We focus on an optimization problem on parameterized surfaces of genus one. In particular we trade off the penalty functions for bending a toroidal path and for applying a twist to it and aim to find local minima of this cost function. This analysis forms a key element in demonstrating the different regular homotopy classes of tori. A generalization of this surface optimization, which considers curvature as well as any shearing of its parameter grid, may be used to find the most optimal direct path from an arbitrary closed manifold of genus one into one of the four basic representatives of the four regular homotopy classes of tori.
Title
Bending and Torsion Minimization of Toroidal Loops
Published
2012-06-08
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
Other Identifiers
EECS-2012-165
Type
Text
Extent
15 p
Archive
The Engineering Library
Usage Statement
Researchers may make free and open use of the UC Berkeley Library’s digitized public domain materials. However, some materials in our online collections may be protected by U.S. copyright law (Title 17, U.S.C.). Use or reproduction of materials protected by copyright beyond that allowed by fair use (Title 17, U.S.C. § 107) requires permission from the copyright owners. The use or reproduction of some materials may also be restricted by terms of University of California gift or purchase agreements, privacy and publicity rights, or trademark law. Responsibility for determining rights status and permissibility of any use or reproduction rests exclusively with the researcher. To learn more or make inquiries, please see our permissions policies (https://www.lib.berkeley.edu/about/permissions-policies).
