Feature/gjk algorithm

include/omath/3d_primitives/mesh.hpp

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+//
+// Created by Vladislav on 09.11.2025.
+//
+#pragma once
+#include "omath/linear_algebra/triangle.hpp"
+#include <omath/linear_algebra/mat.hpp>
+#include <omath/linear_algebra/vector3.hpp>
+#include <utility>
+#include <vector>
+
+namespace omath::primitives
+{
+    template<class Mat4X4, class RotationAngles, class MeshTypeTrait, class Type = float>
+    class Mesh final
+    {
+    public:
+        using NumericType = Type;
+
+    private:
+        using Vbo = std::vector<Vector3<NumericType>>;
+        using Vao = std::vector<Vector3<std::size_t>>;
+
+    public:
+        Vbo m_vertex_buffer;
+        Vao m_vertex_array_object;
+
+        Mesh(Vbo vbo, Vao vao, const Vector3<NumericType> scale = {1, 1, 1,})
+            : m_vertex_buffer(std::move(vbo)), m_vertex_array_object(std::move(vao)), m_scale(scale)
+        {
+        }
+        void set_origin(const Vector3<NumericType>& new_origin)
+        {
+            m_origin = new_origin;
+            m_to_world_matrix = std::nullopt;
+        }
+
+        void set_scale(const Vector3<NumericType>& new_scale)
+        {
+            m_scale = new_scale;
+            m_to_world_matrix = std::nullopt;
+        }
+
+        void set_rotation(const RotationAngles& new_rotation_angles)
+        {
+            m_rotation_angles = new_rotation_angles;
+            m_to_world_matrix = std::nullopt;
+        }
+
+        [[nodiscard]]
+        const Vector3<NumericType>& get_origin() const
+        {
+            return m_origin;
+        }
+
+        [[nodiscard]]
+        const Vector3<NumericType>& get_scale() const
+        {
+            return m_scale;
+        }
+
+        [[nodiscard]]
+        const RotationAngles& get_rotation_angles() const
+        {
+            return m_rotation_angles;
+        }
+
+        [[nodiscard]]
+        const Mat4X4& get_to_world_matrix() const
+        {
+            if (m_to_world_matrix)
+                return m_to_world_matrix.value();
+            m_to_world_matrix =
+                    mat_translation(m_origin) * mat_scale(m_scale) * MeshTypeTrait::rotation_matrix(m_rotation_angles);
+
+            return m_to_world_matrix.value();
+        }
+
+        [[nodiscard]]
+        Vector3<float> vertex_to_world_space(const Vector3<float>& vertex) const
+        {
+            auto abs_vec = get_to_world_matrix() * mat_column_from_vector(vertex);
+
+            return {abs_vec.at(0, 0), abs_vec.at(1, 0), abs_vec.at(2, 0)};
+        }
+
+        [[nodiscard]]
+        Triangle<Vector3<float>> make_face_in_world_space(const Vao::const_iterator vao_iterator) const
+        {
+            return {vertex_to_world_space(m_vertex_buffer.at(vao_iterator->x)),
+                    vertex_to_world_space(m_vertex_buffer.at(vao_iterator->y)),
+                    vertex_to_world_space(m_vertex_buffer.at(vao_iterator->z))};
+        }
+
+    private:
+        Vector3<NumericType> m_origin;
+        Vector3<NumericType> m_scale;
+
+        RotationAngles m_rotation_angles;
+
+        mutable std::optional<Mat4X4> m_to_world_matrix;
+    };
+} // namespace omath::primitives

include/omath/collision/gjk_algorithm.hpp

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+//
+// Created by Vlad on 11/9/2025.
+//
+
+#pragma once
+#include "mesh_collider.hpp"
+#include "omath/linear_algebra/vector3.hpp"
+#include "simplex.hpp"
+
+namespace omath::collision
+{
+    template<class ColliderType>
+    class GjkAlgorithm final
+    {
+    public:
+        [[nodiscard]]
+        static ColliderType::VertexType find_support_vertex(const ColliderType& collider_a,
+                                                            const ColliderType& collider_b,
+                                                            const ColliderType::VertexType& direction)
+        {
+            return collider_a.find_abs_furthest_vertex(direction) - collider_b.find_abs_furthest_vertex(-direction);
+        }
+
+        [[nodiscard]]
+        static bool is_collide(const ColliderType& collider_a, const ColliderType& collider_b)
+        {
+            // Get initial support point in any direction
+            auto support = find_support_vertex(collider_a, collider_b, {1, 0, 0});
+
+            Simplex<typename ColliderType::VertexType> simplex;
+            simplex.push_front(support);
+
+            auto direction = -support;
+
+            while (true)
+            {
+                support = find_support_vertex(collider_a, collider_b, direction);
+
+                if (support.dot(direction) <= 0.f)
+                    return false;
+
+                simplex.push_front(support);
+
+                if (simplex.handle(direction))
+                    return true;
+            }
+        }
+    };
+} // namespace omath::collision

include/omath/collision/mesh_collider.hpp

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+//
+// Created by Vlad on 11/9/2025.
+//
+
+#pragma once
+#include "omath/linear_algebra/vector3.hpp"
+
+namespace omath::collision
+{
+    template<class MeshType>
+    class MeshCollider
+    {
+    public:
+        using NumericType = typename MeshType::NumericType;
+
+        using VertexType = Vector3<NumericType>;
+        explicit MeshCollider(MeshType mesh): m_mesh(std::move(mesh))
+        {
+        }
+
+        [[nodiscard]]
+        const Vector3<float>& find_furthest_vertex(const Vector3<float>& direction) const
+        {
+            return *std::ranges::max_element(m_mesh.m_vertex_buffer, [&direction](const auto& first, const auto& second)
+                                             { return first.dot(direction) < second.dot(direction); });
+        }
+
+        [[nodiscard]]
+        Vector3<float> find_abs_furthest_vertex(const Vector3<float>& direction) const
+        {
+            return m_mesh.vertex_to_world_space(find_furthest_vertex(direction));
+        }
+
+    private:
+        MeshType m_mesh;
+    };
+} // namespace omath::collision