Interval implicitization of rational curves

Computer Aided Geometric Design

Volumn 21, Issue 4, 2004, Pages 401-415

  Chen, Falai ^a   Deng, Lin ^a  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

Interval algebraic curve; Interval arithmetic; Interval implicitization

Indexed keywords

ALGEBRA; ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; COMPUTATIONAL METHODS; COMPUTER AIDED MANUFACTURING; PROBLEM SOLVING; SET THEORY;

INTERVAL ALGEBRAIC CURVES; INTERVAL ARITHMETIC; INTERVAL IMPLICITIZATION;

COMPUTER AIDED DESIGN;

EID: 1842453914     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cagd.2004.02.001     Document Type: Article

References (17)

1. Chen F.L. Approximate implicitization of rational curves. Chinese J. Comput. 1998;855-859. (in Chinese).
2. Chen F.L., Low W.P. Degree reduction of interval Bézier curves. Computer-Aided Design. 32:(8):2000;571-582.
3. Dokken, T., 1997. Aspects of intersection algorithms and approximations. Ph.D. Thesis, University of Oslo, Norway.
4. Dokken T. Approximate implicitization. Lyche T., Schumaker L. Mathematical Methods in CAGD, Oslo 2000. 2001;81-102 Vanderbilt University Press.
5. Dokken T., Kellermann H.K., Tegnander C. An approach to weak approximation implicitization. Lyche T., Schumaker L. Mathematical methods in CAGD, Oslo 2000. 2001;103-112 Vanderbilt University Press.
6. Hoffmann C.M. Implicit curves and surfaces in CAGD. IEEE Comput. Graph. Appl. 13:1993;79-88.
7. Hu C.Y., Maekawa T., Sherbrooke E.C., Patrikalakis N.M. Robust interval algorithm for curve intersections. Computer-Aided Design. 28:(6/7):1996;495-506.
8. Juttler B. Least-squares fitting of algebraic spline curves via normal vector estimation. Cipolla R., Martin R.R. Mathematics of Surfaces IX. 2000;263-280 Springer, London.
9. Moore R.E. Interval Analysis. 1966;Prentice Hall, Englewood Cliffs, NJ.
10. Mudur S.P., Koparkar P.A. Interval methods for processing geometric objects. IEEE Comput. Graph. Appl. 4:(2):1984;7-17.
11. Patrikalakis N.M. Robustness issues in geometric and solid modeling. Computer-Aided Design. 32:(11):2000;. (special issue).
12. Sederberg T.W. Planar piecewise algebraic curves. Computer Aided Geometric Design. 1:1984;241-255.
13. Sederberg T.W., Farouki R.T. Approximation by interval Bézier curves. IEEE Comput. Graph. Appl. 15:(2):1992;87-95.
14. Sederberg T.W., Chen F.L. Implicitization using moving curves and surfaces. Computer Graphics Proceedings, Los Angeles, CA, Annual Conference Series. 1995;301-308.
15. Sederberg T.W., Zheng J., Klimaszewski K., Dokken T. Approximate implicitization using monoid curves and surfaces. Graphical Models and Image Processing. 61:1999;177-198.
16. Velho L., Gomes J. Approximate conversion from parametric to implicit surfaces. Computer Graphics Forum. 15:(5):1996;327-337.
17. Xu G., Bajaj C.L., Xue W. Regular algebraic curve segments (I) - Definitions and characteristics. Computer Aided Geometric Design. 17:2000;485-501.