CONSTRUCTING PIECEWISE ALGEBRAIC BLENDING SURFACES
CONSTRUCTING PIECEWISE ALGEBRAIC BLENDING SURFACES
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DOI：
10.1142/9789812794833_0002
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发表时间：
2004-03
期刊：
影响因子：
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通讯作者：
Y. Feng;Falai Chen;J. Deng;Changsong Chen;Xing Tang
中科院分区：
文献类型：
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作者：
Y. Feng;Falai Chen;J. Deng;Changsong Chen;Xing Tang
构造代数过渡曲面是几何造型中的一个重要问题。在这一章中，我们回顾了这一问题的一些方法，并总结了我们小组的成员最近研究的分片代数曲面的构造的主要结果。我们开始简要介绍了曲面过渡的问题，其次是一些符号和初步的知识，从计算代数几何，这将在后面的部分使用。然后，我们讨论了四种方法-直接方法，Gröbner基方法，吴的方法，并syzygy模块方法-构造分片代数过渡曲面。我们还提供了许多例子来说明这些方法与比较。这一章的结尾是几句话。
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 remarks.