# reynard-algorithms Documentation

> Comprehensive documentation for the reynard-algorithms package

This documentation provides detailed information about all algorithms, data structures, and mathematical foundations included in the reynard-algorithms package.

## 📚 Documentation Structure

### [Mathematical Theory](./mathematical-theory/)

- [Union-Find Theory](./mathematical-theory/union-find.md)
- [Bloom Filter Theory](./mathematical-theory/bloom-filter.md)
- [Priority Queue Theory](./mathematical-theory/priority-queue.md)
- [LRU Cache Theory](./mathematical-theory/lru-cache.md)
- [Fenwick Tree Theory](./mathematical-theory/fenwick-tree.md)
- [Interval Tree Theory](./mathematical-theory/interval-tree.md)
- [Segment Tree Theory](./mathematical-theory/segment-tree.md)
- [Trie Theory](./mathematical-theory/trie.md)

### [Data Structures](./algorithms/data-structures/)

- [Union-Find](./algorithms/data-structures/union-find.md)
- [Bloom Filter](./algorithms/data-structures/bloom-filter.md)
- [Priority Queue](./algorithms/data-structures/priority-queue.md)
- [LRU Cache](./algorithms/data-structures/lru-cache.md)
- [Fenwick Tree](./algorithms/data-structures/fenwick-tree.md)
- [Interval Tree](./algorithms/data-structures/interval-tree.md)
- [Segment Tree](./algorithms/data-structures/segment-tree.md)
- [Trie](./algorithms/data-structures/trie.md)

### [Spatial Structures](./algorithms/spatial-structures/)

- [Spatial Hashing](./algorithms/spatial-structures/spatial-hashing.md)
- [Quadtree](./algorithms/spatial-structures/quadtree.md)
- [R-Tree](./algorithms/spatial-structures/r-tree.md)
- [K-d Tree](./algorithms/spatial-structures/kdtree.md)
- [Octree](./algorithms/spatial-structures/octree.md)
- [BVH](./algorithms/spatial-structures/bvh.md)

### [Geometry Operations](./algorithms/geometry/)

- [Basic Geometry](./algorithms/geometry/basic-geometry.md)
- [Bresenham's Line](./algorithms/geometry/bresenham.md)
- [Delaunay Triangulation](./algorithms/geometry/delaunay.md)
- [Convex Hull](./algorithms/geometry/convex-hull.md)
- [Simplex Noise](./algorithms/geometry/simplex-noise.md)
- [Marching Squares](./algorithms/geometry/marching-squares.md)
- [Poisson Disk Sampling](./algorithms/geometry/poisson-disk.md)
- [Wave Function Collapse](./algorithms/geometry/wave-function-collapse.md)
- [Voronoi Diagram](./algorithms/geometry/voronoi.md)
- [Polygon Clipping](./algorithms/geometry/polygon-clipping.md)
- [Line Segment Intersection](./algorithms/geometry/line-intersection.md)
- [OBB](./algorithms/geometry/obb.md)
- [Minimum Bounding Box](./algorithms/geometry/min-bounding-box.md)

### [Collision Detection](./algorithms/collision-detection/)

- [AABB Collision](./algorithms/collision-detection/aabb.md)
- [SAT Collision](./algorithms/collision-detection/sat.md)
- [Sweep and Prune](./algorithms/collision-detection/sweep-and-prune.md)

### [Pathfinding](./algorithms/pathfinding/)

- [A* Pathfinding](./algorithms/pathfinding/astar.md)
- [Jump Point Search](./algorithms/pathfinding/jps.md)
- [Theta*](./algorithms/pathfinding/theta-star.md)
- [Flow Field](./algorithms/pathfinding/flow-field.md)
- [HPA*](./algorithms/pathfinding/hpa-star.md)

### [Examples](./examples/)

- [Basic Usage](./examples/basic-usage.md)
- [Game Engine Integration](./examples/game-engine-integration.md)
- [Performance Optimization](./examples/performance-optimization.md)

### [Performance Analysis](./performance/)

- [Benchmarking Guide](./performance/benchmarking.md)
- [Memory Management](./performance/memory-management.md)
- [Optimization Strategies](./performance/optimization-strategies.md)

## 🚀 Quick Start

For a quick introduction to using the algorithms, see the [Basic Usage Examples](./examples/basic-usage.md).

## 📖 Mathematical Foundations

All algorithms in this package are built on solid mathematical foundations. Each algorithm includes:

- **Mathematical Theory**: The underlying mathematical principles
- **Complexity Analysis**: Time and space complexity with proofs
- **Implementation Details**: How mathematical concepts translate to code
- **Performance Analysis**: Real-world performance characteristics

## 🔧 API Reference

For detailed API documentation, see the individual algorithm pages or refer to the TypeScript definitions in the source code.

## 📊 Performance

This package includes comprehensive performance monitoring and optimization tools. See the [Performance Analysis](./performance/) section for detailed benchmarks and optimization strategies.