Which triangulation method does alphaTriangulation?

I would like to know if alphaShape employes Delaunay triangulation in alphaTriangulation function. Maybe it's a subset of it.

Thanks!

Answer 1

[John D'Errico]

An alpha shape starts with a Delaunay triangulation. Then some parts of it are deleted as defined by the alpha shape. (Having written alpha shape tools myself, I know of what I speak.) But we can see that it does exactly that, based on an example.

XY = rand(100,2);
DT = delaunayTriangulation(XY);
T = alphaShape(XY,.15);
plot(T)
hold on
triplot(DT.ConnectivityList,DT.Points(:,1),DT.Points(:,2),'r')

See that the two triangulations are the same, where a triangle remains from the alpha shape. The alpha shape plot would have the edges in black there, but they are entirely hidden by the red edges from triplot.

As I said, it starts with the Delaunay triangulation, then deletes. So that which remains is indeed a pure subset of the Delaunay triangulation.