A Trust Region Method for Constructing Triangle-mesh Approximations of Parametric Minimal Surfaces
نویسنده
چکیده
Given a function f0 defined on the unit square Ω with values in R, we construct a piecewise linear function f on a triangulation of Ω such that f agrees with f0 on the boundary nodes, and the image of f has minimal surface area. The problem is formulated as that of minimizing a discretization of a least squares functional whose critical points are uniformly parameterized minimal surfaces. The nonlinear least squares problem is treated by a trust region method in which the trust region radius is defined by a stepwise-variable Sobolev metric. Test results demonstrate the effectiveness of the method. keywords: minimal surface; triangle mesh; trust region; variable metric method
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