Computational Topology Counterexamples with 3D Visualization of Bezier Curves

J. Li; T. J. Peters; D. Marsh; K. E. Jordan

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arXiv · 1210.1867

Computational Topology Counterexamples with 3D Visualization of Bezier Curves

J. Li·T. J. Peters·D. Marsh·K. E. Jordan

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Abstract

For applications in computing, Bezier curves are pervasive and are defined by a piecewise linear curve L which is embedded in R^3 and yields a smooth polynomial curve C embedded in R^3. It is of interest to understand when L and C have the same embeddings. One class of counterexamples is shown for L being unknotted, while C is knotted. Another class of counterexamples is created where L is equilateral and simple, while C is self-intersecting. These counterexamples were discovered using curve visualizing software and numerical algorithms that produce general procedures to create more examples.

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BibTeX RIS

J. Li, T. J. Peters, D. Marsh, K. E. Jordan. 2012-10-05. Computational Topology Counterexamples with 3D Visualization of Bezier Curves. https://arxiv.org/abs/1210.1867

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