TY - JOUR
AU - Li, Ji
AU - Peters, T. J.
AU - Jordan, K. E.
PY - 2014/10/01
Y2 - 2024/10/14
TI - Computational topology for approximations of knots
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 15
IS - 2
SE -
DO - 10.4995/agt.2014.2281
UR - https://polipapers.upv.es/index.php/AGT/article/view/2281
SP - 203-220
AB - <p>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:</p><ol><li>Hausdorff distance, and</li><li>a sum of total curvature and derivative.</li></ol><p>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:</p><p> (i) <em>a priori</em> bounds on the number of subdivision iterations sufficient to achieve a PL approximation that is ambient isotopic to the original B\'ezier curve, and</p><p> (ii) improved iteration bounds over those previously established.</p><p> </p>
ER -