Computational Topology Counterexamples with 3D Visualization of Bézier Curves
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 b...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Universitat Politècnica de València
2012-10-01
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| Series: | Applied General Topology |
| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/1624 |
| Summary: | 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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| ISSN: | 1576-9402 1989-4147 |