    EXPECT_FLOAT_EQ(b.x, 2.f);
+    EXPECT_FLOAT_EQ(b.y, 7.f);
+    EXPECT_FLOAT_EQ(b.z, 2.f);
+}
+
+TEST(AabbTests, BottomDefaultIsYUp)
+{
+    constexpr AABB box{{0.f, 0.f, 0.f}, {2.f, 4.f, 6.f}};
+    EXPECT_EQ(box.bottom(), box.bottom<UpAxis::Y>());
+}
+
+TEST(AabbTests, TopAndBottomAreSymmetric)
+{
+    constexpr AABB box{{-1.f, -2.f, -3.f}, {1.f, 2.f, 3.f}};
+    EXPECT_FLOAT_EQ(box.top<UpAxis::Y>().y, -box.bottom<UpAxis::Y>().y);
+    EXPECT_FLOAT_EQ(box.top<UpAxis::Z>().z, -box.bottom<UpAxis::Z>().z);
+}
+
+// --- is_collide() ---
+
+TEST(AabbTests, OverlappingBoxesCollide)
+{
+    constexpr AABB a{{-1.f, -1.f, -1.f}, {1.f, 1.f, 1.f}};
+    constexpr AABB b{{0.f, 0.f, 0.f}, {2.f, 2.f, 2.f}};
+    EXPECT_TRUE(a.is_collide(b));
+    EXPECT_TRUE(b.is_collide(a));
+}
+
+TEST(AabbTests, SeparatedBoxesDoNotCollide)
+{
+    constexpr AABB a{{-1.f, -1.f, -1.f}, {1.f, 1.f, 1.f}};
+    constexpr AABB b{{2.f, 2.f, 2.f}, {4.f, 4.f, 4.f}};
+    EXPECT_FALSE(a.is_collide(b));
+    EXPECT_FALSE(b.is_collide(a));
+}
+
+TEST(AabbTests, TouchingFacesCollide)
+{
+    constexpr AABB a{{-1.f, -1.f, -1.f}, {1.f, 1.f, 1.f}};
+    constexpr AABB b{{1.f, -1.f, -1.f}, {3.f, 1.f, 1.f}};
+    EXPECT_TRUE(a.is_collide(b));
+    EXPECT_TRUE(b.is_collide(a));
+}
+
+TEST(AabbTests, ContainedBoxCollides)
+{
+    constexpr AABB outer{{-3.f, -3.f, -3.f}, {3.f, 3.f, 3.f}};
+    constexpr AABB inner{{-1.f, -1.f, -1.f}, {1.f, 1.f, 1.f}};
+    EXPECT_TRUE(outer.is_collide(inner));
+    EXPECT_TRUE(inner.is_collide(outer));
+}
+
+TEST(AabbTests, SeparatedOnXAxisDoNotCollide)
+{
+    constexpr AABB a{{0.f, 0.f, 0.f}, {1.f, 1.f, 1.f}};
+    constexpr AABB b{{2.f, 0.f, 0.f}, {3.f, 1.f, 1.f}};
+    EXPECT_FALSE(a.is_collide(b));
+}
+
+TEST(AabbTests, SeparatedOnYAxisDoNotCollide)
+{
+    constexpr AABB a{{0.f, 0.f, 0.f}, {1.f, 1.f, 1.f}};
+    constexpr AABB b{{0.f, 2.f, 0.f}, {1.f, 3.f, 1.f}};
+    EXPECT_FALSE(a.is_collide(b));
+}
+
+TEST(AabbTests, SeparatedOnZAxisDoNotCollide)
+{
+    constexpr AABB a{{0.f, 0.f, 0.f}, {1.f, 1.f, 1.f}};
+    constexpr AABB b{{0.f, 0.f, 2.f}, {1.f, 1.f, 3.f}};
+    EXPECT_FALSE(a.is_collide(b));
+}
+
+TEST(AabbTests, IdenticalBoxesCollide)
+{
+    constexpr AABB a{{-1.f, -1.f, -1.f}, {1.f, 1.f, 1.f}};
+    EXPECT_TRUE(a.is_collide(a));
+}
+
+TEST(AabbTests, DegeneratePointBoxCollidesWhenInsideOther)
+{
+    constexpr AABB box{{-1.f, -1.f, -1.f}, {1.f, 1.f, 1.f}};
+    constexpr AABB point{{0.f, 0.f, 0.f}, {0.f, 0.f, 0.f}};
+    EXPECT_TRUE(box.is_collide(point));
+    EXPECT_TRUE(point.is_collide(box));
+}
+
+TEST(AabbTests, DegeneratePointBoxDoesNotCollideWhenOutside)
+{
+    constexpr AABB box{{-1.f, -1.f, -1.f}, {1.f, 1.f, 1.f}};
+    constexpr AABB point{{5.f, 0.f, 0.f}, {5.f, 0.f, 0.f}};
+    EXPECT_FALSE(box.is_collide(point));
+    EXPECT_FALSE(point.is_collide(box));
+}

tests/general/unit_test_cry_pred_engine_trait.cpp

@@ -0,0 +1,275 @@
+//
+// Created by Vladislav on 20.04.2026.
+//
+#include <gtest/gtest.h>
+#include <omath/engines/cry_engine/traits/pred_engine_trait.hpp>
+#include <omath/projectile_prediction/projectile.hpp>
+#include <omath/projectile_prediction/target.hpp>
+
+using namespace omath;
+using namespace omath::cry_engine;
+
+// ---- predict_projectile_position ----
+
+TEST(CryPredEngineTrait, PredictProjectilePositionAtTimeZero)
+{
+    projectile_prediction::Projectile p;
+    p.m_origin       = {1.f, 2.f, 3.f};
+    p.m_launch_offset = {4.f, 5.f, 6.f};
+    p.m_launch_speed  = 100.f;
+    p.m_gravity_scale = 1.f;
+
+    const auto pos = PredEngineTrait::predict_projectile_position(p, 0.f, 0.f, 0.f, 9.81f);
+
+    // At t=0 no velocity is applied, just origin+offset
+    EXPECT_NEAR(pos.x, 5.f, 1e-4f);
+    EXPECT_NEAR(pos.y, 7.f, 1e-4f);
+    EXPECT_NEAR(pos.z, 9.f, 1e-4f);
+}
+
+TEST(CryPredEngineTrait, PredictProjectilePositionZeroAnglesForwardIsY)
+{
+    // Cry engine forward = +Y. At pitch=0, yaw=0 the projectile travels along +Y.
