De Casteljau's algorithm is an extrapolation method

C. Carstensen; G. Mühlbach; G. Schmidt

doi:10.1016/0167-8396(94)00020-S

De Casteljau's algorithm is an extrapolation method

C. Carstensen
, G. Mühlbach^*
, G. Schmidt

^*Corresponding author for this work

Institute of Applied Mathematics

Research output: Contribution to journal › Article › Research › peer review

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.

Original language	English
Pages (from-to)	371-380
Number of pages	10
Journal	Computer aided geometric design
Volume	12
Issue number	4
DOIs	https://doi.org/10.1016/0167-8396(94)00020-S
Publication status	Published - Jun 1995

Keywords

Bernstein polynomials
CAGD
De Casteljau's algorithm
E-algorithm
Extrapolation algorithms
GNA-algorithm
Recurrence scheme

ASJC Scopus subject areas

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

Access to Document

10.1016/0167-8396(94)00020-S

Cite this

@article{d6e7195899854b4a9876d5d6191bb3d5,

title = "De Casteljau's algorithm is an extrapolation method",

abstract = "One of the most important recursive schemes in CAGD is De Casteljau's algorithm for the evaluation of B{\'e}zier 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",

author = "C. Carstensen and G. M{\"u}hlbach and G. Schmidt",

year = "1995",

month = jun,

doi = "10.1016/0167-8396(94)00020-S",

language = "English",

volume = "12",

pages = "371--380",

journal = "Computer aided geometric design",

issn = "0167-8396",

publisher = "Elsevier BV",

number = "4",

}

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 - https://www.scopus.com/pages/publications/0029323577

U2 - 10.1016/0167-8396(94)00020-S

DO - 10.1016/0167-8396(94)00020-S

M3 - Article

AN - SCOPUS:0029323577

SN - 0167-8396

VL - 12

SP - 371

EP - 380

JO - Computer aided geometric design

JF - Computer aided geometric design

IS - 4

ER -

De Casteljau's algorithm is an extrapolation method

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this