## 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

### Keywords:

cubic B-splines; $$C^2$$-splines
Full Text:

### References:

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