+    projectile_prediction::Projectile p;
+    p.m_origin       = {0.f, 0.f, 0.f};
+    p.m_launch_speed  = 10.f;
+    p.m_gravity_scale = 0.f; // no gravity so we isolate direction
+
+    const auto pos = PredEngineTrait::predict_projectile_position(p, 0.f, 0.f, 1.f, 9.81f);
+
+    EXPECT_NEAR(pos.x, 0.f, 1e-4f);
+    EXPECT_NEAR(pos.y, 10.f, 1e-4f);
+    EXPECT_NEAR(pos.z, 0.f, 1e-4f);
+}
+
+TEST(CryPredEngineTrait, PredictProjectilePositionGravityDropsZ)
+{
+    projectile_prediction::Projectile p;
+    p.m_origin       = {0.f, 0.f, 0.f};
+    p.m_launch_speed  = 10.f;
+    p.m_gravity_scale = 1.f;
+
+    const auto pos = PredEngineTrait::predict_projectile_position(p, 0.f, 0.f, 2.f, 9.81f);
+
+    // z = 0 - (9.81 * 1) * (4) * 0.5 = -19.62
+    EXPECT_NEAR(pos.z, -9.81f * 4.f * 0.5f, 1e-3f);
+}
+
+TEST(CryPredEngineTrait, PredictProjectilePositionGravityScaleZeroNoZDrop)
+{
+    projectile_prediction::Projectile p;
+    p.m_origin       = {0.f, 0.f, 0.f};
+    p.m_launch_speed  = 10.f;
+    p.m_gravity_scale = 0.f;
+
+    const auto pos = PredEngineTrait::predict_projectile_position(p, 0.f, 0.f, 3.f, 9.81f);
+
+    EXPECT_NEAR(pos.z, 0.f, 1e-4f);
+}
+
+TEST(CryPredEngineTrait, PredictProjectilePositionWithLaunchOffset)
+{
+    projectile_prediction::Projectile p;
+    p.m_origin        = {5.f, 0.f, 0.f};
+    p.m_launch_offset = {0.f, 0.f, 2.f};
+    p.m_launch_speed  = 10.f;
+    p.m_gravity_scale = 0.f;
+
+    const auto pos = PredEngineTrait::predict_projectile_position(p, 0.f, 0.f, 1.f, 0.f);
+
+    // launch position = {5, 0, 2}, travels along +Y by 10
+    EXPECT_NEAR(pos.x, 5.f,  1e-4f);
+    EXPECT_NEAR(pos.y, 10.f, 1e-4f);
+    EXPECT_NEAR(pos.z, 2.f,  1e-4f);
+}
+
+// ---- predict_target_position ----
+
+TEST(CryPredEngineTrait, PredictTargetPositionGroundedStationary)
+{
+    projectile_prediction::Target t;
+    t.m_origin     = {10.f, 20.f, 5.f};
+    t.m_velocity   = {0.f, 0.f, 0.f};
+    t.m_is_airborne = false;
+
+    const auto pred = PredEngineTrait::predict_target_position(t, 5.f, 9.81f);
+
+    EXPECT_NEAR(pred.x, 10.f, 1e-6f);
+    EXPECT_NEAR(pred.y, 20.f, 1e-6f);
+    EXPECT_NEAR(pred.z,  5.f, 1e-6f);
+}
+
+TEST(CryPredEngineTrait, PredictTargetPositionGroundedMoving)
+{
+    projectile_prediction::Target t;
+    t.m_origin     = {0.f, 0.f, 0.f};
+    t.m_velocity   = {3.f, 4.f, 0.f};
+    t.m_is_airborne = false;
+
+    const auto pred = PredEngineTrait::predict_target_position(t, 2.f, 9.81f);
+
+    EXPECT_NEAR(pred.x, 6.f,  1e-6f);
+    EXPECT_NEAR(pred.y, 8.f,  1e-6f);
+    EXPECT_NEAR(pred.z, 0.f,  1e-6f); // grounded — no gravity
+}
+
+TEST(CryPredEngineTrait, PredictTargetPositionAirborneGravityDropsZ)
+{
+    projectile_prediction::Target t;
+    t.m_origin     = {0.f, 0.f, 20.f};
+    t.m_velocity   = {0.f, 0.f, 0.f};
+    t.m_is_airborne = true;
+
+    const auto pred = PredEngineTrait::predict_target_position(t, 2.f, 9.81f);
+
+    // z = 20 - 9.81 * 4 * 0.5 = 20 - 19.62 = 0.38
+    EXPECT_NEAR(pred.z, 20.f - 9.81f * 4.f * 0.5f, 1e-4f);
+}
+
+TEST(CryPredEngineTrait, PredictTargetPositionAirborneMovingWithGravity)
+{
+    projectile_prediction::Target t;
+    t.m_origin     = {0.f, 0.f, 50.f};
+    t.m_velocity   = {10.f, 5.f, 0.f};
+    t.m_is_airborne = true;
+
+    const auto pred = PredEngineTrait::predict_target_position(t, 3.f, 9.81f);
+
+    EXPECT_NEAR(pred.x, 30.f, 1e-4f);
+    EXPECT_NEAR(pred.y, 15.f, 1e-4f);
+    EXPECT_NEAR(pred.z, 50.f - 9.81f * 9.f * 0.5f, 1e-4f);
+}
+
+// ---- calc_vector_2d_distance ----
+
+TEST(CryPredEngineTrait, CalcVector2dDistance_3_4_5)
+{
+    EXPECT_NEAR(PredEngineTrait::calc_vector_2d_distance({3.f, 4.f, 999.f}), 5.f, 1e-5f);
+}
+
+TEST(CryPredEngineTrait, CalcVector2dDistance_ZeroVector)
+{
+    EXPECT_NEAR(PredEngineTrait::calc_vector_2d_distance({0.f, 0.f, 0.f}), 0.f, 1e-6f);
+}
+
+TEST(CryPredEngineTrait, CalcVector2dDistance_ZIgnored)
+{
+    // Z does not affect the 2D distance
+    EXPECT_NEAR(PredEngineTrait::calc_vector_2d_distance({0.f, 5.f, 100.f}),
+                PredEngineTrait::calc_vector_2d_distance({0.f, 5.f, 0.f}), 1e-6f);
+}
+
+// ---- get_vector_height_coordinate ----
+
+TEST(CryPredEngineTrait, GetVectorHeightCoordinate_ReturnsZ)
+{
+    // Cry engine up = +Z
+    EXPECT_FLOAT_EQ(PredEngineTrait::get_vector_height_coordinate({1.f, 2.f, 7.f}), 7.f);
+}
+
+// ---- calc_direct_pitch_angle ----
+
+TEST(CryPredEngineTrait, CalcDirectPitchAngle_Flat)
+{
+    // Target at same height → pitch = 0
+    EXPECT_NEAR(PredEngineTrait::calc_direct_pitch_angle({0.f, 0.f, 0.f}, {0.f, 100.f, 0.f}), 0.f, 1e-4f);
+}
+
+TEST(CryPredEngineTrait, CalcDirectPitchAngle_LookingUp)
+{
+    // Target at 45° above (equal XY distance and Z height)
+    // direction to {0, 1, 1} normalized = {0, 0.707, 0.707}, asin(0.707) = 45°
+    EXPECT_NEAR(PredEngineTrait::calc_direct_pitch_angle({0.f, 0.f, 0.f}, {0.f, 1.f, 1.f}), 45.f, 1e-3f);
+}
+
+TEST(CryPredEngineTrait, CalcDirectPitchAngle_LookingDown)
+{
+    // Target directly below
+    EXPECT_NEAR(PredEngineTrait::calc_direct_pitch_angle({0.f, 0.f, 10.f}, {0.f, 0.f, 0.f}), -90.f, 1e-3f);
