The quickhull algorithm in pure Julia for finding convex hulls, Delaunay triangulations, and Voronoi diagrams in N dimensions.
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> 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)
Quickhull.jl is competitive with Qhull's performance even when exact arithmetic is used, although it has fewer features.
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:
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.
- QHull.jl, DirectQHull.jl – wrappers for Qhull
- DelaunayTriangulation.jl – 2D Delaunay triangulation and Voronoi tesselation with many features
- TetGen.jl – wrapper for 3D Delaunay tetrahedralization library TetGen