Geometer

Implementations of computational geometry algorithms from scratch in Rust.

🚧👷‍♂️ Work In Progress: This repos is under heavy development right now and just in its nascent stages.

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Currently the algorithms are implemented following Joseph O'Rourke's Computational Geometry in C.

This is very much a work in progress, I'm just stepping through the text and implementing things as I go. I'm also a Rust newb so I'm frequently stumbling through the implementations, finding I made a terrible design decision, and going back to reimplement things. As such the API is in constant flux.

My goal for this repo is to eventually have a complete implementation of the algorithms described in the text, which will serve as the basis of a computational geometry library in Rust. I will then build from there, exploring more modern concepts and algorithms. My priorities are to have relatively easy-to-read code, a great test suite, and nice visualizations. I will have these three objectives in mind as I build out this repo.

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Features

Currently Supported for 2D Polygons

• Area
• Triangulation - $O(n^2)$
• Rotation and translation
• Bounding box computation
• Determination of extreme and interior points - $O(n^3)$ and $O(n^4)$ (for benchmarking)

On the Roadmap

• Convex Hull (2D and 3D)
• Voronoi Diagram
• Benchmarking of different algorithms
• Animated visualizations of algorithms

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Visualizer

A visualizer is provided using rerun.io. You must have the rerun viewer installed for this to work, you can follow their instructions here. This method worked well for me:

cargo install rerun-cli --locked

Here are some example visualizations (add the -h option for further CLI documentation):

cargo run --features visualizer -- -v triangulation -f interesting_polygon_archive -p skimage_horse

cargo run --features visualizer -- -v extreme-points -f interesting_polygon_archive -p skimage_horse

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Benchmarks

Some simple benchmarking capabilities are provided using Criterion.rs. These are mostly to provide empirical intuition on the runtime of algorithms. Currently only a couple benchmarks are setup, more will be added as more algorithms are implemented.

You can run the benchmarks yourself with

cargo bench --bench extreme_points --bench interior_points

Here is a visualization of one of the benchmarks to compute extreme points, comparing computing them from extreme edges $O(n^3)$ versus computing them from interior points with triangle checks $O(n^4)$:

These are both obviously bad algorithms, but they are what is implemented at the moment and provide some basis for comparison.

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