+}
+
+TEST(CryPredEngineTrait, CalcDirectPitchAngle_LookingDirectlyUp)
+{
+    EXPECT_NEAR(PredEngineTrait::calc_direct_pitch_angle({0.f, 0.f, 0.f}, {0.f, 0.f, 100.f}), 90.f, 1e-3f);
+}
+
+// ---- calc_direct_yaw_angle ----
+
+TEST(CryPredEngineTrait, CalcDirectYawAngle_ForwardAlongY)
+{
+    // Cry engine forward = +Y → yaw = 0
+    EXPECT_NEAR(PredEngineTrait::calc_direct_yaw_angle({0.f, 0.f, 0.f}, {0.f, 100.f, 0.f}), 0.f, 1e-4f);
+}
+
+TEST(CryPredEngineTrait, CalcDirectYawAngle_AlongPositiveX)
+{
+    // direction = {1, 0, 0}, yaw = -atan2(1, 0) = -90°
+    EXPECT_NEAR(PredEngineTrait::calc_direct_yaw_angle({0.f, 0.f, 0.f}, {100.f, 0.f, 0.f}), -90.f, 1e-3f);
+}
+
+TEST(CryPredEngineTrait, CalcDirectYawAngle_AlongNegativeX)
+{
+    // direction = {-1, 0, 0}, yaw = -atan2(-1, 0) = 90°
+    EXPECT_NEAR(PredEngineTrait::calc_direct_yaw_angle({0.f, 0.f, 0.f}, {-100.f, 0.f, 0.f}), 90.f, 1e-3f);
+}
+
+TEST(CryPredEngineTrait, CalcDirectYawAngle_BackwardAlongNegY)
+{
+    // direction = {0, -1, 0}, yaw = -atan2(0, -1) = ±180°
+    const float yaw = PredEngineTrait::calc_direct_yaw_angle({0.f, 0.f, 0.f}, {0.f, -100.f, 0.f});
+    EXPECT_NEAR(std::abs(yaw), 180.f, 1e-3f);
+}
+
+TEST(CryPredEngineTrait, CalcDirectYawAngle_OffOriginCamera)
+{
+    // Same relative direction regardless of camera position
+    const float yaw_a = PredEngineTrait::calc_direct_yaw_angle({0.f, 0.f, 0.f}, {0.f, 100.f, 0.f});
+    const float yaw_b = PredEngineTrait::calc_direct_yaw_angle({50.f, 50.f, 0.f}, {50.f, 150.f, 0.f});
+    EXPECT_NEAR(yaw_a, yaw_b, 1e-4f);
+}
+
+// ---- calc_viewpoint_from_angles ----
+
+TEST(CryPredEngineTrait, CalcViewpointFromAngles_45Degrees)
+{
+    projectile_prediction::Projectile p;
+    p.m_origin      = {0.f, 0.f, 0.f};
+    p.m_launch_speed = 10.f;
+
+    // Target along +Y at distance 10; pitch=45° → height = 10 * tan(45°) = 10
+    const Vector3<float> target{0.f, 10.f, 0.f};
+    const auto vp = PredEngineTrait::calc_viewpoint_from_angles(p, target, 45.f);
+
+    EXPECT_NEAR(vp.x, 0.f,  1e-4f);
+    EXPECT_NEAR(vp.y, 10.f, 1e-4f);
+    EXPECT_NEAR(vp.z, 10.f, 1e-3f);
+}
+
+TEST(CryPredEngineTrait, CalcViewpointFromAngles_ZeroPitch)
+{
+    projectile_prediction::Projectile p;
+    p.m_origin      = {0.f, 0.f, 5.f};
+    p.m_launch_speed = 1.f;
+
+    const Vector3<float> target{3.f, 4.f, 0.f};
+    const auto vp = PredEngineTrait::calc_viewpoint_from_angles(p, target, 0.f);
+
+    // tan(0) = 0 → viewpoint Z = origin.z + 0 = 5
+    EXPECT_NEAR(vp.x, 3.f, 1e-4f);
+    EXPECT_NEAR(vp.y, 4.f, 1e-4f);
+    EXPECT_NEAR(vp.z, 5.f, 1e-4f);
+}
+
+TEST(CryPredEngineTrait, CalcViewpointXYMatchesPredictedTargetXY)
+{
+    projectile_prediction::Projectile p;
+    p.m_origin      = {1.f, 2.f, 3.f};
+    p.m_launch_speed = 50.f;
+
+    const Vector3<float> target{10.f, 20.f, 5.f};
+    const auto vp = PredEngineTrait::calc_viewpoint_from_angles(p, target, 30.f);
+
+    // X and Y always match the predicted target position
+    EXPECT_NEAR(vp.x, target.x, 1e-4f);
+    EXPECT_NEAR(vp.y, target.y, 1e-4f);
+}

tests/general/unit_test_mat.cpp

@@ -220,8 +220,8 @@ TEST(UnitTestMatStandalone, Equanity)
     constexpr omath::Vector3<float> left_handed = {0, 2, 10};
     constexpr omath::Vector3<float> right_handed = {0, 2, -10};
 
-    const auto proj_left_handed = omath::mat_perspective_left_handed(90.f, 16.f / 9.f, 0.1, 1000);
+    const auto proj_left_handed = omath::mat_perspective_left_handed(90.f, 16.f / 9.f, 0.1f, 1000.f);
-    const auto proj_right_handed = omath::mat_perspective_right_handed(90.f, 16.f / 9.f, 0.1, 1000);
+    const auto proj_right_handed = omath::mat_perspective_right_handed(90.f, 16.f / 9.f, 0.1f, 1000.f);
 
     auto ndc_left_handed = proj_left_handed * omath::mat_column_from_vector(left_handed);
     auto ndc_right_handed = proj_right_handed * omath::mat_column_from_vector(right_handed);

tests/general/unit_test_projection.cpp

@@ -5,8 +5,13 @@
 #include <complex>
 #include <gtest/gtest.h>
 #include <omath/3d_primitives/aabb.hpp>
+#include <omath/engines/cry_engine/camera.hpp>
+#include <omath/engines/frostbite_engine/camera.hpp>
+#include <omath/engines/iw_engine/camera.hpp>
 #include <omath/engines/opengl_engine/camera.hpp>
 #include <omath/engines/source_engine/camera.hpp>
+#include <omath/engines/unreal_engine/camera.hpp>
+#include <omath/linear_algebra/triangle.hpp>
 #include <omath/projection/camera.hpp>
 #include <print>
 #include <random>
@@ -511,3 +516,673 @@ TEST(UnitTestProjection, AabbUnityEngineStraddlesNearNotCulled)
     const omath::primitives::Aabb<float> aabb{{-1.f, -1.f, -5.f}, {1.f, 1.f, 5.f}};
     EXPECT_FALSE(cam.is_aabb_culled_by_frustum(aabb));
 }
+
+TEST(UnitTestProjection, CalcViewAnglesFromViewMatrix_LookingForward)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const omath::source_engine::ViewAngles angles{
+        omath::source_engine::PitchAngle::from_degrees(0.f),
