Details
| Original language | English |
|---|---|
| Pages (from-to) | 371-380 |
| Number of pages | 10 |
| Journal | Computer aided geometric design |
| Volume | 12 |
| Issue number | 4 |
| Publication status | Published - Jun 1995 |
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.
Keywords
- Bernstein polynomials, CAGD, De Casteljau's algorithm, E-algorithm, Extrapolation algorithms, GNA-algorithm, Recurrence scheme
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- Automotive Engineering
- Engineering(all)
- Aerospace Engineering
- Computer Science(all)
- Computer Graphics and Computer-Aided Design
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In: Computer aided geometric design, Vol. 12, No. 4, 06.1995, p. 371-380.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - De Casteljau's algorithm is an extrapolation method
AU - Carstensen, C.
AU - Mühlbach, G.
AU - Schmidt, G.
PY - 1995/6
Y1 - 1995/6
N2 - 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.
AB - 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.
KW - Bernstein polynomials
KW - CAGD
KW - De Casteljau's algorithm
KW - E-algorithm
KW - Extrapolation algorithms
KW - GNA-algorithm
KW - Recurrence scheme
UR - http://www.scopus.com/inward/record.url?scp=0029323577&partnerID=8YFLogxK
U2 - 10.1016/0167-8396(94)00020-S
DO - 10.1016/0167-8396(94)00020-S
M3 - Article
AN - SCOPUS:0029323577
VL - 12
SP - 371
EP - 380
JO - Computer aided geometric design
JF - Computer aided geometric design
SN - 0167-8396
IS - 4
ER -