{
    "api": "YAML JSON TOON Database",
    "version": "1.0.0",
    "format": "json",
    "dataset": {
        "id": 59,
        "slug": "spatial-data-structures",
        "title": "Spatial Data Structures",
        "description": "Spatial indexing structures for multi-dimensional data: k-d trees, R-trees, quadtrees, octrees, grid files, and space-filling curves (Z-order, Hilbert).",
        "category": "Data Structures",
        "category_slug": "data-structures",
        "tags": "spatial,kd-tree,rtree,quadtree,octree,space-filling-curves,geospatial,nearest-neighbor",
        "view_count": 0,
        "created_at": 1778695229,
        "updated_at": 1778695229
    },
    "data": {
        "structures": [
            {"name": "k-d Tree (k-dimensional tree)", "dimensions": "Any k", "query_time": "O(n^(1-1/k)) average for nearest neighbor", "space": "O(n)", "description": "Binary tree alternating split axis at each level; partitions k-dimensional space", "operations": ["nearest neighbor", "range search", "k-nearest neighbors"], "use_cases": ["3D graphics (ray tracing acceleration)", "Point cloud processing", "Recommendation systems (k-NN)", "Robotics path planning"], "notes": "Not suitable for high dimensions (curse of dimensionality); best for k ≤ 20"},
            {"name": "R-Tree", "dimensions": "2D/3D spatial", "query_time": "O(log n) average", "space": "O(n)", "description": "Balanced tree grouping nearby objects with minimum bounding rectangles (MBRs); optimized for disk storage", "operations": ["range search", "nearest neighbor", "spatial join", "window query"], "use_cases": ["GIS systems (PostGIS, SpatiaLite)", "Location-based services", "Game engines (collision detection)", "Database spatial indexes"], "notes": "Variants: R*-tree (better split strategy), R+-tree (no overlap), STR-packed (bulk loading)"},
            {"name": "Quadtree", "dimensions": "2D", "query_time": "O(log n) average", "space": "O(n)", "description": "Recursive subdivision of 2D space into 4 quadrants; leaf nodes contain points or regions", "operations": ["point query", "range search", "nearest neighbor", "region query"], "use_cases": ["2D game collision detection", "Image compression (quadtree encoding)", "Mesh generation", "Sparse matrix storage"], "notes": "Point quadtree (stores points) vs region quadtree (stores areas); unbalanced without care"},
            {"name": "Octree", "dimensions": "3D", "query_time": "O(log n) average", "space": "O(n)", "description": "3D extension of quadtree; recursively subdivides space into 8 octants", "operations": ["point query", "range search", "frustum culling", "collision detection"], "use_cases": ["3D game engines (Unreal, Unity)", "Point cloud processing (LiDAR)", "Voxel engines (Minecraft-like)", "3D mesh simplification"], "notes": "Essential for 3D spatial partitioning; often combined with frustum culling for rendering"},
            {"name": "Grid File", "dimensions": "2D/low-dimensional", "query_time": "O(1) for exact match, O(k) for range", "space": "O(n + grid_size)", "description": "Uniform grid overlaying space; each cell points to objects within it", "operations": ["point query", "range search", "nearest neighbor"], "use_cases": ["Particle systems", "Molecular dynamics", "Simple collision detection", "Real-time physics engines"], "notes": "Simple but suffers from curse of dimensionality; cell size critically affects performance"},
            {"name": "Z-Order Curve (Morton Order)", "dimensions": "Any k", "query_time": "O(log n) with B-tree", "space": "O(n)", "description": "Maps multi-dimensional points to 1D by interleaving binary representations; preserves locality", "operations": ["range search via B-tree on Z-values", "nearest neighbor"], "use_cases": ["Geohashing (geographic indexing)", "GPU spatial sorting", "Database indexing (HBase, Accumulo)", "Texture memory layout"], "notes": "Can use standard B-tree/B+-tree on Z-values; locality preservation not as good as Hilbert curve"},
            {"name": "Hilbert Curve", "dimensions": "2D (extendable)", "query_time": "O(log n) with B-tree", "space": "O(n)", "description": "Space-filling curve with better locality preservation than Z-order; maps 2D to 1D continuously", "operations": ["range search", "nearest neighbor via 1D index"], "use_cases": ["Image processing", "Database indexing (better locality than Z-order)", "Distributed hash tables", "Cache-oblivious algorithms"], "notes": "More complex to compute than Z-order but significantly better spatial locality; used in Google S2 Geometry"}
        ]
    }
}