Computational Topology Counterexamples with 3D Visualization of Bézier Curves

• Li, J. ^[1] ; Peters, T.J. ^[1] ; Marsh, D. ^[2] ; Jordan, K.E. ^[3]
  1. [1] University of Connecticut

     University of Connecticut

     Town of Mansfield, Estados Unidos

     
  2. [2] Pratt and Whitney
  3. [3] IBM T.J. Watson Research, Cambridge Research Center

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• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 13, Nº. 2, 2012, págs. 115-134
• Idioma: inglés
• DOI: 10.4995/agt.2012.1624
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• Resumen

  • 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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