Parametric Self-supporting Surfaces via Direct Computation of Airy Stress Functions

摘要

This paper presents a method that employs parametric surfaces asrnsurface geometry representations at any stage of a computationalrnprocess to compute self-supporting surfaces. This approach can berndifferentiated from existing relevant methods because such methodsrnrepresent surfaces by a triangulated mesh surface or a network con-rnsisting of lines. The proposed method is based on the theory of Airyrnstress functions. Although some existing methods are also basedrnon this theory, they apply its discrete version to discrete geome-rntries. The proposed method simultaneously applies the theory tornparametric surfaces directly and the discrete theory to the edges ofrnparametric patches. The discontinuous boundary between contin-rnuous patches naturally corresponds to ribs seen in traditional vaultrnmasonry buildings. We use nonuniform rational B-spline surfacesrnin this study; however, the basic idea can be applied to other para-rnmetric surfaces. A variety of self-supporting surfaces obtained byrnthe proposed computational scheme is presented.