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Subdivision rules for general meshes. (English) Zbl 1036.65019

Cohen, Albert (ed.) et al., Curve und surface fitting, Saint-Malo 2002. Fifth international conference on curves and surfaces, Saint-Malo, France, June 27 – July 3, 2002. Brentwood, TN: Nashboro Press (ISBN 0-9728482-1-5/hbk). Modern Methods in Mathematics, 229-237 (2003).
Summary: We show that in many subdivision schemes, a single step can be described as the composition of several simpler steps. Usually, such a composition consists of steps increasing the complexity of the mesh, followed by an alternating step (duality) where the primitives of the mesh, i.e. vertices, edges, and faces, map to each other. The advantages of this approach over more traditional descriptions of the subdivision are the simpler implementation, the generality, and a new insight into the subdivision process.
For the entire collection see [Zbl 1023.00023].

MSC:

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
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