Use of Delaunay Triangulation and Voronoi Diagram to find alpha shape using Edelsbrunner's algorithm

707 Views Asked by At

I am learning how to find the shape of a set of points in 2-D. I understand that Alpha Shape method is a good way to find the shape of a set of points.

Alpha Shape was originally introduced by H. Edelsbrunner, D. G. Kirckpatrick and R. Seidel. On the shape of a set of points in the plane.

They used Delaunay Triangulation and Voronoi Diagram to find the boundary points and boundary edges.

I can understand how to do Delaunay Triangulation and Voronoi Diagram, but I could not understand how this two idea helps to find the boundary point and boundary edges?

I look at the document "Introduction to Alpha Shapes" by Kaspar Fischer which illustrated the above method. But I still have doubts.

Can anyone please help me to understand this ideas? Thanks for your help.