Computational Topology Counterexamples with 3D Visualization of Bézier Curves

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

doi:10.4995/agt.2012.1624

Authors

Ji Li University of Connecticut
T. J. Peters University of Connecticut
D. Marsh Pratt and Whitney
K. E. Jordan IBM T.J. Watson Research ; Cambridge Research Center

DOI:

https://doi.org/10.4995/agt.2012.1624

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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Author Biographies

Ji Li, University of Connecticut

Department of Mathematics

T. J. Peters, University of Connecticut

Department of Computer Science and Engineering

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