Constructing piecewise algebraic blending surfaces. (English) Zbl 1086.65504
Chen, Falai (ed.) et al., Geometric computation. River Edge, NJ: World Scientific (ISBN 981-238-799-4/hbk). Lecture Notes Series on Computing 11, 34-64 (2004).
Summary: Constructing algebraic blending surfaces is an important problem in geometric modeling. In this chapter, we review some methods for this problem and summarize the main results on the construction of piecewise algebraic surfaces investigated recently by members of our group.
This chapter is organized into seven sections. We begin with a brief introduction to the problem of surface blending, followed by some notations and preliminary knowledge from computational algebraic geometry which will be used in later sections. We then discuss four methods – direct method, Gröbner basis method, Wu’s method, and syzygy module method – for constructing piecewise algebraic blending surfaces. We also provide many examples to illustrate these methods with comparison. The chapter is concluded with a few remark.
For the entire collection see [Zbl 1073.65004].
This chapter is organized into seven sections. We begin with a brief introduction to the problem of surface blending, followed by some notations and preliminary knowledge from computational algebraic geometry which will be used in later sections. We then discuss four methods – direct method, Gröbner basis method, Wu’s method, and syzygy module method – for constructing piecewise algebraic blending surfaces. We also provide many examples to illustrate these methods with comparison. The chapter is concluded with a few remark.
For the entire collection see [Zbl 1073.65004].
MSC:
| 65D17 | Computer-aided design (modeling of curves and surfaces) |
| 14Q10 | Computational aspects of algebraic surfaces |
| 16E05 | Syzygies, resolutions, complexes in associative algebras |
