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arXiv · 1911.04615

Fairing of Discrete Planar Curves by Discrete Euler's Elasticae

Sebastián Elías Graiff Zurita·Kenji Kajiwara
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Abstract

After characterizing the integrable discrete analogue of the Euler's elastica, we focus our attention on the problem of approximating a given discrete planar curve by an appropriate discrete Euler's elastica. We carry out the fairing process via a $L^2\!$-distance minimization to avoid the numerical instabilities. The optimization problem is solved via a gradient-driven optimization method (IPOPT). This problem is non-convex and the result strongly depends on the initial guess, so that we use a discrete analogue of the algorithm provided by Brander et al., which gives an initial guess to the optimization method.

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Sebastián Elías Graiff Zurita, Kenji Kajiwara. 2019-11-11. Fairing of Discrete Planar Curves by Discrete Euler's Elasticae. https://doi.org/10.14495/jsiaml.11.73

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