api: "YAML JSON TOON Database"
version: 1.0.0
format: toon
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: 3
  created_at: 1781275786
  updated_at: 1781275786
data:
  structures
    [7]{name,dimensions,query_time,space,description,operations,use_cases,notes}:
      "k-d Tree (k-dimensional tree)","Any k","O(n^(1-1/k)) average for nearest neighbor",O(n),"Binary tree alternating split axis at each level; partitions k-dimensional space",["nearest neighbor","range search","k-nearest neighbors"],["3D graphics (ray tracing acceleration)","Point cloud processing","Recommendation systems (k-NN)","Robotics path planning"],"Not suitable for high dimensions (curse of dimensionality); best for k ≤ 20"
      R-Tree,"2D/3D spatial","O(log n) average",O(n),"Balanced tree grouping nearby objects with minimum bounding rectangles (MBRs); optimized for disk storage",["range search","nearest neighbor","spatial join","window query"],["GIS systems (PostGIS, SpatiaLite)","Location-based services","Game engines (collision detection)","Database spatial indexes"],"Variants: R*-tree (better split strategy), R+-tree (no overlap), STR-packed (bulk loading)"
      Quadtree,2D,"O(log n) average",O(n),"Recursive subdivision of 2D space into 4 quadrants; leaf nodes contain points or regions",["point query","range search","nearest neighbor","region query"],["2D game collision detection","Image compression (quadtree encoding)","Mesh generation","Sparse matrix storage"],"Point quadtree (stores points) vs region quadtree (stores areas); unbalanced without care"
      Octree,3D,"O(log n) average",O(n),"3D extension of quadtree; recursively subdivides space into 8 octants",["point query","range search","frustum culling","collision detection"],["3D game engines (Unreal, Unity)","Point cloud processing (LiDAR)","Voxel engines (Minecraft-like)","3D mesh simplification"],"Essential for 3D spatial partitioning; often combined with frustum culling for rendering"
      "Grid File",2D/low-dimensional,"O(1) for exact match, O(k) for range","O(n + grid_size)","Uniform grid overlaying space; each cell points to objects within it",["point query","range search","nearest neighbor"],["Particle systems","Molecular dynamics","Simple collision detection","Real-time physics engines"],"Simple but suffers from curse of dimensionality; cell size critically affects performance"
      "Z-Order Curve (Morton Order)","Any k","O(log n) with B-tree",O(n),"Maps multi-dimensional points to 1D by interleaving binary representations; preserves locality",["range search via B-tree on Z-values","nearest neighbor"],["Geohashing (geographic indexing)","GPU spatial sorting","Database indexing (HBase, Accumulo)","Texture memory layout"],"Can use standard B-tree/B+-tree on Z-values; locality preservation not as good as Hilbert curve"
      "Hilbert Curve","2D (extendable)","O(log n) with B-tree",O(n),"Space-filling curve with better locality preservation than Z-order; maps 2D to 1D continuously",["range search","nearest neighbor via 1D index"],["Image processing","Database indexing (better locality than Z-order)","Distributed hash tables","Cache-oblivious algorithms"],"More complex to compute than Z-order but significantly better spatial locality; used in Google S2 Geometry"