https://github.com/augustt198/quickhull.jl

https://github.com/augustt198/quickhull.jl

Last synced: about 2 months ago
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• Host: GitHub
• URL: https://github.com/augustt198/quickhull.jl
• Owner: augustt198
• License: mit
• Created: 2024-06-22T03:08:18.000Z (7 months ago)
• Default Branch: main
• Last Pushed: 2024-08-28T16:48:01.000Z (4 months ago)
• Last Synced: 2024-08-28T18:31:19.173Z (4 months ago)
• Language: Julia
• Size: 2.13 MB
• Stars: 15
• Watchers: 1
• Forks: 2
• Open Issues: 1
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Quickhull.jl

[![](https://img.shields.io/badge/docs-stable-blue.svg)](https://augustt198.github.io/Quickhull.jl/stable)

[![](https://img.shields.io/badge/docs-dev-blue.svg)](https://augustt198.github.io/Quickhull.jl/dev)

The quickhull algorithm in pure Julia for finding

convex hulls, Delaunay triangulations, and Voronoi diagrams in N dimensions.

```julia

julia> using Quickhull

julia> hull = quickhull(randn(3, 500))

Hull of 500 points in 3 dimensions

  - 31 Hull vertices: Int32[297, 438  …  147, 376]

  - 58 Hull facets: TriangleFace{Int32}[TriangleFace(139, 249, 243)  …  TriangleFace(104, 147, 243)]

julia> using GLMakie, GeometryBasics

julia> wireframe(GeometryBasics.Mesh(hull))

julia> scatter!(points(hull), color=:black)

```



```julia

julia> tri = delaunay(rand(2, 100));

julia> f = Figure()

julia> wireframe!(Axis(f[1,1]), GeometryBasics.Mesh(tri))

julia> linesegments!(Axis(f[1,2]), voronoi_edge_points(tri), color=:red)

```



## Qhull Comparison

Quickhull.jl is competitive with [Qhull](http://www.qhull.org/)'s performance even

when exact arithmetic is used, although it has fewer features.



## Robustness

`quickhull` can be run with various hyperplane kernels. A hyperplane

kernel is a method of calculating hyperplane-point distances. By default,

an exact kernel is used (i.e. the sign of the distance is always correct)

to ensure robustness. Robustness can be traded for speed by choosing an inexact

kernel, for instance:

```julia

quickhull(pts, Quickhull.Options(kernel = Quickhull.HyperplaneKernelInexact))

```

It should be noted that if an inexact kernel is used – particularly

on inputs with coplanar or nearly coplanar points – the topology of the

hull can become corrupted, and an error will probably occur.

## Related Packages

- [QHull.jl](https://github.com/JuliaPolyhedra/QHull.jl), [DirectQHull.jl](https://github.com/JuhaHeiskala/DirectQhull.jl/) – wrappers for [Qhull](http://www.qhull.org/)

- [DelaunayTriangulation.jl](https://github.com/JuliaGeometry/DelaunayTriangulation.jl) – 2D Delaunay triangulation and Voronoi tesselation with many features

- [TetGen.jl](https://github.com/JuliaGeometry/TetGen.jl) – wrapper for 3D Delaunay tetrahedralization

library [TetGen](https://wias-berlin.de/software/index.jsp?id=TetGen&lang=1)