Surfaces with piecewise linear support functions over spherical triangulations. (English) Zbl 1163.68344

Almegaard, Henrik; Bagger, Anne; Gravesen, Jens; Jüttler, Bert; Šír, Zbynek

Martin, Ralph (ed.) et al., Mathematics of surfaces XII. 12th IMA international conference, Sheffield, UK, September 4–6, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-73842-8/pbk). Lecture Notes in Computer Science 4647, 42-63 (2007).

Summary: Given a smooth surface patch we construct an approximating piecewise linear structure. More precisely, we produce a mesh for which virtually all vertices have valency three. We present two methods for the construction of meshes whose facets are tangent to the original surface. These two methods can deal with elliptic and hyperbolic surfaces, respectively. In order to describe and to derive the construction, which is based on a projective duality, we use the so-called support function representation of the surface and of the mesh, where the latter one has a piecewise linear support function.
For the entire collection see [Zbl 1122.68007].

MSC:

68U05	Computer graphics; computational geometry (digital and algorithmic aspects)
65D18	Numerical aspects of computer graphics, image analysis, and computational geometry
52C99	Discrete geometry