Polygon Generation

After generating ramdom points as polygons' centers, we use LaGriT to connect the points and make a Delauney triangulation, from which we derive the hybrid dual polygons¹. We derive the dual mesh of the triangulation using the utility MKDual from the MSTK package.

Figure. 1
Triangulation using LaGriT and visualization of the Voronoi polygons

Figure. 2
Extract dual polygon mesh using MKDual. The polygons are not strictly Voronoi diagrams.

The output from the MKDual utility contains node information (IDs and coordinates) and connectivity (polygons). We then process this output, writing the information of each polygon into separate files in AVS format. At this point, the workflow splits into 2 branches. The user has the options to generate a full 3D computational mesh model (with surface and subsurface structures), or a more abstract intermediate-scale model.

Notes on hybrid dual polygons

Figure. 3
Connecting the centers of circumcircles of a Delaunay triangulation produces the Voronoi diagram (in red).

In Figure. 3, there are some centers of the circumcircles that fall outside of the triangle. This happens when the triangle has an angle greater than 90 degrees.