+        omath::source_engine::YawAngle::from_degrees(0.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::source_engine::Camera({0, 0, 0}, angles, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto result = omath::source_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(result.pitch.as_degrees(), 0.f, k_eps);
+    EXPECT_NEAR(result.yaw.as_degrees(), 0.f, k_eps);
+}
+
+TEST(UnitTestProjection, CalcViewAnglesFromViewMatrix_PositivePitchAndYaw)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const omath::source_engine::ViewAngles angles{
+        omath::source_engine::PitchAngle::from_degrees(30.f),
+        omath::source_engine::YawAngle::from_degrees(45.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::source_engine::Camera({0, 0, 0}, angles, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto result = omath::source_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(result.pitch.as_degrees(), 30.f, k_eps);
+    EXPECT_NEAR(result.yaw.as_degrees(), 45.f, k_eps);
+}
+
+TEST(UnitTestProjection, CalcViewAnglesFromViewMatrix_NegativePitchAndYaw)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const omath::source_engine::ViewAngles angles{
+        omath::source_engine::PitchAngle::from_degrees(-45.f),
+        omath::source_engine::YawAngle::from_degrees(-90.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::source_engine::Camera({0, 0, 0}, angles, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto result = omath::source_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(result.pitch.as_degrees(), -45.f, k_eps);
+    EXPECT_NEAR(result.yaw.as_degrees(), -90.f, k_eps);
+}
+
+TEST(UnitTestProjection, CalcViewAnglesFromViewMatrix_OffOriginCameraIgnored)
+{
+    // The forward vector from the view matrix does not depend on camera origin,
+    // so the same angles should be recovered regardless of position.
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const omath::source_engine::ViewAngles angles{
+        omath::source_engine::PitchAngle::from_degrees(20.f),
+        omath::source_engine::YawAngle::from_degrees(60.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::source_engine::Camera({100.f, 200.f, -50.f}, angles, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto result = omath::source_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(result.pitch.as_degrees(), 20.f, k_eps);
+    EXPECT_NEAR(result.yaw.as_degrees(), 60.f, k_eps);
+}
+
+TEST(UnitTestProjection, CalcViewAnglesFromViewMatrix_RollAlwaysZero)
+{
+    // Roll cannot be encoded in the forward vector, so it is always 0 in the result.
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const omath::source_engine::ViewAngles angles{
+        omath::source_engine::PitchAngle::from_degrees(10.f),
+        omath::source_engine::YawAngle::from_degrees(30.f),
+        omath::source_engine::RollAngle::from_degrees(15.f)
+    };
+    const auto cam = omath::source_engine::Camera({0, 0, 0}, angles, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto result = omath::source_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_FLOAT_EQ(result.roll.as_degrees(), 0.f);
+}
+
+TEST(UnitTestProjection, CalcOriginFromViewMatrix_AtOrigin)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const auto cam = omath::source_engine::Camera({0, 0, 0}, {}, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto origin = omath::source_engine::Camera::calc_origin_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(origin.x, 0.f, k_eps);
+    EXPECT_NEAR(origin.y, 0.f, k_eps);
+    EXPECT_NEAR(origin.z, 0.f, k_eps);
+}
+
+TEST(UnitTestProjection, CalcOriginFromViewMatrix_ArbitraryPosition)
+{
+    constexpr float k_eps = 1e-3f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const omath::source_engine::ViewAngles angles{
+        omath::source_engine::PitchAngle::from_degrees(0.f),
+        omath::source_engine::YawAngle::from_degrees(0.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::source_engine::Camera({100.f, 200.f, -50.f}, angles, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto origin = omath::source_engine::Camera::calc_origin_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(origin.x, 100.f, k_eps);
+    EXPECT_NEAR(origin.y, 200.f, k_eps);
+    EXPECT_NEAR(origin.z, -50.f, k_eps);
+}
+
+TEST(UnitTestProjection, CalcOriginFromViewMatrix_WithRotation)
+{
+    // Origin recovery must work even when the camera is rotated.
+    constexpr float k_eps = 1e-3f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const omath::source_engine::ViewAngles angles{
+        omath::source_engine::PitchAngle::from_degrees(30.f),
+        omath::source_engine::YawAngle::from_degrees(45.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::source_engine::Camera({300.f, -100.f, 75.f}, angles, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto origin = omath::source_engine::Camera::calc_origin_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(origin.x, 300.f, k_eps);
+    EXPECT_NEAR(origin.y, -100.f, k_eps);
+    EXPECT_NEAR(origin.z, 75.f, k_eps);
+}
+
+TEST(UnitTestProjection, CalcOriginFromViewMatrix_IndependentOfAngles)
+{
+    // Same position, different orientations — should always recover the same origin.
