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Merriman, Barry; Ruuth, Steven J.

Diffusion generated motion of curves on surfaces. (English) Zbl 1123.65011

J. Comput. Phys. 225, No. 2, 2267-2282 (2007).
Summary: We present a new method for computing the curvature-driven motion of a curve constrained to move on a given surface. It is based on the diffusion generated motion algorithm, and retains both the novel simplicity of that method, as well as the natural extension to curves with junctions, to general geometric motion laws, and to higher dimensions. The result is an extremely simple algorithm for curvature-dependent motion on surfaces, wherein the only evolution operation is linear diffusion in three-dimensional Euclidean space.

Cited in 15 Documents

MSC:

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry

Keywords:

diffusion generated motion; curvature motion; implicit surfaces; diffusion; closest point representation; numerical examples; algorithm

Software:

Surface Evolver
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Full Text: DOI

References:

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