ISSN 2079-3537      

 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             

Scientific Visualization, 2021, volume 13, number 1, pages 54 - 68, DOI: 10.26583/sv.13.1.05

Minimal Surface Form Finding and Visualization using Stretched Grid Method

Authors: E.V. Popov1,A, T.P. Popova2,B

A Nizhegorodsky State Architectural and Civil Engineering University

B National Research University Higher School of Economics

1 ORCID: 0000-0002-3058-2369, popov_eugene@list.ru

2 ORCID: 0000-0002-1351-222X, tatpop@list.ru

 

Abstract

Geometric and computational approach based on the theory of Stretched Grid Method (SGM) has been developed for the minimal surfaces form finding. For example, SGM is advantageous for engineering problem solution relative to an arbitrary tensile fabric structures design in comparison with other approaches. The SGM fundamental properties concerning convergence of the method and applicability have been proved in this paper. The proof is based on the theorem about the first surface quadratic form behavior together with convergence to minimum surface area. An efficient computer procedure based on the approach described in this paper has been worked out. The procedure is included into CAD system aimed at tensile fabric structures designing.

 

Keywords: Minimal surface, first surface quadratic form, Stretched Grid Method, Tensile fabric structure.