Implicitization of parametric curves via Lagrange interpolation

被引：6

作者：

Sun, Yongli ^{[1
]}

Yu, Jianping

机构：

[1] Beijing Univ Chem Technol, Sch Sci, Dept Math & Comp Sci, Beijing 100029, Peoples R China

[2] Univ Sci & Technol Beijing, Sch Appl Sci, Dept Math & Mechanizat, Beijing 100083, Peoples R China

来源：

COMPUTING | 2006年 / 77卷 / 04期

关键词：

implicitization; curve; Bezout resultant; Lagrange interpolation;

D O I：

10.1007/s00607-006-0163-5

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A simple algorithm for finding the implicit equation of a parametric plane curve given by its parametric equations is presented. The algorithm is based on an efficient computation of the Bezout resultant and Lagrange interpolation. One of main features of our approach is the fact that it considerably reduces the problem of computing intermediate expressions.

引用

页码：379 / 386

页数：8

共 28 条

[1] AN IMPLICITIZATION ALGORITHM WITH FEWER VARIABLES [J].

ALONSO, C ;

GUTIERREZ, J ;

RECIO, T .

COMPUTER AIDED GEOMETRIC DESIGN, 1995, 12 (03) :251-258

[2]

[Anonymous], 1996, CURVES SURFACES COMP

[3]

[Anonymous], 1998, USING ALGEBRAIC GEOM, DOI DOI 10.1007/978-1-4757-6911-1

[4]

Becker T., 1993, Graduate Texts in Mathematics

[5]

BUSE L, 2001, P 2001 INT S SYMB AL, P48

[6] IMPLICITIZATION OF SURFACES IN P3 IN THE PRESENCE OF BASE POINTS [J].

Buse, Laurent ;

Cox, David ;

D'Andrea, Carlos .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2003, 2 (02) :189-214

[7] The mu-basis of a rational ruled surface [J].

Chen, F ;

Zheng, JM ;

Sederberg, TW .

COMPUTER AIDED GEOMETRIC DESIGN, 2001, 18 (01) :61-72

[8]

Chionh E.-W., 1992, Mathematical Methods in Computer Aided Geometric Design, VII, P101

[9]

CORLESS RM, 2000, ART INTEL SYMB COMP, P174

[10] On the validity of implicitization by moving quadrics for rational surfaces with no base points [J].

Cox, D ;

Goldman, R ;

Zhang, M .

JOURNAL OF SYMBOLIC COMPUTATION, 2000, 29 (03) :419-440

← 1 2 3 →