Any Dimension Polygonal Approximation Based on Equidistance Principle

In this paper, we present a new and more general version of polygonal approximation problem (GPA). Given an N−vertex polygonal curve P in the n-dimensional space <n, we approximate P by finding another M−vertex polygonal curve Ṗ , such that the vertices of Ṗ are an ordered subsequence of the curve points along P . The definition of the classical polygonal approximation problem (PA) demands the Ṗ vertices to be a subset of P vertices. Therefore, the solutions of GPA problem approximates better the polygonal curve P than the solutions of PA problem. The optimal or a suboptimal solution of GPA is achieved when the approximation errors per line segment are equal. Our method is very flexible on changes of error criteria and on curve dimension yielding an alternative and in many cases better solution than the optimal PA methods with about the same computation cost.