Visualizing the tightening of knots

11 years 5 months ago
Visualizing the tightening of knots
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. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric al...
Jason Cantarella, Michael Piatek, Eric Rawdon
Added 25 Jun 2010
Updated 25 Jun 2010
Type Conference
Year 2005
Authors Jason Cantarella, Michael Piatek, Eric Rawdon
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