Isotopic Equivalence from Bezier Curve Subdivision

Authors :: Li, J.
Peters, T. J .
Roulier, J. A.
Publication Year :: 2012
Abstract: We prove that the control polygon of a Bezier curve B becomes homeomorphic and ambient isotopic to B via subdivision, and we provide closed-form formulas to compute the number of iterations to ensure these topological characteristics. We first show that the exterior angles of control polygons converge exponentially to zero under subdivision.<br />Comment: arXiv admin note: substantial text overlap with arXiv:1211.0353