BOVE is a simple tool for creating special types of convex three dimensional objects. The program attempts to create solid objects with faces of equal size and shape. The steps used to render these shapes is exposed through BOVE's user interface so a quick explaination of how to use BOVE should give a good idea of how this works.
To create such an object, say a 10 sided object, then BOVE first spreads 10 particles over the surface of a sphere. Then, it simulates the forces on the particles as if each particle were electrostatically charged. This has the effect of moving the particles into different positions such that each particle is equi-distant from its neighbours. Of course, in order to stop the particles flying off into infinity they are confined to the surface of the sphere during the simulation.
After some time, the particles come to rest (or a small enough speed) and the simulation is stopped. Tesselation is then performed between the particles to produce a triangular lattice. This creates an object with 2n-4 trianglular faces, so for our 10 particles we have 16 faces. We then find the midpoints In the context of BOVE, the midpoint of a triangle is the position on the surface of the sphere that is closest and equi-distant from each vertex of the triangle. of the triangles and draw lines between these, creating polygons with the particles as their centers. We thus end up with a n sided shape.
The best way to understand BOVE is to use it, so let's get started with a new object ... next