纽结近似的计算拓扑
Computational Topology for Approximations of Knots
摘要：
在光滑结点的分段线性近似下，环境同位素等价性的保持在分子建模和模拟中是突出的。给出了关于（1）Hausdorff距离和（2）全曲率与导数之和的充分条件。高次贝塞尔曲线通常用作光滑表示，其中计算效率是一个实际问题。细分可以为给定的贝塞尔曲线产生PL近似，满足上述两个条件。主要贡献是：（i）关于足以实现PL近似的细分迭代次数的先验界限，所述PL近似是原始贝塞尔曲线的环境同位素，以及（ii）在先前建立的那些上改进的迭代界限。
英文摘要：
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 Bezier 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 Bezier curve, and (ii) improved iteration bounds over those previously established.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
