Spatial Poisson Point Process Visualization with Voronoi Diagrams

To create a comprehensive visualization of a spatial Poisson point process, you can employ geometric tessellation techniques such as Voronoi diagrams (also known as Voronoi tessellation) or Delaunay triangulation. These mathematical structures partition the spatial domain into cells or triangles based on the proximity relationships between points in the point pattern. In MATLAB implementation, you can generate Poisson point patterns using the random number generation functions and then apply built-in geometric functions for tessellation. The key steps involve: 1. Generating random points using poissrnd or rand functions for homogeneous Poisson processes 2. Applying voronoin() function for Voronoi diagram creation or delaunayTriangulation() for Delaunay triangulation 3. Using plot functions like voronoi() or triplot() for visualization The Voronoi tessellation divides the space into regions where each region contains all points closer to a given Poisson point than to any other, while Delaunay triangulation creates a triangulation where no point lies inside the circumcircle of any triangle. These geometric representations help in analyzing spatial patterns, nearest neighbor distances, and spatial distribution characteristics of the point process. By combining MATLAB's computational capabilities with these geometric algorithms, you can produce both mathematically accurate and visually informative representations of Poisson point processes, suitable for spatial analysis and pattern recognition applications.