Place the Vertices Anywhere on the Curve and Simplify.

A polygonal curve is simplified to reduce its number of vertices, while maintaining similarity to its original shape. Numerous results have been published for vertex-restricted simplification, in which the vertices of the simplified curve are a subset of the vertices of the input curve. In curve-restricted simplification, i.e. when the vertices of the simplified curve are allowed to be placed on the edges of the input curve, the number of vertices may be much more reduced. In this paper, we present algorithms for computing curve-restricted simplifications of polygonal curves under the local Hausdorff distance measure. [ABSTRACT FROM AUTHOR]