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, and  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 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.
['Jin Li', 'Thomas J. Peters', 'Kirk E. Jordan']
Computational Topology for Approximations of Knots