Computational topology for approximations of knots
The preservation of ambient isotopic equivalence under piecewise linear (PL) approximation for smooth knots are prominent in molecular modeling and simulation. Sufficient conditions are given regarding: • Hausdorff distance, and • a sum of total curvature and derivative. High degree Bézier curves a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2014-10-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/2281 |
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| author | Ji Li T. J. Peters K. E. Jordan |
| author_facet | Ji Li T. J. Peters K. E. Jordan |
| author_sort | Ji Li |
| collection | DOAJ |
| description | The preservation of ambient isotopic equivalence under piecewise linear (PL) approximation for smooth knots are prominent in molecular modeling and simulation. Sufficient conditions are given regarding:
• Hausdorff distance, and
• a sum of total curvature and derivative.
High degree Bézier curves are often used as smooth representations, where computational efficiency is a practical concern. Subdivision can produce PL approximations for a given B\'ezier curve, fulfilling the above two conditions. The primary contributions are:
(i) a priori bounds on the number of subdivision iterations sufficient to achieve a PL approximation that is ambient isotopic to the original B\'ezier curve, and
(ii) improved iteration bounds over those previously established. |
| first_indexed | 2024-12-12T14:33:08Z |
| format | Article |
| id | doaj.art-a89dbdcf12b44cf49fccd1f6f412e5f7 |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-12-12T14:33:08Z |
| publishDate | 2014-10-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-a89dbdcf12b44cf49fccd1f6f412e5f72022-12-22T00:21:27ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472014-10-0115220322010.4995/agt.2014.22811793Computational topology for approximations of knotsJi Li0T. J. Peters1K. E. Jordan2University of ConnecticutUniversity of ConnecticutCambridge Research CenterThe preservation of ambient isotopic equivalence under piecewise linear (PL) approximation for smooth knots are prominent in molecular modeling and simulation. Sufficient conditions are given regarding: • Hausdorff distance, and • a sum of total curvature and derivative. High degree Bézier curves are often used as smooth representations, where computational efficiency is a practical concern. Subdivision can produce PL approximations for a given B\'ezier curve, fulfilling the above two conditions. The primary contributions are: (i) a priori bounds on the number of subdivision iterations sufficient to achieve a PL approximation that is ambient isotopic to the original B\'ezier curve, and (ii) improved iteration bounds over those previously established.http://polipapers.upv.es/index.php/AGT/article/view/2281Knot approximationambient isotopyBézier curvesubdivisionpiecewise linear approximation. |
| spellingShingle | Ji Li T. J. Peters K. E. Jordan Computational topology for approximations of knots Applied General Topology Knot approximation ambient isotopy Bézier curve subdivision piecewise linear approximation. |
| title | Computational topology for approximations of knots |
| title_full | Computational topology for approximations of knots |
| title_fullStr | Computational topology for approximations of knots |
| title_full_unstemmed | Computational topology for approximations of knots |
| title_short | Computational topology for approximations of knots |
| title_sort | computational topology for approximations of knots |
| topic | Knot approximation ambient isotopy Bézier curve subdivision piecewise linear approximation. |
| url | http://polipapers.upv.es/index.php/AGT/article/view/2281 |
| work_keys_str_mv | AT jili computationaltopologyforapproximationsofknots AT tjpeters computationaltopologyforapproximationsofknots AT kejordan computationaltopologyforapproximationsofknots |