Computational Topology Counterexamples with 3D Visualization of Bézier Curves

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


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

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147