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          |
+-----------------------------------------------------+

[download]

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.

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.
"Too many [] have been sedated by an oppressive environment of political correctness and risk aversion."

In reply to Re^5: Better maps with Math::Geometry::Voronoi, and a Challenge for Math Monks by BrowserUk
in thread Better maps with Math::Geometry::Voronoi, and a Challenge for Math Monks by samtregar

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