Efficiently Approximating Polygonal Paths in Three Dimensions

Gill Barequet, Danny Z. Chen, Ovidiu Daescu, and Michael T. Goodrich

Center for Geometric Computing
Department of Computer Science
Johns Hopkins University
Baltimore, MD 21218
[barequet|goodrich]@cs.jhu.edu
Dept. of Computer Science and Engineering
University of Notre Dame
Notre Dame, IN 46556
[chen|odaescu]@cse.nd.edu

Abstract

In this paper we present efficient algorithms for solving polygonal path approximation problems in three dimensions. Given an n-vertex polygonal curve P in R3, we approximate P by another polygonal curve P' of m vertices in R3, such that the vertex sequence of P' is an ordered subsequence of the vertices of P. The goal is to either minimize the size m of P' for a given error tolerance epsilon (called the min-# problem), or to minimize the deviation error epslion between P and P' for a given size m of P' (called the min-epsilon problem). Our techniques enable us to develop efficient near-quadratic-time algorithms for solving the min-# and min-epsilon problems in 3-D.