Stony Brook Algorithm Repository

Simplifying Polygons


Input Description: A polygon or polyhedron \(p\), with \(n\) vertices.
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.


Douglas-Peucker line simplification algorithm implementation by Jack Snoeyink (rating 8)
QSlim (rating 8)
Cocone (rating 7)
CGAL (rating 7)
simplify-geometry (rating 5)
rdp (rating 5)
Skeletonization Software (rating 4)

Recommended Books

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

Related Problems

Convex Hull

Discrete Fourier Transform

Minkowski Sum

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