Computational Topology for Approximations of Knots
نویسندگان
چکیده
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: (1) Hausdorff distance, and (2) a 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 Bézier 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 Bézier curve, and (ii) improved iteration bounds over those previously established.
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ورودعنوان ژورنال:
- CoRR
دوره abs/1401.3370 شماره
صفحات -
تاریخ انتشار 2013