Spatial point pattern analysis by using Voronoi diagrams and Delaunay tessellations - A comparative study

Given a spatial point pattern, we use various characteristics of its Voronoi diagram and Delaunay tessellation to extract information of the dependence between points. In particular, we use the characteristics to construct statistics for testing complete spatial randomness. It is shown that the minimum angle of a typical Delaunay triangle is sensitive to both regularity and clustering alternatives, whilst the triangle's area or perimeter is more sensitive to clustering than regularity. These statistics are also sensitive to the Baddeley-Silverman cell process.