2012/10/09 by J. Li, Ji Li, Thomas Peters +6
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced machining processes and optimization #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Geometric Topology (math.GT) #Tribology and Lubrication Engineering #cs.CG #math.GT
paper · pdf · doi:10.48550/arxiv.1210.2686
arxiv created 2012/10/09 · openalex publication_date 2012/10/09 · arxiv updated 2012/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Properties of a parametric curve in R3 are often determined by analysis of its piecewise linear (PL) approximation. For Bezier curves, there are standard algorithms, known as subdivision, that recursively create PL curves that converge to the curve in distance . The exterior angles of PL curves under subdivision are shown to converge to 0 at the rate of O(√((1)/(2i))), where i is the number of subdivisions. This angular convergence is useful for determining self-intersections and knot type.