Adds Unreal Engine math implementations

Adds Unreal Engine-specific implementations for camera and projectile prediction calculations.

This includes:
- Defining constants and data types tailored for Unreal Engine's coordinate system and conventions.
- Implementing functions for calculating forward, right, and up vectors, view matrices, and perspective projection matrices.
- Providing camera trait for look-at angle calculations and projection matrix generation.
- Implements projectile prediction traits and utilities.

include/omath/engines/unreal_engine/camera.hpp

@@ -0,0 +1,13 @@
+//
+// Created by Vlad on 3/22/2025.
+//
+
+#pragma once
+#include "omath/engines/unreal_engine/constants.hpp"
+#include "omath/projection/camera.hpp"
+#include "traits/camera_trait.hpp"
+
+namespace omath::unreal_engine
+{
+    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait>;
+} // namespace omath::unity_engine

include/omath/engines/unreal_engine/constants.hpp

@@ -0,0 +1,26 @@
+//
+// Created by Vlad on 3/22/2025.
+//
+
+#pragma once
+
+#include <omath/angle.hpp>
+#include <omath/mat.hpp>
+#include <omath/vector3.hpp>
+#include <omath/view_angles.hpp>
+
+namespace omath::unreal_engine
+{
+    constexpr Vector3<float> k_abs_up = {0, 0, 1};
+    constexpr Vector3<float> k_abs_right = {0, 1, 0};
+    constexpr Vector3<float> k_abs_forward = {1, 0, 0};
+
+    using Mat4X4 = Mat<4, 4, float, MatStoreType::ROW_MAJOR>;
+    using Mat3X3 = Mat<4, 4, float, MatStoreType::ROW_MAJOR>;
+    using Mat1X3 = Mat<1, 3, float, MatStoreType::ROW_MAJOR>;
+    using PitchAngle = Angle<float, -90.f, 90.f, AngleFlags::Clamped>;
+    using YawAngle = Angle<float, -180.f, 180.f, AngleFlags::Normalized>;
+    using RollAngle = Angle<float, -180.f, 180.f, AngleFlags::Normalized>;
+
+    using ViewAngles = omath::ViewAngles<PitchAngle, YawAngle, RollAngle>;
+} // namespace omath::unity_engine

include/omath/engines/unreal_engine/formulas.hpp

@@ -0,0 +1,26 @@
+//
+// Created by Vlad on 3/22/2025.
+//
+
+#pragma once
+#include "omath/engines/unreal_engine/constants.hpp"
+
+namespace omath::unreal_engine
+{
+    [[nodiscard]]
+    Vector3<float> forward_vector(const ViewAngles& angles) noexcept;
+
+    [[nodiscard]]
+    Vector3<float> right_vector(const ViewAngles& angles) noexcept;
+
+    [[nodiscard]]
+    Vector3<float> up_vector(const ViewAngles& angles) noexcept;
+
+    [[nodiscard]] Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& 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) noexcept;
+} // namespace omath::unity_engine

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

@@ -0,0 +1,24 @@
+//
+// Created by Vlad on 8/10/2025.
+//
+
+#pragma once
+#include "omath/engines/unreal_engine/formulas.hpp"
+#include "omath/projection/camera.hpp"
+
+namespace omath::unreal_engine
+{
+    class CameraTrait final
+    {
+    public:
+        [[nodiscard]]
+        static ViewAngles calc_look_at_angle(const Vector3<float>& cam_origin, const Vector3<float>& look_at) noexcept;
+
+        [[nodiscard]]
+        static Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept;
+        [[nodiscard]]
+        static Mat4X4 calc_projection_matrix(const projection::FieldOfView& fov, const projection::ViewPort& view_port,
+                                             float near, float far) noexcept;
+    };
+
+} // namespace omath::unity_engine

