Parametrized surfaces in ℙ3 of bidegree (1, 2)

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Volumn , Issue , 2004, Pages 141-148

  Elkadi, Mohamed ^a   Galligo, André ^a   Lê, Thi Ha ^a  

^a UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

Author keywords

Conics; Implicit equations; Singular locus; Surfaces of bidegree (1, 2)

Indexed keywords

COMBINATORIAL MATHEMATICS; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; LINEAR EQUATIONS;

COMPUTER AIDED GEOMETRIC DESIGN; CONTINUOUS PARAMETERS; GEOMETRIC MODELING; PARAMETRIZED SURFACES;

COMPUTER AIDED DESIGN;

EID: 27644513311     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (13)

1. L. ANDERSSON, J. PETERS, AND N. STEWART, Self-intersection of composite curves and surfaces, Computer Aided Geometric Design, 15 (1998), pp. 507-527.
2. L. BUSÉ AND C. D'ANDREA, Inversion of parametrized hypersurfaces by means of subresultants, preprint, (2004).
3. E.-W. CHIONH AND R. N. GOLDMAN, Degree, multiplicity, and inversion formulas for rational surfaces using u-resultants, Computer Aided Geometric Design, 9 (1992), pp. 93-108.
4. A. COFFMAN, A. J. SCHWARTZ, AND C. STANTON, The algebra and geometry of steiner and other quadratically parametrizable surfaces, Comput. Aided Geom. Des., 13 (1996), pp. 257-286.
5. ELKADI, M. AND MOURRAIN, B., Residue and Implicitization Problem for Rational Surfaces, Appl. Algebra Eng. Commun. Comput., 14 (2004), pp. 361-379.
6. G. FARIN, Curves and surfaces for computer aided geometric design. A practical guide, Academic Press, Inc., Boston, MA, 1993.
7. A. GALLIGO AND J. PAVONE, A sampling algorithm for parametric surface self-intersection, preprint, (2004).
8. A. GALLIGO AND M. STILLMAN, The geometry of bicubic surfaces and splines, preprint, (2004).
9. R. HARTSHORNE, Algebraic Geometry, Springer-Verlag, 1977.
10. C. PAULY, private communication.
11. S. PEREZ-DIAZ, J. SCHICHO, AND J. SENDRA, Properness and inversion of rational parametrizations of surfaces, Appl. Alg. Eng. Comm. Comp., 13 (2002), pp. 29-51.
12. G. D. REIS, B. MOURRAIN, AND J.-P. TÉCOURT, On the representations of 3d surfaces, ECG Report, (2002).
13. I. SHAFAREVITCH, Basic Algebraic Geometry, New-York, Springer-Verlag, 1974.