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arXiv · 1211.0354

Isotopic Equivalence from Bezier Curve Subdivision

J. Li·T. J . Peters·J. A. Roulier
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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.

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J. Li, T. J . Peters, J. A. Roulier. 2013-09-29. Isotopic Equivalence from Bezier Curve Subdivision. https://arxiv.org/abs/1211.0354

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