MiniQhull (Qhull-based Delaunay triangulation).

The MiniQhull julia package provides a single function delaunay overloaded with 3 methods:

delaunay(dim::Integer, numpoints::Integer, points::AbstractVector) -> Matrix{Int32}

Compute the Delaunay triangulation of a cloud of points in an arbitrary dimension dim. The length of vector points must be dim*numpoints. Vector points holds data in "component major order", i.e., components are consequitive within the vector. The returned matrix has shape (dim+1, nsimplices), where nsimplices is the number of simplices in the computed Delaunay triangulation.

delaunay(points::AbstractMatrix) -> Matrix{Int32}

In this variant, the cloud of points is specified by a matrix with size(matrix) == (dim, numpoints).

delaunay(points::AbstractVector) -> Matrix{Int32}

In this variant, the cloud of points is specified with a vector of dim-element vectors or tuples. It is also possible to use a vector of other tuple-like types, like SVector from StaticArrays.jl.

You can override the default set of flags that Qhull uses by passing an additional flags argument:

delaunay(dim::Integer, numpoints::Integer, points::AbstractVector, flags::AbstractString) -> Matrix{Int32}
delaunay(points::AbstractMatrix, flags::AbstractString) -> Matrix{Int32}
delaunay(points::AbstractVector, flags::AbstractString) -> Matrix{Int32}

The default set of flags is qhull d Qt Qbb Qc Qz for up to 3 dimensions, and qhull d Qt Qbb Qc Qx for higher dimensions. The flags you pass override the default flags, i.e. you have to pass all the flags that Qhull should use.

using MiniQhull
dim          = 2
numpoints    = 4
coordinates  = [0,0,0,1,1,0,1,1]
connectivity = delaunay(dim, numpoints, coordinates)
# output
3×2 Array{Int32,2}:
 4  4
 2  3
 1  1

using MiniQhull
coordinates  = [0 0 1 1; 0 1 0 1]
connectivity = delaunay(coordinates)
# output
3×2 Array{Int32,2}:
 4  4
 2  3
 1  1

using MiniQhull, StaticArrays
dim = 5
npts = 500
pts = [SVector{dim, Float64}(rand(dim)) for i = 1:npts];
flags = "qhull d Qbb Qc QJ Pp" # custom flags
connectivity = delaunay(pts, flags)

MiniQhull is a registered Julia package. MiniQhull can be installed using the command:

pkg> add MiniQhull

MiniQhull depends two binary dependencies which are build for all Platforms by BinaryBuilder:

• Qhull_jll
• QhullMiniWrapper_jll