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CAGD
2004

Shape characterization of subdivision surfaces--case studies

9 years 1 months ago
Shape characterization of subdivision surfaces--case studies
For subdivision surfaces, it is important to characterize local shape near flat spots and points where the surface is not twice continuously differentiable. Applying general principles derived in [PR0x], this paper characterizes shape near such points for the subdivision schemes devised by Catmull and Clark and by Loop. For generic input data, both schemes fail to converge to the hyperbolic or elliptic limit shape suggested by the geometry of the input mesh: the limit shape is a function of the valence of the extraordinary point rather than the mesh geometry. We characterize the meshes for which the schemes behave as expected and indicate modifications of the schemes that prevent convergence to the wrong shape. We also introduce a type of chart that, for a specific scheme, can help a designer to detect early when a mesh will lead to undesirable curvature behavior. Key words: subdivision surface, curvature, shape
Kestutis Karciauskas, Jörg Peters, Ulrich Rei
Added 16 Dec 2010
Updated 16 Dec 2010
Type Journal
Year 2004
Where CAGD
Authors Kestutis Karciauskas, Jörg Peters, Ulrich Reif
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