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| ASCII Text | x | ||
| Jason Cantarella, Michael Piatek, Eric Rawdon, "Visualizing the tightening of knots," Visualization Conference, IEEE, pp. 73, 16th IEEE Visualization 2005 (VIS 2005), 2005. | |||
| BibTex | x | ||
| @article{ 10.1109/VIS.2005.129, author = {Jason Cantarella and Michael Piatek and Eric Rawdon}, title = {Visualizing the tightening of knots}, journal ={Visualization Conference, IEEE}, volume = {0}, year = {2005}, isbn = {0-7803-9462-3}, pages = {73}, doi = {http://doi.ieeecomputersociety.org/10.1109/VIS.2005.129}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - CONF JO - Visualization Conference, IEEE TI - Visualizing the tightening of knots SN - 0-7803-9462-3 SP EP A1 - Jason Cantarella, A1 - Michael Piatek, A1 - Eric Rawdon, PY - 2005 KW - collision detection KW - contact KW - flexible models KW - tight knots KW - ideal knots KW - ropelength KW - nonlinear optimization KW - constrained least squares VL - 0 JA - Visualization Conference, IEEE ER - | |||
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.