NDLI: Visualizing the tightening of knots

Content Provider	IEEE Xplore Digital Library
Author	Cantarella, J. Piatek, M. Rawdon, E.
Copyright Year	2005
Description	Author affiliation: Georgia Univ., Athens, GA, USA (Cantarella, J.)
Abstract	The study of physical models for knots has recently received much interest in the mathematics community. In this paper, we consider the ropelength model, which considers knots tied in an idealized rope. This model is interesting in pure mathematics, and has been applied to the study of a variety of problems in the natural sciences as well. Modeling and visualizing the tightening of knots in this idealized rope poses some interesting challenges in computer graphics. In particular, self-contact in a deformable rope model is a difficult problem which cannot be handled by standard techniques. In this paper, we describe a solution based on reformulating the contact problem and using constrained-gradient techniques from nonlinear optimization. The resulting animations reveal new properties of the tightening flow and provide new insights into the geometric structure of tight knots and links.
Starting Page	575
Ending Page	582
File Size	3230211
Page Count	8
File Format	PDF
ISBN	0780394623
DOI	10.1109/VISUAL.2005.1532844
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2005-10-23
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Mathematical model Deformable models Mathematics Computer graphics Constraint optimization Solid modeling Application software Computational modeling Data visualization Animation
Content Type	Text
Resource Type	Article

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2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
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