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Parametric self-supporting surfaces via direct computation of airy stress functions

Miki M., Igarashi T. and Block P.
ACM Transactions on Graphics - SIGGRAPH 2015
ACM
New York, NY, USA
2015
doi: 10.1145/2766888

This paper presents a method that employs parametric surfaces as surface geometry representations at any stage of a computational process to compute self-supporting surfaces. This approach can be differentiated from existing relevant methods because such methods represent surfaces by a triangulated mesh surface or a network consisting of lines. The proposed method is based on the theory of Airy stress functions. Although some existing methods are also based on this theory, they apply its discrete version to discrete geometries. The proposed method simultaneously applies the theory to parametric surfaces directly and the discrete theory to the edges of parametric patches. The discontinuous boundary between continuous patches naturally corresponds to ribs seen in traditional vault masonry buildings. We use non-uniform rational B-spline surfaces in this study; however, the basic idea can be applied to other parametric surfaces. A variety of self-supporting surfaces obtained by the proposed computational scheme is presented.

BibTeX

@article{Miki2015,
    author  = "Miki, M. and Igarashi, T. and Block, P. ",
    title   = "Parametric self-supporting surfaces via direct computation of airy stress functions",
    journal = "ACM Transactions on Graphics - SIGGRAPH 2015",
    year    = "2015",
    volume  = "34",
    number  = "4",
    pages   = "89:1-11",
    month   = "",
    doi     = "10.1145/2766888",
    note    = "",
}

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