Computational Topology Counterexamples with 3D Visualization of Bezier Curves
Geometric Topology
2012-11-15 v1
Abstract
For applications in computing, Bezier curves are pervasive and are defined by a piecewise linear curve L which is embedded in R^3 and yields a smooth polynomial curve C embedded in R^3. It is of interest to understand when L and C have the same embeddings. One class of counterexamples 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.
Keywords
Cite
@article{arxiv.1210.1867,
title = {Computational Topology Counterexamples with 3D Visualization of Bezier Curves},
author = {J. Li and T. J. Peters and D. Marsh and K. E. Jordan},
journal= {arXiv preprint arXiv:1210.1867},
year = {2012}
}
Comments
21 pages, 19 figures