Fairing of discrete planar curves by discrete Euler's elasticae

• Zurita Sebastián Elías Graiff

  Graduate School of Mathematics

• Kajiwara Kenji

  Institute of Mathematics for Industry

Abstract

After characterizing the integrable discrete analogue of the Euler's elastica, we focus our attention on the problem of approximating a given discrete planar curve by an appropriate discrete Euler's elastica. We carry out the fairing process via a $L^2\!$-distance minimization to avoid the numerical instabilities. The optimization problem is solved via a gradient-driven optimization method (IPOPT). This problem is non-convex and the result strongly depends on the initial guess, so that we use a discrete analogue of the algorithm provided by Brander et al., which gives an initial guess to the optimization method.

Journal

• JSIAM Letters

  JSIAM Letters 11 (0), 73-76, 2019

  The Japan Society for Industrial and Applied Mathematics

Keywords

• Euler's elastica
• integrability
• discrete curve
• discrete differential geometry
• fairing

Details

• CRID: 1390002184855500416
• NII Article ID: 130007771236
• DOI: 10.14495/jsiaml.11.73
• ISSN: 18830617
• ISSN: 18830609
• Web Site: https://www.jstage.jst.go.jp/article/jsiaml/11/0/11_73/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed