api: YAML JSON TOON Database
version: 1.0.0
format: yaml
dataset:
  id: 490
  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: 2
  created_at: 1781275786
  updated_at: 1781275786
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