+    constexpr float k_eps = 1e-3f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    constexpr omath::Vector3<float> expected_origin{50.f, 50.f, 50.f};
+
+    const omath::source_engine::ViewAngles angles_a{
+        omath::source_engine::PitchAngle::from_degrees(0.f),
+        omath::source_engine::YawAngle::from_degrees(0.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+    const omath::source_engine::ViewAngles angles_b{
+        omath::source_engine::PitchAngle::from_degrees(-60.f),
+        omath::source_engine::YawAngle::from_degrees(135.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+
+    const auto cam_a = omath::source_engine::Camera(expected_origin, angles_a, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+    const auto cam_b = omath::source_engine::Camera(expected_origin, angles_b, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto origin_a = omath::source_engine::Camera::calc_origin_from_view_matrix(cam_a.get_view_matrix());
+    const auto origin_b = omath::source_engine::Camera::calc_origin_from_view_matrix(cam_b.get_view_matrix());
+
+    EXPECT_NEAR(origin_a.x, expected_origin.x, k_eps);
+    EXPECT_NEAR(origin_a.y, expected_origin.y, k_eps);
+    EXPECT_NEAR(origin_a.z, expected_origin.z, k_eps);
+
+    EXPECT_NEAR(origin_b.x, expected_origin.x, k_eps);
+    EXPECT_NEAR(origin_b.y, expected_origin.y, k_eps);
+    EXPECT_NEAR(origin_b.z, expected_origin.z, k_eps);
+}
+
+// ---- Unity engine camera tests ----
+
+TEST(UnitTestProjection, Unity_CalcViewAnglesFromViewMatrix_LookingForward)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(60.f);
+    const omath::unity_engine::ViewAngles angles{
+        omath::unity_engine::PitchAngle::from_degrees(0.f),
+        omath::unity_engine::YawAngle::from_degrees(0.f),
+        omath::unity_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::unity_engine::Camera({0, 0, 0}, angles, {1280.f, 720.f}, fov, 0.03f, 1000.f);
+
+    const auto result = omath::unity_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(result.pitch.as_degrees(), 0.f, k_eps);
+    EXPECT_NEAR(result.yaw.as_degrees(), 0.f, k_eps);
+}
+
+TEST(UnitTestProjection, Unity_CalcViewAnglesFromViewMatrix_PositivePitchAndYaw)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(60.f);
+    const omath::unity_engine::ViewAngles angles{
+        omath::unity_engine::PitchAngle::from_degrees(30.f),
+        omath::unity_engine::YawAngle::from_degrees(45.f),
+        omath::unity_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::unity_engine::Camera({0, 0, 0}, angles, {1280.f, 720.f}, fov, 0.03f, 1000.f);
+
+    const auto result = omath::unity_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(result.pitch.as_degrees(), 30.f, k_eps);
+    EXPECT_NEAR(result.yaw.as_degrees(), 45.f, k_eps);
+}
+
+TEST(UnitTestProjection, Unity_CalcViewAnglesFromViewMatrix_NegativePitchAndYaw)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(60.f);
+    const omath::unity_engine::ViewAngles angles{
+        omath::unity_engine::PitchAngle::from_degrees(-45.f),
+        omath::unity_engine::YawAngle::from_degrees(-90.f),
+        omath::unity_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::unity_engine::Camera({0, 0, 0}, angles, {1280.f, 720.f}, fov, 0.03f, 1000.f);
+
+    const auto result = omath::unity_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(result.pitch.as_degrees(), -45.f, k_eps);
+    EXPECT_NEAR(result.yaw.as_degrees(), -90.f, k_eps);
+}
+
+TEST(UnitTestProjection, Unity_CalcOriginFromViewMatrix_AtOrigin)
+{
+    constexpr float k_eps = 1e-4f;
+    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 origin = omath::unity_engine::Camera::calc_origin_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(origin.x, 0.f, k_eps);
+    EXPECT_NEAR(origin.y, 0.f, k_eps);
+    EXPECT_NEAR(origin.z, 0.f, k_eps);
+}
+
+TEST(UnitTestProjection, Unity_CalcOriginFromViewMatrix_ArbitraryPosition)
+{
+    constexpr float k_eps = 1e-3f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(60.f);
+    const omath::unity_engine::ViewAngles angles{
+        omath::unity_engine::PitchAngle::from_degrees(0.f),
+        omath::unity_engine::YawAngle::from_degrees(0.f),
+        omath::unity_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::unity_engine::Camera({100.f, 200.f, -50.f}, angles, {1280.f, 720.f}, fov, 0.03f, 1000.f);
+
+    const auto origin = omath::unity_engine::Camera::calc_origin_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(origin.x, 100.f, k_eps);
+    EXPECT_NEAR(origin.y, 200.f, k_eps);
+    EXPECT_NEAR(origin.z, -50.f, k_eps);
+}
+
+TEST(UnitTestProjection, Unity_CalcOriginFromViewMatrix_WithRotation)
+{
+    constexpr float k_eps = 1e-3f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(60.f);
+    const omath::unity_engine::ViewAngles angles{
+        omath::unity_engine::PitchAngle::from_degrees(30.f),
+        omath::unity_engine::YawAngle::from_degrees(45.f),
+        omath::unity_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::unity_engine::Camera({300.f, -100.f, 75.f}, angles, {1280.f, 720.f}, fov, 0.03f, 1000.f);
+
+    const auto origin = omath::unity_engine::Camera::calc_origin_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(origin.x, 300.f, k_eps);
+    EXPECT_NEAR(origin.y, -100.f, k_eps);
+    EXPECT_NEAR(origin.z, 75.f, k_eps);
+}
+// ---- Camera basis vectors at zero angles ----
+
+TEST(UnitTestProjection, SourceEngine_ZeroAngles_BasisVectors)
+{
+    constexpr float k_eps = 1e-5f;
+    const auto cam = omath::source_engine::Camera({}, {}, {1920.f, 1080.f},
+                                                  omath::projection::FieldOfView::from_degrees(90.f), 0.01f, 1000.f);
