api: YAML JSON TOON Database
version: 1.0.0
format: toon
dataset:
  id: 2900
  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)."
  summary: "Data structures for multidimensional and geographic data: k-d trees, R-trees, quadtrees, octrees, grid files and the Z-order and Hilbert space-filling curves, each with dimensions, query time, space, operations, uses and notes."
  use_when[2]: "You need nearest-neighbor, range or collision queries in two or more dimensions.","You are choosing a spatial index for a map, a game or a database."
  caveats[2]: Performance degrades in high dimensions; many structures work well only in two or three.,Choice depends on whether data is static or changes often.
  related[4]: tree-data-structures,geometric-formulas,complexity-analysis,nosql-databases-overview
  entry_count: 7
  fields[8]{section,field,type,example}:
    structures,name,string,k-d Tree (k-dimensional tree)
    structures,dimensions,string,Any k
    structures,query_time,string,O(n^(1-1/k)) average for nearest neighbor
    structures,space,string,O(n)
    structures,description,string,Binary tree alternating split axis at each leve…
    structures,operations,array,"[3 items]"
    structures,use_cases,array,"[4 items]"
    structures,notes,string,Not suitable for high dimensions (curse of dime…
  category: Data Structures
  category_slug: data-structures
  tags: "spatial,kd-tree,rtree,quadtree,octree,space-filling-curves,geospatial,nearest-neighbor"
  view_count: 46
  created_at: 1778695229
  updated_at: 1778695229
data:
  structures[7]:
    - 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[3]: nearest neighbor,range search,k-nearest neighbors
      use_cases[4]: 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[4]: range search,nearest neighbor,spatial join,window query
      use_cases[4]: "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[4]: point query,range search,nearest neighbor,region query
      use_cases[4]: 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[4]: point query,range search,frustum culling,collision detection
      use_cases[4]: "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[3]: point query,range search,nearest neighbor
      use_cases[4]: 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[2]: range search via B-tree on Z-values,nearest neighbor
      use_cases[4]: 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[2]: range search,nearest neighbor via 1D index
      use_cases[4]: 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