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docs/collision/collider_interface.md

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+# `omath::collision::ColliderInterface` — Abstract collider base class
+
+> Header: `omath/collision/collider_interface.hpp`
+> Namespace: `omath::collision`
+> Depends on: `omath/linear_algebra/vector3.hpp`
+
+`ColliderInterface` is the abstract base class for all colliders used by the GJK and EPA algorithms. Any shape that can report its furthest vertex along a given direction can implement this interface and be used for collision detection.
+
+---
+
+## API
+
+```cpp
+namespace omath::collision {
+
+template<class VecType = Vector3<float>>
+class ColliderInterface {
+public:
+    using VectorType = VecType;
+
+    virtual ~ColliderInterface() = default;
+
+    // Return the world-space position of the vertex furthest along `direction`.
+    [[nodiscard]]
+    virtual VectorType find_abs_furthest_vertex_position(
+        const VectorType& direction) const = 0;
+
+    // Get the collider's origin (center / position).
+    [[nodiscard]]
+    virtual const VectorType& get_origin() const = 0;
+
+    // Reposition the collider.
+    virtual void set_origin(const VectorType& new_origin) = 0;
+};
+
+} // namespace omath::collision
+```
+
+---
+
+## Implementing a custom collider
+
+To create a new collider shape, derive from `ColliderInterface` and implement the three pure-virtual methods:
+
+```cpp
+#include "omath/collision/collider_interface.hpp"
+
+class SphereCollider final
+    : public omath::collision::ColliderInterface<omath::Vector3<float>>
+{
+public:
+    SphereCollider(omath::Vector3<float> center, float radius)
+        : m_center(center), m_radius(radius) {}
+
+    [[nodiscard]]
+    omath::Vector3<float> find_abs_furthest_vertex_position(
+        const omath::Vector3<float>& direction) const override
+    {
+        return m_center + direction.normalized() * m_radius;
+    }
+
+    [[nodiscard]]
+    const omath::Vector3<float>& get_origin() const override
+    { return m_center; }
+
+    void set_origin(const omath::Vector3<float>& new_origin) override
+    { m_center = new_origin; }
+
+private:
+    omath::Vector3<float> m_center;
+    float m_radius;
+};
+```
+
+---
+
+## Notes
+
+* **Template parameter**: The default vector type is `Vector3<float>`, but any vector type with a `dot()` method can be used.
+* **GJK/EPA compatibility**: Both `GjkAlgorithm` and `EpaAlgorithm` accept any type satisfying the `ColliderInterface` contract through their template parameters.
+
+---
+
+## See also
+
+* [GJK Algorithm](gjk_algorithm.md) — collision detection using GJK.
+* [EPA Algorithm](epa_algorithm.md) — penetration depth via EPA.
+* [Mesh Collider](mesh_collider.md) — concrete collider wrapping a `Mesh`.
+* [Simplex](simplex.md) — simplex data structure used by GJK/EPA.
+
+---
+
+*Last updated: Feb 2026*