Add documentation for collision detection and mesh classes

Co-authored-by: orange-cpp <59374393+orange-cpp@users.noreply.github.com>
2026-02-13 07:03:25 +00:00 · 2025-11-13 15:19:36 +00:00
parent d118e88f6b
commit 190a8bf91e
11 changed files with 2482 additions and 0 deletions
--- a/docs/3d_primitives/mesh.md
+++ b/docs/3d_primitives/mesh.md
@@ -0,0 +1,465 @@
+# `omath::primitives::Mesh` — 3D mesh with transformation support
+
+> Header: `omath/3d_primitives/mesh.hpp`
+> Namespace: `omath::primitives`
+> Depends on: `omath::Vector3<T>`, `omath::Mat4X4`, `omath::Triangle<Vector3<T>>`
+> Purpose: represent and transform 3D meshes in different engine coordinate systems
+
+---
+
+## Overview
+
+`Mesh` represents a 3D polygonal mesh with vertex data and transformation capabilities. It stores:
+* **Vertex buffer (VBO)** — array of 3D vertex positions
+* **Index buffer (VAO)** — array of triangular faces (indices into VBO)
+* **Transformation** — position, rotation, and scale with caching
+
+The mesh supports transformation from local space to world space using engine-specific coordinate systems through the `MeshTrait` template parameter.
+
+---
+
+## Template Declaration
+
+```cpp
+template<class Mat4X4, class RotationAngles, class MeshTypeTrait, class Type = float>
+class Mesh final;
+```
+
+### Template Parameters
+
+* `Mat4X4` — Matrix type for transformations (typically `omath::Mat4X4`)
+* `RotationAngles` — Rotation representation (e.g., `ViewAngles` with pitch/yaw/roll)
+* `MeshTypeTrait` — Engine-specific transformation trait (see [Engine Traits](#engine-traits))
+* `Type` — Scalar type for vertex coordinates (default `float`)
+
+---
+
+## Type Aliases
+
+```cpp
+using NumericType = Type;
+```
+
+Common engine-specific aliases:
+
+```cpp
+// Source Engine
+using Mesh = omath::primitives::Mesh<Mat4X4, ViewAngles, MeshTrait, float>;
+
+// Unity Engine  
+using Mesh = omath::primitives::Mesh<Mat4X4, ViewAngles, MeshTrait, float>;
+
+// Unreal Engine
+using Mesh = omath::primitives::Mesh<Mat4X4, ViewAngles, MeshTrait, float>;
+
+// Frostbite, IW Engine, OpenGL similar...
+```
+
+Use the pre-defined type aliases in engine namespaces:
+```cpp
+using namespace omath::source_engine;
+Mesh my_mesh = /* ... */;  // Uses SourceEngine::Mesh
+```
+
+---
+
+## Data Members
+
+### Vertex Data
+
+```cpp
+std::vector<Vector3<NumericType>> m_vertex_buffer;        // VBO: vertex positions
+std::vector<Vector3<std::size_t>> m_vertex_array_object;  // VAO: face indices
+```
+
+* `m_vertex_buffer` — array of vertex positions in **local space**
+* `m_vertex_array_object` — array of triangular faces, each containing 3 indices into `m_vertex_buffer`
+
+**Public access**: These members are public for direct manipulation when needed.
+
+---
+
+## Constructor
+
+```cpp
+Mesh(std::vector<Vector3<NumericType>> vbo,
+     std::vector<Vector3<std::size_t>> vao,
+     Vector3<NumericType> scale = {1, 1, 1});
+```
+
+Creates a mesh from vertex and index data.
+
+**Parameters**:
+* `vbo` — vertex buffer (moved into mesh)
+* `vao` — index buffer / vertex array object (moved into mesh)
+* `scale` — initial scale (default `{1, 1, 1}`)
+
+**Example**:
+```cpp
+std::vector<Vector3<float>> vertices = {
+    {0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}
+};
+
+std::vector<Vector3<std::size_t>> faces = {
+    {0, 1, 2},  // Triangle 1
+    {0, 1, 3},  // Triangle 2
+    {0, 2, 3},  // Triangle 3
+    {1, 2, 3}   // Triangle 4
+};
+
+using namespace omath::source_engine;
+Mesh tetrahedron(std::move(vertices), std::move(faces));
+```
+
+---
+
+## Transformation Methods
+
+### Setting Transform Components
+
+```cpp
+void set_origin(const Vector3<NumericType>& new_origin);
+void set_scale(const Vector3<NumericType>& new_scale);
+void set_rotation(const RotationAngles& new_rotation_angles);
+```
+
+Update the mesh's transformation. **Side effect**: invalidates the cached transformation matrix, which will be recomputed on the next `get_to_world_matrix()` call.
