Fairing of discrete planar curves to integrable discrete analogue of Euler’s elasticae

Abstract

We construct a method for fairing a given discrete planar curve by using the integrable discrete analog of Euler’s elastica, which is a discrete version of the approximation algorithm presented by Brander et al. We first give a brief review of the integrable discrete analog of Euler’s elastica proposed by Bobenko and Suris, then we present a detailed account of the fairing algorithm, and we apply this method to an architectural problem of characterizing the keylines of Japanese handmade pantiles.

Keywords

• Euler’s elastica
• integrable systems
• discrete curve
• discrete differential geometry