2013/12/19 by J. Li, Li, J., Thomas Peters +3
Computer Science · Engineering · #3D Shape Modeling and Analysis #57M50 #57Q37 #57Q55 #68R10 #Advanced Numerical Analysis Techniques #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.1401.3370
openalex publication_date 2013/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.