+
+**Example**:
+```cpp
+mesh.set_origin({10, 0, 5});
+mesh.set_scale({2, 2, 2});
+
+ViewAngles angles;
+angles.pitch = PitchAngle::from_degrees(45.0f);
+angles.yaw = YawAngle::from_degrees(30.0f);
+mesh.set_rotation(angles);
+```
+
+### Getting Transform Components
+
+```cpp
+[[nodiscard]] const Vector3<NumericType>& get_origin() const;
+[[nodiscard]] const Vector3<NumericType>& get_scale() const;
+[[nodiscard]] const RotationAngles& get_rotation_angles() const;
+```
+
+Retrieve current transformation components.
+
+### Transformation Matrix
+
+```cpp
+[[nodiscard]] const Mat4X4& get_to_world_matrix() const;
+```
+
+Returns the cached local-to-world transformation matrix. The matrix is computed lazily on first access after any transformation change:
+
+```
+M = Translation(origin) × Scale(scale) × Rotation(angles)
+```
+
+The rotation matrix is computed using the engine-specific `MeshTrait::rotation_matrix()` method.
+
+**Caching**: The matrix is stored in a `mutable std::optional` and recomputed only when invalidated by `set_*` methods.
+
+---
+
+## Vertex Transformation
+
+### `vertex_to_world_space`
+
+```cpp
+[[nodiscard]]
+Vector3<float> vertex_to_world_space(const Vector3<float>& vertex) const;
+```
+
+Transforms a vertex from local space to world space by multiplying with the transformation matrix.
+
+**Algorithm**:
+1. Convert vertex to column matrix: `[x, y, z, 1]ᵀ`
+2. Multiply by transformation matrix: `M × vertex`
+3. Extract the resulting 3D position
+
+**Usage**:
+```cpp
+Vector3<float> local_vertex{1, 0, 0};
+Vector3<float> world_vertex = mesh.vertex_to_world_space(local_vertex);
+```
+
+**Note**: This is used internally by `MeshCollider` to provide world-space support functions for GJK/EPA.
+
+---
+
+## Face Transformation
+
+### `make_face_in_world_space`
+
+```cpp
+[[nodiscard]]
+Triangle<Vector3<float>> make_face_in_world_space(
+    const std::vector<Vector3<std::size_t>>::const_iterator vao_iterator
+) const;
+```
+
+Creates a triangle in world space from a face index iterator.
+
+**Parameters**:
+* `vao_iterator` — iterator to an element in `m_vertex_array_object`
+
+**Returns**: `Triangle` with all three vertices transformed to world space.
