分野別セミナー

Abstract:
After characterizing the discrete Euler’s elastica proposed by Sogo (“Variational discretization of Euler’s Elastica problem”, 2006), we consider the problem of approximating a given discrete plane curve by an appropriate discrete Euler’s elastica, according to a suitable criteria. We have decided to do the approximation process via a L2-distance minimization, because other approaches presented numerical instabilities. The optimization problem was solved via a gradient-driven optimization method (IPOPT). This optimization problem is non-convex and the result strongly depends on the initial guess. So, we have decided to discretize the algorithm provided by Brander et al. (“Approximation by planar elastic curves”, 2016), which gives an initial guess to the IPOPT method.