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A subdivision scheme for surfaces of revolution. (English) Zbl 0970.68177

This paper describes a simple and efficient non-stationary subdivision scheme of order \(4.\) This curve scheme unifies known subdivision rules for cubic B-splines, splines-in-tension and a certain class of trigonometric splines capable of reproducing circles. The curves generated by this unified subdivision scheme are \(C^{2}\) splines whose segments are either polynomial, hyperbolic or trigonometric functions, depending on a single tension parameter. This curve scheme easily generalizes to a surface scheme over quadrilateral meshes. The authors hypothesize that this surface scheme produces limit surfaces that are \(C^{2}\) continuous everywhere except at extraordinary vertices where the surfaces are \(C^{1}\) continuous. In the particular case where the tension parameters are all set to \(1,\) the scheme reproduces a variant of the Catmull–Clark subdivision scheme. As an application, this scheme is used to generate surfaces of revolution from a given profile curve.

MSC:

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
68U10 Computing methodologies for image processing
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References:

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