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Computational topology for approximations of knots

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Computational topology for approximations of knots

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Li, J.; Peters, TJ.; Jordan, KE. (2014). Computational topology for approximations of knots. Applied General Topology. 15(2):203-220. https://doi.org/10.4995/agt.2014.2281

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/43628

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Title: Computational topology for approximations of knots
Author: Li, Ji Peters, T. J. Jordan, K. E.
Issued date:
Abstract:
[EN] 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 ...[+]
Subjects: Knot approximation , Ambient isotopy , Bézier curve , Subdivision , Piecewise linear approximation
Copyrigths: Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
Source:
Applied General Topology. (issn: 1576-9402 ) (eissn: 1989-4147 )
DOI: 10.4995/agt.2014.2281
Publisher:
Editorial Universitat Politècnica de València
Publisher version: https://doi.org/10.4995/agt.2014.2281
Project ID:
info:eu-repo/grantAgreement/NSF//1053077/US/EAGER: Visualization of Protein Folding for Nano-Machine Design/
info:eu-repo/grantAgreement/NSF//0923158/US/MRI: Development of a Gesture Based Virtual Reality System for Research in Virtual Worlds/
Thanks:
The first, two authors acknowledge, with appreciation, partial support from NSF Grants 1053077 and 0923158 and also from IBM. The findings presented are the responsibility of these authors, not of the funding programs.
Type: Artículo

References

Amenta, N., Peters, T. J., & Russell, A. C. (2003). Computational topology: ambient isotopic approximation of 2-manifolds. Theoretical Computer Science, 305(1-3), 3-15. doi:10.1016/s0304-3975(02)00691-6

L. E. Andersson, S. M. Dorney, T. J. Peters and N. F. Stewart, Polyhedral perturbations that preserve topological form, CAGD 12, no. 8 (1995), 785-799.

Burr, M., Choi, S. W., Galehouse, B., & Yap, C. K. (2012). Complete subdivision algorithms, II: Isotopic meshing of singular algebraic curves. Journal of Symbolic Computation, 47(2), 131-152. doi:10.1016/j.jsc.2011.08.021 [+]
Amenta, N., Peters, T. J., & Russell, A. C. (2003). Computational topology: ambient isotopic approximation of 2-manifolds. Theoretical Computer Science, 305(1-3), 3-15. doi:10.1016/s0304-3975(02)00691-6

L. E. Andersson, S. M. Dorney, T. J. Peters and N. F. Stewart, Polyhedral perturbations that preserve topological form, CAGD 12, no. 8 (1995), 785-799.

Burr, M., Choi, S. W., Galehouse, B., & Yap, C. K. (2012). Complete subdivision algorithms, II: Isotopic meshing of singular algebraic curves. Journal of Symbolic Computation, 47(2), 131-152. doi:10.1016/j.jsc.2011.08.021

Chazal, F., & Cohen-Steiner, D. (2005). A condition for isotopic approximation. Graphical Models, 67(5), 390-404. doi:10.1016/j.gmod.2005.01.005

W. Cho, T. Maekawa and N. M. Patrikalakis, Topologically reliable approximation in terms of homeomorphism of composite Bézier curves, CAGD 13 (1996), 497-520.

Denne, E., & Sullivan, J. M. (2008). Convergence and Isotopy Type for Graphs of Finite Total Curvature. Discrete Differential Geometry, 163-174. doi:10.1007/978-3-7643-8621-4_8

G. E. Farin, Curves and surfaces for computer-aided geometric design: A practical code, Academic Press, Inc., 1996.

Hirsch, M. W. (1976). Differential Topology. Graduate Texts in Mathematics. doi:10.1007/978-1-4684-9449-5

J. Li, T. J. Peters, D. Marsh and K. E. Jordan, Computational topology counterexamples with 3D visualization of Bézier curves, Applied General Topology 13, no. 2 (2012), 115-134.

Lin, L., & Yap, C. (2011). Adaptive Isotopic Approximation of Nonsingular Curves: the Parameterizability and Nonlocal Isotopy Approach. Discrete & Computational Geometry, 45(4), 760-795. doi:10.1007/s00454-011-9345-9

T. Maekawa, N. M. Patrikalakis, T. Sakkalis and G. Yu, Analysis and applications of pipe surfaces, CAGD 15, no. 5 (1998), 437-458.

Milnor, J. W. (1950). On the Total Curvature of Knots. The Annals of Mathematics, 52(2), 248. doi:10.2307/1969467

G. Monge, Application de l'analyse à la géométrie, Bachelier, Paris, 1850.

Moore, E. L. F., Peters, T. J., & Roulier, J. A. (2007). Preserving computational topology by subdivision of quadratic and cubic Bézier curves. Computing, 79(2-4), 317-323. doi:10.1007/s00607-006-0208-9

G. Morin and R. Goldman, On the smooth convergence of subdivision and degree elevation for Bézier curves, CAGD 18 (2001), 657-666.

J. Munkres, Topology, Prentice Hall, 2nd edition, 1999.

D. Nairn, J. Peters and D. Lutterkort, Sharp, quantitative bounds on the distance between a polynomial piece and its Bézier control polygon, CAGD 16 (1999), 613-63.

Reid, M., & Szendroi, B. (2005). Geometry and Topology. doi:10.1017/cbo9780511807510

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