+
+**Example**:
+```cpp
+for (auto it = mesh.m_vertex_array_object.begin(); 
+     it != mesh.m_vertex_array_object.end(); 
+     ++it) {
+    Triangle<Vector3<float>> world_triangle = mesh.make_face_in_world_space(it);
+    // Render or process the triangle
+}
+```
+
+---
+
+## Usage Examples
+
+### Creating a Box Mesh
+
+```cpp
+using namespace omath::source_engine;
+
+std::vector<Vector3<float>> box_vbo = {
+    // Bottom face
+    {-0.5f, -0.5f, 0.0f}, { 0.5f, -0.5f, 0.0f},
+    { 0.5f,  0.5f, 0.0f}, {-0.5f,  0.5f, 0.0f},
+    // Top face  
+    {-0.5f, -0.5f, 1.0f}, { 0.5f, -0.5f, 1.0f},
+    { 0.5f,  0.5f, 1.0f}, {-0.5f,  0.5f, 1.0f}
+};
+
+std::vector<Vector3<std::size_t>> box_vao = {
+    // Bottom
+    {0, 1, 2}, {0, 2, 3},
+    // Top
+    {4, 6, 5}, {4, 7, 6},
+    // Sides
+    {0, 4, 5}, {0, 5, 1},
+    {1, 5, 6}, {1, 6, 2},
+    {2, 6, 7}, {2, 7, 3},
+    {3, 7, 4}, {3, 4, 0}
+};
+
+Mesh box(std::move(box_vbo), std::move(box_vao));
+box.set_origin({0, 0, 50});
+box.set_scale({10, 10, 10});
+```
+
+### Transforming Mesh Over Time
+
+```cpp
+void update_mesh(Mesh& mesh, float delta_time) {
+    // Rotate mesh
+    auto rotation = mesh.get_rotation_angles();
+    rotation.yaw = YawAngle::from_degrees(
+        rotation.yaw.as_degrees() + 45.0f * delta_time
+    );
+    mesh.set_rotation(rotation);
+    
+    // Oscillate position
+    auto origin = mesh.get_origin();
+    origin.z = 50.0f + 10.0f * std::sin(current_time * 2.0f);
+    mesh.set_origin(origin);
+}
+```
+
+### Collision Detection
+
+```cpp
+using namespace omath::collision;
+using namespace omath::source_engine;
+
+Mesh mesh_a(vbo_a, vao_a);
+mesh_a.set_origin({0, 0, 0});
+
+Mesh mesh_b(vbo_b, vao_b);
+mesh_b.set_origin({5, 0, 0});
+
+MeshCollider collider_a(std::move(mesh_a));
+MeshCollider collider_b(std::move(mesh_b));
+
+auto result = GjkAlgorithm<MeshCollider<Mesh>>::check_collision(
+    collider_a, collider_b
+);
+```
+
+### Rendering Transformed Triangles
+
+```cpp
+void render_mesh(const Mesh& mesh) {
+    for (auto it = mesh.m_vertex_array_object.begin();
+         it != mesh.m_vertex_array_object.end();
+         ++it) {
+        
+        Triangle<Vector3<float>> tri = mesh.make_face_in_world_space(it);
+        
+        // Draw triangle with your renderer
+        draw_triangle(tri.m_vertex1, tri.m_vertex2, tri.m_vertex3);
+    }
+}
+```
+
+---
+
+## Engine Traits
+
+Each game engine has a corresponding `MeshTrait` that provides the `rotation_matrix` function:
+
+```cpp
+class MeshTrait final {
+public:
+    [[nodiscard]]
+    static Mat4X4 rotation_matrix(const ViewAngles& rotation);
+};
+```
+
+### Available Engines
+
+| Engine | Namespace | Header |
+|--------|-----------|--------|
+| Source Engine | `omath::source_engine` | `engines/source_engine/mesh.hpp` |
+| Unity | `omath::unity_engine` | `engines/unity_engine/mesh.hpp` |
+| Unreal | `omath::unreal_engine` | `engines/unreal_engine/mesh.hpp` |
+| Frostbite | `omath::frostbite_engine` | `engines/frostbite_engine/mesh.hpp` |
+| IW Engine | `omath::iw_engine` | `engines/iw_engine/mesh.hpp` |
+| OpenGL | `omath::opengl_engine` | `engines/opengl_engine/mesh.hpp` |
+
+**Example** (Source Engine):
+```cpp
+using namespace omath::source_engine;
+
+// Uses source_engine::MeshTrait automatically
+Mesh my_mesh(vertices, indices);
+```
+
+See [MeshTrait Documentation](#mesh-trait-documentation) for engine-specific details.
