Problem: Find a polygon or polyhedron p' with n' vertices, where the shape of p' is close to p while n' << n.
Excerpt from The Algorithm Design Manual: Polygon simplification has two primary applications. The first is in cleaning up a noisy representation of a polygon, perhaps obtained by scanning a picture of an object. By processing it, we hope to remove the noise and reconstruct the original object. The second is in data compression, where given a large and complicated object, we seek to simplify it by reducing detail. Ideally, we obtain a polygon with far fewer vertices that looks essentially the same. This can be a big win in computer graphics, where replacing a large model with a smaller model might have little visual impact but be significantly faster to render.
|Computational Geometry : Algorithms and Applications by Mark De Berg, Marc Van Kreveld, Mark Overmars, and O. Schwartskopf||Computational Geometry in C by Joseph O'Rourke||Discrete Voronoi Skeletons by R. Ogniewicz|