+    const auto fwd   = cam.get_abs_forward();
+    const auto right = cam.get_abs_right();
+    const auto up    = cam.get_abs_up();
+
+    EXPECT_NEAR(fwd.x,   omath::source_engine::k_abs_forward.x, k_eps);
+    EXPECT_NEAR(fwd.y,   omath::source_engine::k_abs_forward.y, k_eps);
+    EXPECT_NEAR(fwd.z,   omath::source_engine::k_abs_forward.z, k_eps);
+
+    EXPECT_NEAR(right.x, omath::source_engine::k_abs_right.x, k_eps);
+    EXPECT_NEAR(right.y, omath::source_engine::k_abs_right.y, k_eps);
+    EXPECT_NEAR(right.z, omath::source_engine::k_abs_right.z, k_eps);
+
+    EXPECT_NEAR(up.x,    omath::source_engine::k_abs_up.x, k_eps);
+    EXPECT_NEAR(up.y,    omath::source_engine::k_abs_up.y, k_eps);
+    EXPECT_NEAR(up.z,    omath::source_engine::k_abs_up.z, k_eps);
+}
+
+TEST(UnitTestProjection, UnityEngine_ZeroAngles_BasisVectors)
+{
+    constexpr float k_eps = 1e-5f;
+    const auto cam = omath::unity_engine::Camera({}, {}, {1280.f, 720.f},
+                                                 omath::projection::FieldOfView::from_degrees(60.f), 0.03f, 1000.f);
+    const auto fwd   = cam.get_abs_forward();
+    const auto right = cam.get_abs_right();
+    const auto up    = cam.get_abs_up();
+
+    EXPECT_NEAR(fwd.x,   omath::unity_engine::k_abs_forward.x, k_eps);
+    EXPECT_NEAR(fwd.y,   omath::unity_engine::k_abs_forward.y, k_eps);
+    EXPECT_NEAR(fwd.z,   omath::unity_engine::k_abs_forward.z, k_eps);
+
+    EXPECT_NEAR(right.x, omath::unity_engine::k_abs_right.x, k_eps);
+    EXPECT_NEAR(right.y, omath::unity_engine::k_abs_right.y, k_eps);
+    EXPECT_NEAR(right.z, omath::unity_engine::k_abs_right.z, k_eps);
+
+    EXPECT_NEAR(up.x,    omath::unity_engine::k_abs_up.x, k_eps);
+    EXPECT_NEAR(up.y,    omath::unity_engine::k_abs_up.y, k_eps);
+    EXPECT_NEAR(up.z,    omath::unity_engine::k_abs_up.z, k_eps);
+}
+
+TEST(UnitTestProjection, OpenGLEngine_ZeroAngles_BasisVectors)
+{
+    constexpr float k_eps = 1e-5f;
+    const auto cam = omath::opengl_engine::Camera({}, {}, {1920.f, 1080.f},
+                                                  omath::projection::FieldOfView::from_degrees(90.f), 0.01f, 1000.f);
+    const auto fwd   = cam.get_abs_forward();
+    const auto right = cam.get_abs_right();
+    const auto up    = cam.get_abs_up();
+
+    EXPECT_NEAR(fwd.x,   omath::opengl_engine::k_abs_forward.x, k_eps);
+    EXPECT_NEAR(fwd.y,   omath::opengl_engine::k_abs_forward.y, k_eps);
+    EXPECT_NEAR(fwd.z,   omath::opengl_engine::k_abs_forward.z, k_eps);
+
+    EXPECT_NEAR(right.x, omath::opengl_engine::k_abs_right.x, k_eps);
+    EXPECT_NEAR(right.y, omath::opengl_engine::k_abs_right.y, k_eps);
+    EXPECT_NEAR(right.z, omath::opengl_engine::k_abs_right.z, k_eps);
+
+    EXPECT_NEAR(up.x,    omath::opengl_engine::k_abs_up.x, k_eps);
+    EXPECT_NEAR(up.y,    omath::opengl_engine::k_abs_up.y, k_eps);
+    EXPECT_NEAR(up.z,    omath::opengl_engine::k_abs_up.z, k_eps);
+}
+
+TEST(UnitTestProjection, UnrealEngine_ZeroAngles_BasisVectors)
+{
+    constexpr float k_eps = 1e-5f;
+    const auto cam = omath::unreal_engine::Camera({}, {}, {1920.f, 1080.f},
+                                                  omath::projection::FieldOfView::from_degrees(90.f), 0.01f, 1000.f);
+    const auto fwd   = cam.get_abs_forward();
+    const auto right = cam.get_abs_right();
+    const auto up    = cam.get_abs_up();
+
+    EXPECT_NEAR(fwd.x,   omath::unreal_engine::k_abs_forward.x, k_eps);
+    EXPECT_NEAR(fwd.y,   omath::unreal_engine::k_abs_forward.y, k_eps);
+    EXPECT_NEAR(fwd.z,   omath::unreal_engine::k_abs_forward.z, k_eps);
+
+    EXPECT_NEAR(right.x, omath::unreal_engine::k_abs_right.x, k_eps);
+    EXPECT_NEAR(right.y, omath::unreal_engine::k_abs_right.y, k_eps);
+    EXPECT_NEAR(right.z, omath::unreal_engine::k_abs_right.z, k_eps);
+
+    EXPECT_NEAR(up.x,    omath::unreal_engine::k_abs_up.x, k_eps);
+    EXPECT_NEAR(up.y,    omath::unreal_engine::k_abs_up.y, k_eps);
+    EXPECT_NEAR(up.z,    omath::unreal_engine::k_abs_up.z, k_eps);
+}
+
+TEST(UnitTestProjection, FrostbiteEngine_ZeroAngles_BasisVectors)
+{
+    constexpr float k_eps = 1e-5f;
+    const auto cam = omath::frostbite_engine::Camera({}, {}, {1920.f, 1080.f},
+                                                     omath::projection::FieldOfView::from_degrees(90.f), 0.01f, 1000.f);
+    const auto fwd   = cam.get_abs_forward();
+    const auto right = cam.get_abs_right();
+    const auto up    = cam.get_abs_up();
+
+    EXPECT_NEAR(fwd.x,   omath::frostbite_engine::k_abs_forward.x, k_eps);
+    EXPECT_NEAR(fwd.y,   omath::frostbite_engine::k_abs_forward.y, k_eps);
+    EXPECT_NEAR(fwd.z,   omath::frostbite_engine::k_abs_forward.z, k_eps);
+
+    EXPECT_NEAR(right.x, omath::frostbite_engine::k_abs_right.x, k_eps);
+    EXPECT_NEAR(right.y, omath::frostbite_engine::k_abs_right.y, k_eps);
+    EXPECT_NEAR(right.z, omath::frostbite_engine::k_abs_right.z, k_eps);
+
+    EXPECT_NEAR(up.x,    omath::frostbite_engine::k_abs_up.x, k_eps);
+    EXPECT_NEAR(up.y,    omath::frostbite_engine::k_abs_up.y, k_eps);
+    EXPECT_NEAR(up.z,    omath::frostbite_engine::k_abs_up.z, k_eps);
+}
+
+TEST(UnitTestProjection, CryEngine_ZeroAngles_BasisVectors)
+{
+    constexpr float k_eps = 1e-5f;
+    const auto cam = omath::cry_engine::Camera({}, {}, {1920.f, 1080.f},
+                                               omath::projection::FieldOfView::from_degrees(90.f), 0.01f, 1000.f);
+    const auto fwd   = cam.get_abs_forward();
+    const auto right = cam.get_abs_right();
+    const auto up    = cam.get_abs_up();
+
+    EXPECT_NEAR(fwd.x,   omath::cry_engine::k_abs_forward.x, k_eps);
