Computational Topology Counterexamples with 3D Visualization of Bézier Curves

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

Abstract

For applications in computing, Bézier curves are pervasive and are defined by a piecewise linear curve L which is embedded in R3 and yields a smooth polynomial curve C embedded in R3. It is of interest to understand when L and C have the same embeddings. One class ofc ounterexamples 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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1. Exact computation for existence of a knot counterexample
K. Marinelli, T. J. Peters
Applied General Topology  vol: 20  issue: 1  first page: 251  year: 2019  
doi: 10.4995/agt.2019.10928



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Universitat Politècnica de València

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