Linear Time Calculation of 2D Shortest Polygonal Jordan Curves

The length of curves may be measured by numeric integration if the curves are given by analytic formulas. Not all curves can or should be described parametrically. In this report we use the alternative grid topology approach. The shortest polygonal Jordan curve in a simple closed one-dimensional grid continuum is used to estimate a curve's length. An O(n) algorithm for finding the shortest polygonal Jordan curve is introduced, and its correctness and complexity is discussed. 1 The University of Auckland, Computer Science Department, CITR, Tamaki Campus (Building 731), Glen Innes, Auckland, New Zealand Linear Time Calculation of 2D Shortest Polygonal Jordan Curves Nan Yang and Reinhard Klette Department of Computer Science, The University of Auckland CITR, Tamaki Campus Private Bag 92019, Auckland, New Zealand Abstract: The length of curves may be measured by numeric integration if the curves are given by analytic formulas. Not all curves can or should be described parametrically. In this paper we use the alternative grid topology approach. The shortest polygonal Jordan curve in a simple closed onedimensional grid continuum is used to estimate a curve's length. An O(n) algorithm for nding the shortest polygonal Jordan curve is introduced, and its correctness and complexity is discussed. The length of curves may be measured by numeric integration if the curves are given by analytic formulas. Not all curves can or should be described parametrically. In this paper we use the alternative grid topology approach. The shortest polygonal Jordan curve in a simple closed onedimensional grid continuum is used to estimate a curve's length. An O(n) algorithm for nding the shortest polygonal Jordan curve is introduced, and its correctness and complexity is discussed.