Quasi-harmonic Bézier approximation of minimal surfaces for finding forms of structural membranes

A novel form-finding approach to construct minimal surface from a given boundary by quasi-harmonic Bezier approximation.Quasi-harmonic mask method to generate approximate minimal surfaces by solving a sparse linear system.A framework to construct multi-patch quasi-harmonic Bezier approximation from N-sided boundary curves. Numerical approximation of minimal surface is an important problem in form-finding of structural membranes. In this paper, we present a novel approach to construct minimal surface from a given boundary by quasi-harmonic Bezier approximation. A new energy functional called quasi-harmonic energy functional is proposed as the objective function to obtain the quasi-harmonic Bezier surface from given boundaries. The quasi-harmonic mask is also proposed to generate approximate minimal surfaces by solving a sparse linear system. We propose a framework to construct multi-patch quasi-harmonic Bezier approximation from N-sided boundary curves. The efficiency of the proposed methods is illustrated by several modeling examples.

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