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

@@ -0,0 +1,78 @@
+//
+// Created by Vlad on 8/6/2025.
+//
+#pragma once
+#include "omath/engines/unreal_engine/formulas.hpp"
+#include "omath/projectile_prediction/projectile.hpp"
+#include "omath/projectile_prediction/target.hpp"
+#include <optional>
+
+namespace omath::unreal_engine
+{
+    class PredEngineTrait final
+    {
+    public:
+        constexpr static Vector3<float> predict_projectile_position(const projectile_prediction::Projectile& projectile,
+                                                                    const float pitch, const float yaw,
+                                                                    const float time, const float gravity) noexcept
+        {
+            auto current_pos = projectile.m_origin
+                               + forward_vector({PitchAngle::from_degrees(-pitch), YawAngle::from_degrees(yaw),
+                                                 RollAngle::from_degrees(0)})
+                                         * projectile.m_launch_speed * time;
+            current_pos.y -= (gravity * projectile.m_gravity_scale) * (time * time) * 0.5f;
+
+            return current_pos;
+        }
+        [[nodiscard]]
+        static constexpr Vector3<float> predict_target_position(const projectile_prediction::Target& target,
+                                                                const float time, const float gravity) noexcept
+        {
+            auto predicted = target.m_origin + target.m_velocity * time;
+
+            if (target.m_is_airborne)
+                predicted.y -= gravity * (time * time) * 0.5f;
+
+            return predicted;
+        }
+        [[nodiscard]]
+        static float calc_vector_2d_distance(const Vector3<float>& delta) noexcept
+        {
+            return std::sqrt(delta.x * delta.x + delta.z * delta.z);
+        }
+
+        [[nodiscard]]
+        constexpr static float get_vector_height_coordinate(const Vector3<float>& vec) noexcept
+        {
+            return vec.y;
+        }
+
+        [[nodiscard]]
+        static Vector3<float> calc_viewpoint_from_angles(const projectile_prediction::Projectile& projectile,
+                                                         Vector3<float> predicted_target_position,
+                                                         const std::optional<float> projectile_pitch) noexcept
+        {
+            const auto delta2d = calc_vector_2d_distance(predicted_target_position - projectile.m_origin);
+            const auto height = delta2d * std::tan(angles::degrees_to_radians(projectile_pitch.value()));
+
+            return {predicted_target_position.x, predicted_target_position.y + height, projectile.m_origin.z};
+        }
+        // Due to specification of maybe_calculate_projectile_launch_pitch_angle, pitch angle must be:
+        // 89 look up, -89 look down
+        [[nodiscard]]
+        static float calc_direct_pitch_angle(const Vector3<float>& origin, const Vector3<float>& view_to) noexcept
+        {
+            const auto distance = origin.distance_to(view_to);
+            const auto delta = view_to - origin;
+
+            return angles::radians_to_degrees(std::asin(delta.y / distance));
+        }
+        [[nodiscard]]
+        static float calc_direct_yaw_angle(const Vector3<float>& origin, const Vector3<float>& view_to) noexcept
+        {
+            const auto delta = view_to - origin;
+
+            return angles::radians_to_degrees(std::atan2(delta.z, delta.x));
+        };
+    };
+} // namespace omath::unity_engine

source/engines/unreal_engine/formulas.cpp

@@ -0,0 +1,49 @@
+//
+// 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
+    {
+        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
+    {
+        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
+    {
+        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
+    {
+        return mat_camera_view<float, MatStoreType::ROW_MAJOR>(forward_vector(angles), -right_vector(angles),
+                                                               up_vector(angles), cam_origin);
+    }
+    Mat4X4 rotation_matrix(const ViewAngles& angles) noexcept
+    {
+        return mat_rotation_axis_x<float, MatStoreType::ROW_MAJOR>(angles.pitch)
+               * mat_rotation_axis_y<float, MatStoreType::ROW_MAJOR>(angles.yaw)
+               * mat_rotation_axis_z<float, 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) noexcept
+    {
+        const float fov_half_tan = std::tan(angles::degrees_to_radians(field_of_view) / 2.f);
+
+        return {
+                {1.f / (aspect_ratio * fov_half_tan), 0, 0, 0},
+                {0, 1.f / (fov_half_tan), 0, 0},
+                {0, 0, (far + near) / (far - near), -(2.f * far * near) / (far - near)},
+                {0, 0, -1.f, 0},
+        };
+    }
+} // namespace omath::unity_engine

source/engines/unreal_engine/traits/camera_trait.cpp

@@ -0,0 +1,27 @@
+//
+// Created by Vlad on 8/11/2025.
+//
+#include "omath/engines/unreal_engine/traits/camera_trait.hpp"
+
+namespace omath::unreal_engine
+{
+
+    ViewAngles CameraTrait::calc_look_at_angle(const Vector3<float>& cam_origin, const Vector3<float>& look_at) noexcept
+    {
+        const auto distance = cam_origin.distance_to(look_at);
+        const auto delta = cam_origin - look_at;
+
+        return {PitchAngle::from_radians(-std::asin(delta.z / distance)),
+                YawAngle::from_radians(std::atan2(delta.x, delta.y)), RollAngle::from_radians(0.f)};
+    }
+    Mat4X4 CameraTrait::calc_view_matrix(const ViewAngles& angles, const Vector3<float>& 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 float far) noexcept
+    {
+        return calc_perspective_projection_matrix(fov.as_degrees(), view_port.aspect_ratio(), near, far);
+    }
+} // namespace omath::unity_engine

tests/engines/unit_test_unreal_engine.cpp

@@ -0,0 +1,3 @@
+//
+// Created by Vlad on 8/25/2025.
+//