+
+---
+
+## Performance Considerations
+
+### Matrix Caching
+
+The transformation matrix is computed lazily and cached:
+* **First access**: O(matrix multiply) ≈ 64 float operations
+* **Subsequent access**: O(1) — returns cached matrix
+* **Cache invalidation**: Any `set_*` call invalidates the cache
+
+**Best practice**: Batch transformation updates before accessing the matrix:
+```cpp
+// Good: single matrix recomputation
+mesh.set_origin(new_origin);
+mesh.set_rotation(new_rotation);
+mesh.set_scale(new_scale);
+auto matrix = mesh.get_to_world_matrix();  // Computes once
+
+// Bad: three matrix recomputations
+mesh.set_origin(new_origin);
+auto m1 = mesh.get_to_world_matrix();  // Compute
+mesh.set_rotation(new_rotation);
+auto m2 = mesh.get_to_world_matrix();  // Compute again
+mesh.set_scale(new_scale);
+auto m3 = mesh.get_to_world_matrix();  // Compute again
+```
+
+### Memory Layout
+
+* **VBO**: Contiguous `std::vector` for cache-friendly access
+* **VAO**: Contiguous indices for cache-friendly face iteration
+* **Matrix**: Cached in `std::optional` (no allocation)
+
+### Transformation Cost
+
+* `vertex_to_world_space`: ~15-20 FLOPs per vertex (4×4 matrix multiply)
+* `make_face_in_world_space`: ~60 FLOPs (3 vertices)
+
+For high-frequency transformations, consider:
+* Caching transformed vertices if the mesh doesn't change
+* Using simpler proxy geometry for collision
+* Batching transformations
+
+---
+
+## Coordinate System Details
+
+Different engines use different coordinate systems:
+
+| Engine | Up Axis | Forward Axis | Handedness |
+|--------|---------|--------------|------------|
+| Source | +Z | +Y | Right |
+| Unity | +Y | +Z | Left |
+| Unreal | +Z | +X | Left |
+| Frostbite | +Y | +Z | Right |
+| IW Engine | +Z | +Y | Right |
+| OpenGL | +Y | +Z | Right |
+
+The `MeshTrait::rotation_matrix` function accounts for these differences, ensuring correct transformations in each engine's space.
+
+---
+
+## Limitations & Edge Cases
+
+### Empty Mesh
+
+A mesh with no vertices or faces is valid but not useful:
+```cpp
+Mesh empty_mesh({}, {});  // Valid but meaningless
+```
+
+For collision detection, ensure `m_vertex_buffer` is non-empty.
+
+### Index Validity
+
+No bounds checking is performed on indices in `m_vertex_array_object`. Ensure all indices are valid:
+```cpp
+assert(face.x < mesh.m_vertex_buffer.size());
+assert(face.y < mesh.m_vertex_buffer.size());
+assert(face.z < mesh.m_vertex_buffer.size());
+```
+
+### Degenerate Triangles
+
+Faces with duplicate indices or collinear vertices will produce degenerate triangles. The mesh doesn't validate this; users must ensure clean geometry.
+
+### Thread Safety
+
+* **Read-only**: Safe to read from multiple threads (including const methods)
+* **Modification**: Not thread-safe; synchronize `set_*` calls externally
+* **Matrix cache**: Uses `mutable` member; not thread-safe even for const methods
+
+---
+
+## See Also
+
+- [MeshCollider Documentation](../collision/mesh_collider.md) - Collision wrapper for meshes
+- [GJK Algorithm Documentation](../collision/gjk_algorithm.md) - Uses mesh for collision detection
+- [EPA Algorithm Documentation](../collision/epa_algorithm.md) - Penetration depth with meshes
+- [Triangle Documentation](../linear_algebra/triangle.md) - Triangle primitive
+- [Mat4X4 Documentation](../linear_algebra/mat.md) - Transformation matrices
+- [Box Documentation](box.md) - Box primitive
+- [Plane Documentation](plane.md) - Plane primitive
+
+---
+
+## Mesh Trait Documentation
+
+For engine-specific `MeshTrait` details, see:
+
+- [Source Engine MeshTrait](../engines/source_engine/mesh_trait.md)
+- [Unity Engine MeshTrait](../engines/unity_engine/mesh_trait.md)
+- [Unreal Engine MeshTrait](../engines/unreal_engine/mesh_trait.md)
+- [Frostbite Engine MeshTrait](../engines/frostbite/mesh_trait.md)
+- [IW Engine MeshTrait](../engines/iw_engine/mesh_trait.md)
+- [OpenGL Engine MeshTrait](../engines/opengl_engine/mesh_trait.md)
+
+---
+
+*Last updated: 13 Nov 2025*