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Fairing of discrete planar curves by discrete Euler's elasticae

Sebastián Elías Graiff Zurita, Kenji Kajiwara
2019 JSIAM Letters  
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
more » ... so that we use a discrete analogue of the algorithm provided by Brander et al., which gives an initial guess to the optimization method.
doi:10.14495/jsiaml.11.73 fatcat:mzp7hcqbcrhj7pvhfxs72datju