TY - JOUR
AU - Li, Ji
AU - Peters, T. J.
AU - Marsh, D.
AU - Jordan, K. E.
PY - 2012/10/01
Y2 - 2022/11/29
TI - Computational Topology Counterexamples with 3D Visualization of Bézier Curves
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 13
IS - 2
SE -
DO - 10.4995/agt.2012.1624
UR - https://polipapers.upv.es/index.php/AGT/article/view/1624
SP - 115-134
AB - 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.
ER -