Abstract
In 1978 Doo and Sabin presented a generalization of the subdivision algorithm for biquadratic tensor product splines. Simultaneously, Catmull and Clark presented a similar generalization for bicubic splines. Their algorithms can be applied to arbitrary quadrilateral control nets and yield sequences of control nets that converge to piecewise biquadratic or bicubic surfaces with finitely many so-called extraordinary points.
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© 2002 Springer-Verlag Berlin Heidelberg
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Prautzsch, H., Boehm, W., Paluszny, M. (2002). Stationary subdivision for arbitrary nets. In: Bézier and B-Spline Techniques. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04919-8_16
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DOI: https://doi.org/10.1007/978-3-662-04919-8_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07842-2
Online ISBN: 978-3-662-04919-8
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