Computational Topology Counterexamples with 3D Visualization of Bézier Curves

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

References

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How to Cite

[1]
J. Li, T. J. Peters, D. Marsh, and K. E. Jordan, “Computational Topology Counterexamples with 3D Visualization of Bézier Curves”, Appl. Gen. Topol., vol. 13, no. 2, pp. 115–134, Oct. 2012.

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