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Eigenanalysis and artifacts of subdivision curves and surfaces. (English) Zbl 1004.65025
Iske, Armin (ed.) et al., Tutorials on multiresolution in geometric modelling. European summer school lecture notes, Munich Univ. of Technology, Germany, August 22-30, 2001. Berlin: Springer. 69-92 (2002).
Summary: When refinement methods were first shown to be applicable to data which was not totally regular, an immediate question was ‘how does the limit surface behave around an extraordinary point?’. The technique of eigenanalysis was the answer then and is still the primary technique today.
An issue only now becoming seriously important with the wider use of refinement methods is whether the processes introduce artifacts into the limit surface not implied by the original data. Certainly some examples can be shown, where the artifacts are serious, and a major challenge for the immediate future is whether we can understand them well enough to tune our systems to avoid creating them, or, if not, at least to tell our users how to avoid problems when defining the data for a refinement surface.
For the entire collection see [Zbl 0989.00044].

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