The.Algorithm.Design.Manual.Springer-Verlag.1998

Simplifying Polygons
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Simplifying Polygons
Input description: A polygon or polyhedron p, with n vertices.
Problem description: Find a polygon or polyhedron p' with n' vertices, where the shape of p' is close to
p and n' < n.
Discussion: 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.
Several issues arise in shape simplification:
● Do you want the convex hull? - The simplest way to simplify a polygon is to take the convex hull
of its vertices (see Section ). The convex hull removes all internal concavities from the
polygon. If you were simplifying a robot model for motion planning, this is a good thing, because
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