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

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

* [examples/adaptive_distance_fields/adaptive_distances.ipynb](examples/adaptive_distance_fields/adaptive_distances.ipynb) for an adaptively-sampled distance field, or [AdaptiveDistanceFields.jl](https://github.com/rdeits/AdaptiveDistanceFields.jl) for a more complete example [1]
* [examples/adaptive_mpc/adaptive_mpc.ipynb](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`:

![](http://rdeits.github.io/RegionTrees.jl/img/distance.svg)

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

![](http://rdeits.github.io/RegionTrees.jl/img/mpc.svg)

An adaptive distance field in 3D, from [AdaptiveDistanceFields.jl](https://github.com/rdeits/AdaptiveDistanceFields.jl):

![](http://rdeits.github.io/RegionTrees.jl/img/distance_3d.png)

## Related Packages

* [Morton.jl](https://github.com/JaneliaSciComp/Morton.jl)
* [Interpolations.jl](https://github.com/JuliaMath/Interpolations.jl)
