J.Li
∗
T.J.Peters
†‡
June 4, 2012
Abstract
Ambient isotopy requires a homeomorphism to the initial configuration at each instant of time during deformations. This continued equivalence over time is particularly important for applications in computer visualization synchronized to simulations of geometric models, such as writhing of molecules. We select ambient isotopy as a more appropriate equivalence relation for time varying models than the standard topological equivalence given by homeomorphism. We provide sufficient conditions that guarantee both homeomorphism and ambient isotopy of geometric approximations. This relies on both local and global knotting structures. To apply this result, we particularly choose duce topologically reliable approximations, where we give both convergence rates, and closed-form formulas for finding explicit numbers of subdivision iterations.
∗
Department of Mathematics, University of Connecticut, Storrs, ji.li@uconn.edu
†
Department of Mathematics, Department of Computer Science and Engineering, University of Connecticut, Storrs, tpeters@cse.uconn.edu
‡
This author was partially supported by NSF grants CCF 0429477, CMMI 1053077 and CNS 0923158.
All statements here are the responsibility of the author, not of the National Science Foundation.
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