De Casteljau's algorithm is an extrapolation method

authored by

C. Carstensen, G. Mühlbach, G. Schmidt

Abstract

One of the most important recursive schemes in CAGD is De Casteljau's algorithm for the evaluation of Bézier curves and surfaces. Within the theory of triangular recursive schemes we discuss the De Casteljau's 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.

Organisation(s)

Institute of Applied Mathematics

Type

Article

Journal

Computer aided geometric design

Volume

12

Pages

371-380

No. of pages

10

ISSN

0167-8396

Publication date

06.1995

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Modelling and Simulation, Automotive Engineering, Aerospace Engineering, Computer Graphics and Computer-Aided Design

Electronic version(s)

https://doi.org/10.1016/0167-8396(94)00020-S (Access: Closed)