Red and Silver Pair of Ornaments

Spacing the Points

I've always associated the paper models I've made with the winter holidays; not only does drier indoor air make white glue dry nice and fast, but holiday gift giving is a fitting excuse.

However, to scale down the models, I needed the edges to be much more evenly spaced. Leaving everything up to chance had a certain purity that I liked, but obviously some post-processing was in order, so after picking the points out of a uniform distribution, I ran an algorithm to push nearest pairs of generator points apart slightly, then normalise them back to the surfact of the sphere.

This algorithm does tend towards creating polygons, whose diagonals will be a lot longer than the edges of the nearly-equilateral triangles; such a pentagon is visible in the photo at left.

It turns out that in this case, there's one such almost-pentagon; it's the easiest way to identify the corresponding parts of the two models.


The two models are painted with Testors brand gloss enamel paint. The red came first, and took two coats, while to my surprise, the silver was much easier to work with, and took only one coat.

I was looking for something shiny and thick enough to cover the flakes of toner along the edges. I'm quite happy with the enamel paint, which has the added benefit of giving some waterproofing to the models.

This pair were apparently a hit with my family.

PostScript: Delaunay, Voronoi.