AlphaShape(X::AbstractArray{Float64,2};α::Union{Nothing,Float64}=nothing,
    search::Tuple{Float64,Float64}=(0.0, 10.0),
    MaxSteps::Int=100)::AbstractArray{Float64,3}

Find the alpha shape corresponding to the 2D AbstractArray of points X: [2,npoints], and the α value α.

If α == nothing then a search over the range of values search is done to find the best value. The optimisation objective is the alpha shape area (minimise) subject to all points in X being included in the alpha shape triangulation.

AlphaShapeVolume(A::AbstractArray{Float64,3})

return the sum of volumes of all simplices in the alpha shapes A

    CayleyMenger

Compute the Cayley-Menger matrix from squared
distances dij^2.

https://mathworld.wolfram.com/Cayley-MengerDeterminant.html

For a 2-d triangle the following example would symbolically
represent the matrix for points x1, x2, and x3 where dij^2
is the square Euclidean distance between i and j
Example

julia>:([0    1      1      1
         1    0      d12^2  d13^2
         1    d21^2  0      d23^2
         1    d32^2  d32^2    0])
:([0 1 1 1; 1 0 d12 ^ 2 d13 ^ 2; 1 d21 ^ 2 0 d23 ^ 2; 1 d32 ^ 2 d32 ^ 2 0])

FindAlpha(X::AbstractArray{Float64,2};
    search::Tuple{Float64,Float64}=(0.0, 10.0),
    MaxSteps::Int=100)::Float64

Use BlackBocOptim to find the optimal alpha value (volume minimiser which cotains all points from the input).

GetDelaunayTriangulation(points::AbstractArray{Float64,2})::AbstractArray{Float64,3}

Wrap MiniQhull.jl's delaunay to get a delaunay triangualation in any dimension

SimplexCircumSphere

Find the centre and radius of the circumsphere of a simplex https://westy31.home.xs4all.nl/Circumsphere/ncircumsphere.htm

SimplexCircumSphere

Find the centre and radius of the circumsphere of a simplex https://westy31.home.xs4all.nl/Circumsphere/ncircumsphere.htm

SimplexVolume

Calculate the volume of a simplex using the Cayley Menger matrix

https://westy31.home.xs4all.nl/Circumsphere/ncircumsphere.htm