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