Sobolev Gradients for the Möbius Energy

05/15/2020 ∙ by Philipp Reiter, et al. ∙ 0

Aiming at optimizing the shape of closed embedded curves within prescribed isotopy classes, we use a gradient-based approach to approximate stationary points of the Möbius energy. The gradients are computed with respect to Sobolev inner products similar to the W^3/2,2-inner product. This leads to optimization methods that are significantly more efficient and robust than standard techniques based on L^2-gradients.

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