mjziebarth / acosa Goto Github PK

For certain regular lattices, north and south pole are surrounded with a circle of equally distanced nodes*. For them, multiple Delaunay triangulations exist. For all of them, all Delaunay triangles belong to the same Voronoi node at the respective pole.

In this implementation, a new Voronoi node is created for each of the triangles of said triangulations. They might coincide or be slightly (within tolerance) different. Most likely this is the cause for the algorithm used for Voronoi cell area calculation to return NANs.

Merging duplicate Voronoi nodes would likely solve this issue.

Also, it looks nicer to have just one Voronoi node where it should be only one.

(*) This is also the case for nodes at other places of some regular lattices.

The handling of collinear sets is probably broken.

In the case that the set of nodes cannot be confined to one hemisphere, it's not as intuitive to define what would be a convex hull. Perhaps any set of triangles? It might not even be possible to define it.

Either way, clarify mathematical background on this issue. The current implementation fails in any case, so add a check to the code to make sure that all nodes are inside a hemisphere before returning a hull.

Two kinds of degeneracies are still unhandled. They will currently provoke an exception.

For concyclic nodes (N>4), the Voronoi tesselation consists of only two nodes but N Voronoi-edges. This cannot be displayed in the used network data structures but Voronoi cell areas can be calculated.

Code fails for cocircular nodes generated as follows:

lon=360.0*np.linspace(0, 1.0,num=10)[:-1]
lat=80.0*np.ones(len(lon))

(proper conversion to radians excluded)