Convergence of subdivision and degree elevation

Hartmut Prautzsch, Leif Kobbelt
Adv. Comp. Math. 2 (1994), J.C. Baltzer, pp. 143-154

This paper presents a short, simple, and general proof showing that the control polygons generated by subdivision and degree elevation converge to the underlying splines, box-splines, or multivariate Bézier polynomials, respectively. The proof is based only on a Taylor expansion. Then the results are carried over to rational curves and surfaces. Finally, an even shorter but as simple proof is presented for the fact that subdivided Bézier polygons converge to the corresponding curve.

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