De Casteljauʹs algorithm is an extrapolation method Original Research Article

One of the most important recursive schemes in CAGD is De Casteljauʹs algorithm for the evaluation of Bézier curves and surfaces. Within the theory of triangular recursive schemes we discuss the De Casteljauʹs algorithm as a particular case, i.e. we prove that it is identical to the E-algorithm (or GNA-algorithm) in a particular frame. This result is of theoretical interest since it leads to some classification of recurrence relations in CAGD. Furthermore, it may be regarded as a model example how to obtain known and possibly new recursive schemes in CAGD as examples of the theory of general extrapolation algorithms.