The implicit equation of a canal surface

Journal of Symbolic Computation

Volumn 44, Issue 2, 2009, Pages 111-130

  Dohm, Marc ^a   Zube, Severinas ^b  

^a UNIVERSITÉ CÔTE D'AZUR   (France)

^b VILNIUS UNIVERSITY   (Lithuania)

Author keywords

basis; Canal surface; Implicit equation; Offset; Resultant

Indexed keywords

EID: 56949099568     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2008.06.001     Document Type: Article

References (18)

1. Buse L., Khalil H., and Mourrain B. Resultant-based methods for plane curves intersection problems. Proceedings of the CASC'2005 Conference. Lecture Notes in Computer Science vol. 3718 (2005) 75-92
2. Cecil T.E. Lie Sphere Geometry (1992), Springer
3. Chen F., and Wang W. The mu-basis of a planar rational curve - properties and computation. Graphical Models 64 (2003) 368-381
4. Chen F., Zheng J., and Sederberg T.W. The mu-basis of a rational ruled surface. Computer Aided Geometric Design 18 (2001) 61-72
5. Cox D., Little J., and O'Shea D. Using Algebraic Geometry (1998), Springer
6. Cox D., Sederberg T.W., and Chen F. The moving line ideal basis for planar rational curves. Computer Aided Geometric Design 15 (1998) 803-827
7. Degen W. Cyclides. Handbook of Computer Aided Geometric Design (2002) 575-601
8. Dohm, M., Implicitization of rational ruled surfaces with μ-bases, Journal of Symbolic Computation (in press), Special Issue EACA 2006, preprint available at http://arxiv.org/pdf/math/0702658
9. Kazakeviciute, M., 2005. Blending of natural quadrics with rational canal surfaces, Ph.D. Thesis, Vilnius University
10. Krasauskas R. Minimal rational parametrizations of canal surfaces. Computing 79 (2007) 281-290
11. Krasauskas R., and Mäurer C. Studying cyclides using Laguerre geometry. Computer Aided Geometric Design 17 (2000) 101-126
12. Krasauskas R., and Zube S. Canal surfaces defined by quadratic families of spheres. In: Jttler B., and Piene R. (Eds). Geometric Modeling and Algebraic Geometry (2007), Springer 138-150 Publication: November, 2007
13. Pottmann H., and Peternell M. Application of Laguerre geometry in CAGD. Computer Aided Geometric Design 15 (1998) 165-186
14. Pottmann, H., Peternell, M., Ravani, B., 1998. Contributions to computational line geometry, In: Geometric Modeling and Processing '98, pp. 43-81
15. Pratt M.J. Cyclides in computer aided geometric design. Computer Aided Geometric Design 7 (1990) 221-242
16. Pratt M.J. Cyclides in computer aided geometric design II. Computer Aided Geometric Design 12 (1995) 131-152
17. San Segundo F., and Sendra J.R. Degree formulae for offset curves. Journal of Pure and Applied Algebra 195/3 (2005) 301-335
18. Xu Z., Feng R., and Sun J. Analytic and algebraic properties of canal surfaces. Journal of Computational and Applied Mathematics 195 1-2 (2006) 220-228