In this paper, a class of algorithms for the high order geometric motion of planar curves is developed. The algorithms alternate two simple steps—a convolution and a thresholding step—to evolve planar curves according to combinations of Willmore flow, surface diffusion flow and curvature motion. A distinguishing feature of the methods is that they posses much better stability than typical explicit algorithms. Formal expansions and numerical examples are provided for a variety of high order flows to validate the methods and illustrate their behaviors.
Selim Esedoglu
1
;
Steven J. Ruuth
2
;
Richard Tsai
3
1
University of Michigan, Ann Arbor, United States
2
Simon Fraser University, Burnaby, Canada
3
University of Texas at Austin, United States
Selim Esedoglu; Steven J. Ruuth; Richard Tsai. Threshold dynamics for high order geometric motions. Interfaces and free boundaries, Tome 10 (2008) no. 3, pp. 263-282. doi: 10.4171/ifb/189
@article{10_4171_ifb_189,
author = {Selim Esedoglu and Steven J. Ruuth and Richard Tsai},
title = {Threshold dynamics for high order geometric motions},
journal = {Interfaces and free boundaries},
pages = {263--282},
year = {2008},
volume = {10},
number = {3},
doi = {10.4171/ifb/189},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/189/}
}
TY - JOUR
AU - Selim Esedoglu
AU - Steven J. Ruuth
AU - Richard Tsai
TI - Threshold dynamics for high order geometric motions
JO - Interfaces and free boundaries
PY - 2008
SP - 263
EP - 282
VL - 10
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/189/
DO - 10.4171/ifb/189
ID - 10_4171_ifb_189
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%A Richard Tsai
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%J Interfaces and free boundaries
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%P 263-282
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%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/189/
%R 10.4171/ifb/189
%F 10_4171_ifb_189
