Computational Topology Counterexamples with 3D Visualization of Bézier Curves

[EN] 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.This author was partially supported by NSF grants CCF 0429477, CMMI 1053077 and CNS 0923158, as well as by an IBM Faculty Award and IBM Doctoral Fellowships. All statements here are the responsibility of the author, not of the National Science Foundation nor of IBM.Li, J.; Peters, T.; Marsh, D.; Jordan, K. (2012). Computational Topology Counterexamples with 3D Visualization of Bézier Curves. Applied General Topology. 13(2):115-134. doi:10.4995/agt.2012.1624.11513413