Computational Topology Counterexamples with 3D Visualization of Bézier Curves

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...

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Main Authors: J. Li, T.J. Peters, D. Marsh, K.E. Jordan
Format: Article
Language:English
Published: Universitat Politècnica de València 2012-10-01
Series:Applied General Topology
Online Access:http://polipapers.upv.es/index.php/AGT/article/view/1624
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spelling doaj-451a6eee87964432a4dff77f0a125ba72020-11-24T22:42:41ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472012-10-0113211513410.4995/agt.2012.16241326Computational Topology Counterexamples with 3D Visualization of Bézier CurvesJ. Li0T.J. Peters1D. Marsh2K.E. Jordan3University of ConnecticutUniversity of ConnecticutPratt and WhitneyIBM T.J. Watson Research, Cambridge Research CenterFor 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.http://polipapers.upv.es/index.php/AGT/article/view/1624
collection DOAJ
language English
format Article
sources DOAJ
author J. Li
T.J. Peters
D. Marsh
K.E. Jordan
spellingShingle J. Li
T.J. Peters
D. Marsh
K.E. Jordan
Computational Topology Counterexamples with 3D Visualization of Bézier Curves
Applied General Topology
author_facet J. Li
T.J. Peters
D. Marsh
K.E. Jordan
author_sort J. Li
title Computational Topology Counterexamples with 3D Visualization of Bézier Curves
title_short Computational Topology Counterexamples with 3D Visualization of Bézier Curves
title_full Computational Topology Counterexamples with 3D Visualization of Bézier Curves
title_fullStr Computational Topology Counterexamples with 3D Visualization of Bézier Curves
title_full_unstemmed Computational Topology Counterexamples with 3D Visualization of Bézier Curves
title_sort computational topology counterexamples with 3d visualization of bézier curves
publisher Universitat Politècnica de València
series Applied General Topology
issn 1576-9402
1989-4147
publishDate 2012-10-01
description 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.
url http://polipapers.upv.es/index.php/AGT/article/view/1624
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AT dmarsh computationaltopologycounterexampleswith3dvisualizationofbeziercurves
AT kejordan computationaltopologycounterexampleswith3dvisualizationofbeziercurves
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