Fairing of Discrete Planar Curves by Integrable Discrete Analogue of Euler's Elasticae

TL;DR

This paper introduces a novel method for smoothing discrete planar curves using an integrable discrete analogue of Euler's elastica, with applications demonstrated in architectural keyline characterization.

Contribution

It presents a new fairing algorithm based on integrable discrete Euler's elastica, extending prior continuous models to discrete curves.

Findings

Effective smoothing of discrete curves demonstrated

Application to architectural keyline analysis shown

Algorithm based on integrable discrete elastica

Abstract

We construct a method to fair a given discrete planar curve by using the integrable discrete analogue of Euler's elastica, which is a discrete version of the approximation algorithm presented by D. Brander, et al. We first give a brief review of the integrable discrete analogue of Euler's elastica proposed by A. I. Bobenko and Yu. B. 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.