Re^5: Better maps with Math::Geometry::Voronoi, and a Challenge for Math Monks

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I put this case into the algorithm...

Hm. What do you mean by "put it into the algorithm"?

Four points (o) in a square, gives six bisectors (.), but just four normals(n). (Four pairs of coincident normals.) But they produce just a single vertex (X) ('scuse the crudity):

+-----------------------------------------------------+
|     n                  n                   n        |
|       n                n                 n          |
|         n              n               n            |
|           n            n             n              |
|            o.......................on               |
|            . .n        n         .n.                |
|            .   .n      n       .n  .                |
|            .     .n    n     .n    .                |
|            .       .n  n   .n      .                |
|            .         . n .n        .                |
| nnnnnnnnnnn.nnnnnnnnnn Xnnnnnnnnnnn.nnnnnnnnnnnnnnnn|
|            .         . n .n        .                |
|            .       .n  n   .n      .                |
|            .     .n    n     .n    .                |
|            .   .n      n       .n  .                |
|            . .n        n         .n.                |
|            o.......................o                |
|          n             n             n              |
|        n               n               n            |
|      n                 n                 n          |
+-----------------------------------------------------+

And you can't form any polygons from a single vertex!

Unless you are using the boundaries of the coordinate space to form the missing edges of polygons?

But if that was the case in Sam's problem, his boundary polygons would just always be a rectangle coincident with the boundaries of the coordinate space.