Computational topology for approximations of knots

• Li, Ji ^[1] ; Peters, T. J. ^[1] ; Jordan, K. E. ^[2]
  1. [1] University of Connecticut

     University of Connecticut

     Town of Mansfield, Estados Unidos

     
  2. [2] Cambridge Research Center
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 15, Nº. 2, 2014, págs. 203-220
• Idioma: inglés
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• Resumen

  • The preservation of ambient isotopic equivalence under piecewise linear (PL) approximation for smooth knots are prominent in molecular modeling and simulation. Sufficient conditions are given regarding:Hausdorff distance, anda sum of total curvature and derivative.High degree Bézier curves are often used as smooth representations, where computational efficiency is a practical concern. Subdivision can produce PL approximations for a given B\'ezier curve, fulfilling the above two conditions. The primary contributions are:       (i) a priori bounds on the number of subdivision iterations sufficient to achieve a PL approximation that is ambient isotopic to the original B\'ezier curve, and       (ii) improved iteration bounds over those previously established.