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BIARCS, GLOBAL RADIUS OF CURVATURE, AND THE COMPUTATION OF IDEAL KNOT SHAPES

2005; World Scientific; Linguagem: Inglês

10.1142/9789812703460_0005

0219-9769

Mathias Carlen, Ben Laurie, John H. Maddocks, J. Smutny,

Computational Geometry and Mesh Generation

Series on Knots and EverythingPhysical and Numerical Models in Knot Theory, pp. 75-108 (2005) No AccessBIARCS, GLOBAL RADIUS OF CURVATURE, AND THE COMPUTATION OF IDEAL KNOT SHAPESM. Carlen, B. Laurie, J. H. Maddocks, and J. SmutnyM. CarlenInstitute of Mathematics B, Swiss Federal Institute of Technology, Lausanne, CH-1015, Switzerland, B. Laurie17 Perryn Road, London, W3 7LR, England, J. H. MaddocksInstitute of Mathematics B, Swiss Federal Institute of Technology, Lausanne, CH-1015, Switzerland, and J. SmutnyInstitute of Mathematics B, Swiss Federal Institute of Technology, Lausanne, CH-1015, Switzerlandhttps://doi.org/10.1142/9789812703460_0005Cited by:21 (Source: Crossref) PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: We combine the global radius of curvature characterisation of knot thickness, the biarc discretisation of space curves, and simulated annealing code to compute approximations to the ideal shapes of the trefoil and figure-eight knots. The computations contain no discretisation error, and give rigorous lower bounds on thickness of the true ideal shapes. The introduction of a precise definition of a contact set for an approximately ideal shape allows us to resolve previously unobserved features. 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