Examples of degenerate vertex support

Voronoi cells are irregular polyhedra whose faces are made by random plane cuts due to neighboring particles, and typically all the vertices of these polyhedra have order 3, since creating higher order vertices can only occur if a plane cut intersects an existing vertex.

In order to make the code robust for handling very large systems, Voro++ correctly handles these cases, by taking the approach that if a plane is within a particular numerical tolerance of an existing vertex, it treats the plane as perfectly intersecting that vertex, and it recomputes the cell topology accordingly, allowing it to have perfect representations of objects such as an octahedron. These example codes demonstrate this support:

1. higher_test.cc - this code creates an object by cutting with planes aligned

in a conical arragement along the positive and negative axes in the x, y, and z directions. This results in six very high order vertices, and often many order four vertices.

2. higher_test2.cc - this code creates an approximation to a sphere, by cutting

with many different planes aligned in locally random conical arrangements.