By Dr. E. Kamke
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Clearly, any three planes parallel to the three faces (which are assumed to be mutually diﬀerent) sharing a given vertex intersect in a single point, and the existence of oﬀset structures is therefore guaranteed. The constructions described below are capable of producing meshes with exactly planar faces, as they work without numerical optimization. The remainder of this paper is organized as follows. The next section presents some background information about shell structures in architectural design.
Another technique allows fully regular quadrilateral meshes (except along a seam) through the use of holomorphic discrete 1-forms [GY03]. Unfortunately, this holomorphic requirement leaves little control over the local alignment of the mesh elements and creates potentially large area distortion, even after optimization [JWYG04]. A recent technique proposes a radically diﬀerent approach to conformal parameterization with arbitrary cone singularities [KSS06]: distortion is concentrated at carefully chosen places so as to allow better, global control of area distortion and hence over mesh sizing.
Subdivision methods for 2d and 3d implicit curves. In: Computational Methods for Algebraic Spline Surfaces, pp. 171–186. fr/inria-00130216 28. : Meshing implicit algebraic surfaces: the smooth case. L. ) Mathematical Methods for Curves and Surfaces: Tromso’04, Nashboro, pp. 11–26 (2005) 29. : Curves and surfaces for computer aided geometric design: a practical guide. Comp. science and sci. computing. Academic Press, Boston, MA (1990) 30. : Real algebraic numbers: Complexity analysis and experimentations.