+    EXPECT_NEAR(fwd.y,   omath::cry_engine::k_abs_forward.y, k_eps);
+    EXPECT_NEAR(fwd.z,   omath::cry_engine::k_abs_forward.z, k_eps);
+
+    EXPECT_NEAR(right.x, omath::cry_engine::k_abs_right.x, k_eps);
+    EXPECT_NEAR(right.y, omath::cry_engine::k_abs_right.y, k_eps);
+    EXPECT_NEAR(right.z, omath::cry_engine::k_abs_right.z, k_eps);
+
+    EXPECT_NEAR(up.x,    omath::cry_engine::k_abs_up.x, k_eps);
+    EXPECT_NEAR(up.y,    omath::cry_engine::k_abs_up.y, k_eps);
+    EXPECT_NEAR(up.z,    omath::cry_engine::k_abs_up.z, k_eps);
+}
+
+TEST(UnitTestProjection, IWEngine_ZeroAngles_BasisVectors)
+{
+    constexpr float k_eps = 1e-5f;
+    const auto cam = omath::iw_engine::Camera({}, {}, {1920.f, 1080.f},
+                                              omath::projection::FieldOfView::from_degrees(90.f), 0.01f, 1000.f);
+    const auto fwd   = cam.get_abs_forward();
+    const auto right = cam.get_abs_right();
+    const auto up    = cam.get_abs_up();
+
+    EXPECT_NEAR(fwd.x,   omath::iw_engine::k_abs_forward.x, k_eps);
+    EXPECT_NEAR(fwd.y,   omath::iw_engine::k_abs_forward.y, k_eps);
+    EXPECT_NEAR(fwd.z,   omath::iw_engine::k_abs_forward.z, k_eps);
+
+    EXPECT_NEAR(right.x, omath::iw_engine::k_abs_right.x, k_eps);
+    EXPECT_NEAR(right.y, omath::iw_engine::k_abs_right.y, k_eps);
+    EXPECT_NEAR(right.z, omath::iw_engine::k_abs_right.z, k_eps);
+
+    EXPECT_NEAR(up.x,    omath::iw_engine::k_abs_up.x, k_eps);
+    EXPECT_NEAR(up.y,    omath::iw_engine::k_abs_up.y, k_eps);
+    EXPECT_NEAR(up.z,    omath::iw_engine::k_abs_up.z, k_eps);
+}
+
+// ---- extract_projection_params ----
+
+TEST(UnitTestProjection, ExtractProjectionParams_FovRoundTrip)
+{
+    // Source engine applies a 0.75 scale factor to its projection matrix, so
+    // extract_projection_params (standard formula) does not round-trip with it.
+    // Use Unity engine, which uses a standard projection matrix.
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(75.f);
+    const auto cam = omath::unity_engine::Camera({}, {}, {1280.f, 720.f}, fov, 0.03f, 1000.f);
+
+    const auto params = omath::unity_engine::Camera::extract_projection_params(cam.get_projection_matrix());
+
+    EXPECT_NEAR(params.fov.as_degrees(), 75.f, k_eps);
+}
+
+TEST(UnitTestProjection, ExtractProjectionParams_AspectRatioRoundTrip)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const auto cam = omath::source_engine::Camera({}, {}, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto params = omath::source_engine::Camera::extract_projection_params(cam.get_projection_matrix());
+
+    EXPECT_NEAR(params.aspect_ratio, 1920.f / 1080.f, k_eps);
+}
+
+TEST(UnitTestProjection, ExtractProjectionParams_UnityEngine)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(60.f);
+    const auto cam = omath::unity_engine::Camera({}, {}, {1280.f, 720.f}, fov, 0.03f, 1000.f);
+
+    const auto params = omath::unity_engine::Camera::extract_projection_params(cam.get_projection_matrix());
+
+    EXPECT_NEAR(params.fov.as_degrees(), 60.f, k_eps);
+    EXPECT_NEAR(params.aspect_ratio, 1280.f / 720.f, k_eps);
+}
+
+// ---- Accessors ----
+
+TEST(UnitTestProjection, Accessors_GetFovNearFarOrigin)
+{
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const omath::Vector3<float> origin{10.f, 20.f, 30.f};
+    const auto cam = omath::source_engine::Camera(origin, {}, {1920.f, 1080.f}, fov, 0.1f, 500.f);
+
+    EXPECT_NEAR(cam.get_field_of_view().as_degrees(), 90.f, 1e-4f);
+    EXPECT_FLOAT_EQ(cam.get_near_plane(), 0.1f);
+    EXPECT_FLOAT_EQ(cam.get_far_plane(), 500.f);
+    EXPECT_FLOAT_EQ(cam.get_origin().x, 10.f);
+    EXPECT_FLOAT_EQ(cam.get_origin().y, 20.f);
+    EXPECT_FLOAT_EQ(cam.get_origin().z, 30.f);
+}
+
+// ---- Setters + cache invalidation ----
+
+TEST(UnitTestProjection, SetFieldOfView_InvalidatesProjection)
+{
+    constexpr auto fov_a = omath::projection::FieldOfView::from_degrees(90.f);
+    constexpr auto fov_b = omath::projection::FieldOfView::from_degrees(45.f);
+    auto cam = omath::source_engine::Camera({}, {}, {1920.f, 1080.f}, fov_a, 0.01f, 1000.f);
+
+    const auto proj_before = cam.get_projection_matrix();
+    cam.set_field_of_view(fov_b);
+    const auto proj_after = cam.get_projection_matrix();
+
+    EXPECT_NE(proj_before.at(0, 0), proj_after.at(0, 0));
+    EXPECT_NEAR(cam.get_field_of_view().as_degrees(), 45.f, 1e-4f);
+}
+
+TEST(UnitTestProjection, SetNearPlane_InvalidatesProjection)
+{
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    auto cam = omath::source_engine::Camera({}, {}, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto proj_before = cam.get_projection_matrix();
+    cam.set_near_plane(1.f);
+    const auto proj_after = cam.get_projection_matrix();
+
+    EXPECT_FLOAT_EQ(cam.get_near_plane(), 1.f);
+    EXPECT_NE(proj_before.at(2, 2), proj_after.at(2, 2));
+}
+
+TEST(UnitTestProjection, SetFarPlane_InvalidatesProjection)
+{
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    auto cam = omath::source_engine::Camera({}, {}, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto proj_before = cam.get_projection_matrix();
+    cam.set_far_plane(100.f);
+    const auto proj_after = cam.get_projection_matrix();
+
+    EXPECT_FLOAT_EQ(cam.get_far_plane(), 100.f);
+    EXPECT_NE(proj_before.at(2, 2), proj_after.at(2, 2));
+}
+
+TEST(UnitTestProjection, SetOrigin_InvalidatesViewMatrix)
+{
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    auto cam = omath::source_engine::Camera({0.f, 0.f, 0.f}, {}, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    // Target is off to the side — stays at the same world position while camera
+    // moves laterally, so the projected X must change.
