DECASTELJAU ALGORITHM IS AN EXTRAPOLATION METHOD

被引：2

作者：

CARSTENSEN, C ^{[1
]}

MUHLBACH, G ^{[1
]}

SCHMIDT, G ^{[1
]}

机构：

[1] UNIV HANNOVER,INST ANGEW MATH,WELFENGARTEN 1,D-30167 HANNOVER,GERMANY

来源：

COMPUTER AIDED GEOMETRIC DESIGN | 1995年 / 12卷 / 04期

关键词：

GACD; RECURRENCE SCHEME; DECASTELJAU ALGORITHM; BERNSTEIN POLYNOMIALS; EXTRAPOLATION ALGORITHMS; E-ALGORITHM; GNA-ALGORITHM;

D O I：

10.1016/0167-8396(94)00020-S

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

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

引用

页码：371 / 380

页数：10

共 5 条

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[2]

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[3]

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[4]

Muhlbach, The general Neville-Aitken algorithm and some applications, Numer. Math., 31, pp. 97-110, (1978)

[5]

Muhlbach, On two algorithms for extrapolation with applications to numerical differentiation and integration, Padé Approximation and its Applications, 888, pp. 326-340, (1981)

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