Approximate rational parameterization of implicitly defined surfaces

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3604 LNCS, Issue , 2005, Pages 434-447

  Wurm, Elmar ^a   Jüttler, Bert ^a   Kim, Myung Soo ^b  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^b Seoul National University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CONSTRAINT THEORY; OPTIMIZATION;

QUALITY CONSTRAINTS; RATIONAL PARAMETERIZATION;

LINEAR ALGEBRA;

EID: 33646136253     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11537908_26     Document Type: Conference Paper

References (19)

1. Abhyankar S., Bajaj C.: Automatic Parameterization of Rational Curves and Surfaces I: Conies and Conicoids. Computer Aided Design, 19 (1987), 11-14
2. Abhyankar S., Bajaj C.: Automatic Parameterization of Rational Curves and Surfaces II: Cubics and Cubicoids. Computer Aided Design, 19 (1987), 499-502
3. Bajaj C.: The Emergence of Algebraic Curves and Surfaces, in Geometric Design - Directions in Geometric Computing (R. Martin, ed.), Information Geometers Press, 1993, 1-29.
4. Bajaj C., Xu G.: Spline Approximations of Real Algebraic Surfaces. J. Symb. Comp., Special Issue on Parametric Algebraic Curves and Applications, 23 (1997), 315-333
5. Bajaj C., Holt R.L., Netravali A.N.: Rational Parametrizations of Nonsingular Real Cubic Surfaces. ACM Trans. Graph. 17(1): 1-31 (1998)
6. Costa A.: Examples of a Complete Minimal Immersion in of Genus One and Three Embedded Ends. Bil. Soc. Bras. Mat. 15 (1984), 47-54.
7. Hämmerlin G., Hoffmann K.H.: Numerical Mathematics, Springer, 1991,
8. Hartmann E.: Numerical parameterization of curves and surfaces, Computer Aided Geometric Design 17 (2000), 251-266.
9. Hoffman D. and Meeks W. H. III: A Complete Embedded Minimal Surfaces in with Genus One and Three Ends. J. Diff. Geom. 21 (1985), 109-127.
10. Hoschek J., Lasser D.: Fundamentals of Computer Aided Geometric Design, 1993, A. K. Peters.
11. Jüttler, B., Felis, A., Least-squares fitting of algebraic spline surfaces, Advances in Computational Mathematics 17 (2002), 135-152.
12. Jüttler B. and Rittenschober K., Using line congruences for parameterizing special algebraic surfaces. The Mathematics of Surfaces X (R. Martin and M. Bloor, eds.), pages 223-243, Berlin, 2003. Springer.
13. Kreyszig, E., Differential Geometry, Dover, New York, 1990.
14. Varadý, T., Martin, R: Reverse Engineering, in Handbook of Computer Aided Geometric Design (G. Farin, J. Hoschek, M.-S. Kim, eds.), North-Holland, 2002, 651-681.
15. Pottmann H. and Leopoldseder S.: A concept for parametric surface fitting which avoids the parametrization problem Computer Aided Geometric Design, 20 (2003), 343-362
16. Sampson, P.: Fitting conic sections to very scattered data: an iterative refinement of the Bookstein algorithm, Computer Graphics and Image Processing 18 (1982), 97-108.
17. Schicho J.: Rational parametrization of surfaces, J. Symb. Comp., 26 (1998), 1-30.
18. Sederberg T. W., Snively J.: Parameterizing Cubic Algebraic Surfaces. The Mathematics of Surfaces II (R.R. Martin, ed.), Oxford University Press, (1987), pp. 299-320.
19. Wurm E., Jüttler B.: Approximate Implicitization via Curve Fitting, in Symposium on Geometry Processing (L. Kobbelt, P. Schröder, H. Hoppe, eds.), Eurographics / ACM Siggraph, New York 2003, 240-247.