Generate 3D Voronoi Diagrams Using MPT Toolbox with Excel Topology Data Export

We can utilize the MPT toolbox to generate three-dimensional Voronoi diagrams. Voronoi diagrams represent a spatial partitioning method that divides space into multiple regions based on a given set of seed points, where all points in space are assigned to the region containing their closest seed point. The implementation typically involves computing the Voronoi tessellation using functions like voronoin() for 3D point sets, which returns vertices and connectivity information for each Voronoi cell. The generated Voronoi diagram's topological information can be exported to Excel files for visualization and analysis. Through custom MATLAB scripts, we can extract and write geometric properties such as each region's volume (area in 3D context), surface area (perimeter equivalent), boundary vertices, and adjacency relationships between neighboring regions to Excel spreadsheets using functions like writetable() or xlsxwrite(). This exported data enables detailed examination of spatial characteristics and topological relationships, providing valuable insights for applications in urban planning, geological exploration, and other spatial data analysis domains. The workflow generally involves three key steps: 1) Generating Voronoi tessellation from 3D point clouds, 2) Calculating geometric properties using polyhedral computation methods, and 3) Structuring the topological data into tabular format for Excel export.