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RegionTrees.jl: Quadtrees, Octrees, and their N-Dimensional Cousins

This Julia package is a lightweight framework for defining N-Dimensional region trees. In 2D, these are called region quadtrees, and in 3D they are typically referred to as octrees. A region tree is a simple data structure used to describe some kind of spatial data with varying resolution. Each element in the tree can be a leaf, representing an N-dimensional rectangle of space, or a node which is divided exactly in half along each axis into 2^N children. In addition, each element in a RegionTrees.jl tree can carry an arbitrary data payload. This makes it easy to use RegionTrees to approximate functions or describe other interesting spatial data.

Features

• Lightweight code with few dependencies (only StaticArrays.jl and Iterators.jl are required)
• Optimized for speed and for few memory allocations
  • Liberal use of @generated functions lets us unroll most loops and prevent allocating temporary arrays
• Built-in support for general adaptive sampling techniques

Usage

See examples/demo/demo.ipynb for a tour through the API. You can also check out:

• examples/adaptive_distance_fields/adaptive_distances.ipynb for an adaptively-sampled distance field, or AdaptiveDistanceFields.jl for a more complete example [1]
• examples/adaptive_mpc/adaptive_mpc.ipynb for an adaptive approximation of a model-predictive controller

[1] Frisken et al. "Adaptively Sampled Distance Fields: A General Representation of Shape for Computer Graphics". SIGGRAPH 2000.

Gallery

An adaptively sampled distance field, from examples/adaptive_distances.ipynb:

An adaptively sampled model-predictive control problem, from examples/adaptive_mpc.ipynb:

An adaptive distance field in 3D, from AdaptiveDistanceFields.jl:

Related Packages

• Morton.jl
• Interpolations.jl