Читать книгу Rethinking Prototyping - Группа авторов - Страница 133

Experience in building free-formed envelopes show that single curved elements are much easier to design, to produce and to install than general, double curved panels (Shelden 2002) or (Glaeser and Gruber 2007) even though there has been great improvement in the design of double curved molds (Raun et al 2012) and their repetitive use (Eigensatz et al 2010).

The focus of research over the last ten years has been planar panels, which can either be constructed directly (Glymph et al 2004), optimized from curve networks (Liu et al 2011) or by a physics based approach (Piker 2012). All optimization frameworks share a strong dependency on a good starting value, which determines aesthetics and convergence. Note that the four corners of the conical panels presented in this work already lie in a plane, so planarization is an inherent feature of the method.

The class of developable surfaces subsumes general cones, cylinders and tangent surfaces to a space curve. Numerous papers have dealt with the task of approximating a general shape with a developable surface (e.g. Aumann 2004, Chu and Séquin 2002, Frey 2004 or Liu et al 2006), but most of them require a computational framework to solve non-linear equations or insights into mathematical optimization, (Pottmann et al 2008) or (Zadravec et al 2010) that are not readily available for the practitioner. In computer graphics most papers use triangular meshes to compute developable surfaces (Rose et al 2007), (Julius et al 2005) or (Wang and Tang 2004) but ruling directions play no significant role.