+    const auto screen_before = cam.world_to_screen({500.f, 100.f, 0.f});
+    cam.set_origin({0.f, 100.f, 0.f}); // lateral shift
+    const auto screen_after = cam.world_to_screen({500.f, 100.f, 0.f});
+
+    ASSERT_TRUE(screen_before.has_value());
+    ASSERT_TRUE(screen_after.has_value());
+    EXPECT_NE(screen_before->x, screen_after->x);
+    EXPECT_FLOAT_EQ(cam.get_origin().y, 100.f);
+}
+
+TEST(UnitTestProjection, SetViewPort_InvalidatesProjection)
+{
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    auto cam = omath::source_engine::Camera({}, {}, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto proj_before = cam.get_projection_matrix();
+    // 1280x800 is 8:5, different aspect ratio from 1920x1080 (16:9)
+    cam.set_view_port({1280.f, 800.f});
+    const auto proj_after = cam.get_projection_matrix();
+
+    EXPECT_NE(proj_before.at(0, 0), proj_after.at(0, 0));
+}
+
+TEST(UnitTestProjection, SetViewAngles_InvalidatesViewMatrix)
+{
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    auto cam = omath::source_engine::Camera({}, {}, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto view_before = cam.get_view_matrix();
+    const omath::source_engine::ViewAngles rotated{
+        omath::source_engine::PitchAngle::from_degrees(30.f),
+        omath::source_engine::YawAngle::from_degrees(45.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+    cam.set_view_angles(rotated);
+    const auto view_after = cam.get_view_matrix();
+
+    EXPECT_NE(view_before.at(0, 0), view_after.at(0, 0));
+}
+
+// ---- calc_look_at_angles / look_at ----
+
+TEST(UnitTestProjection, CalcLookAtAngles_ForwardTarget)
+{
+    // Source engine: +X is forward. Camera at origin, target on +X axis.
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const auto cam = omath::source_engine::Camera({0.f, 0.f, 0.f}, {}, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto angles = cam.calc_look_at_angles({100.f, 0.f, 0.f});
+
+    EXPECT_NEAR(angles.pitch.as_degrees(), 0.f, 1e-4f);
+    EXPECT_NEAR(angles.yaw.as_degrees(),   0.f, 1e-4f);
+}
+
+TEST(UnitTestProjection, LookAt_ForwardVectorPointsAtTarget)
+{
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    auto cam = omath::source_engine::Camera({0.f, 0.f, 0.f}, {}, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    cam.look_at({200.f, 0.f, 0.f});
+    const auto fwd = cam.get_abs_forward();
+
+    // After pointing at +X target the forward vector should be ~(1,0,0)
+    EXPECT_NEAR(fwd.x, 1.f, 1e-4f);
+    EXPECT_NEAR(fwd.y, 0.f, 1e-4f);
+    EXPECT_NEAR(fwd.z, 0.f, 1e-4f);
+}
+
+// ---- is_culled_by_frustum (triangle) ----
+
+TEST(UnitTestProjection, TriangleInsideFrustumNotCulled)
+{
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const auto cam = omath::source_engine::Camera({0.f, 0.f, 0.f}, {}, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    // Small triangle directly in front (Source: +X forward)
+    const omath::Triangle<omath::Vector3<float>> tri{
+        {100.f,  0.f,  1.f},
+        {100.f,  1.f, -1.f},
+        {100.f, -1.f, -1.f}
+    };
+    EXPECT_FALSE(cam.is_culled_by_frustum(tri));
+}
+
+TEST(UnitTestProjection, TriangleBehindCameraCulled)
+{
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const auto cam = omath::source_engine::Camera({0.f, 0.f, 0.f}, {}, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    // Triangle entirely behind the camera (-X)
+    const omath::Triangle<omath::Vector3<float>> tri{
+        {-100.f,  0.f,  1.f},
+        {-100.f,  1.f, -1.f},
+        {-100.f, -1.f, -1.f}
+    };
+    EXPECT_TRUE(cam.is_culled_by_frustum(tri));
+}
+
+TEST(UnitTestProjection, TriangleBeyondFarPlaneCulled)
+{
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const auto cam = omath::source_engine::Camera({0.f, 0.f, 0.f}, {}, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    // Triangle beyond the 1000-unit far plane
+    const omath::Triangle<omath::Vector3<float>> tri{
+        {2000.f,  0.f,  1.f},
+        {2000.f,  1.f, -1.f},
+        {2000.f, -1.f, -1.f}
+    };
+    EXPECT_TRUE(cam.is_culled_by_frustum(tri));
+}
+
+TEST(UnitTestProjection, TriangleFarToSideCulled)
+{
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const auto cam = omath::source_engine::Camera({0.f, 0.f, 0.f}, {}, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    // Triangle far outside the side frustum planes
+    const omath::Triangle<omath::Vector3<float>> tri{
+        {100.f, 5000.f,  0.f},
+        {100.f, 5001.f,  1.f},
+        {100.f, 5001.f, -1.f}
+    };
+    EXPECT_TRUE(cam.is_culled_by_frustum(tri));
+}
+
+TEST(UnitTestProjection, TriangleStraddlingFrustumNotCulled)
+{
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const auto cam = omath::source_engine::Camera({0.f, 0.f, 0.f}, {}, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    // Large triangle with vertices on both sides of the frustum — should not be culled
+    const omath::Triangle<omath::Vector3<float>> tri{
+        { 100.f,    0.f,   0.f},
+        { 100.f, 5000.f,   0.f},
+        { 100.f,    0.f, 5000.f}
+    };
+    EXPECT_FALSE(cam.is_culled_by_frustum(tri));
+}