## Solving Surface Fitting Problem by the Characteristic Set Method
*Dingkang Wang*
` dwang@mmrc.iss.ac.cn `
Institute of Systems Science,
**Academia Sinica**
Beijing 100080, P.R. China
### Abstract
Surface fitting problem is one of the most important research topics in CAGD. In most research papers, the surfaces and the curves are expressed in parameter equations. They are generally solved by numerical methods. In this paper, we discuss the surfaces and curves that are expressed in algebraic equations and solved by symbolic computation. Wu Wen-tsun has given a generic point method to solve the surface fitting problem in which surfaces and curves are defined by irreducible polynomial systems. According to the method, the surface fitting problem can be reduced to solving systems of polynomial equations. For the system of polynomial equations, we can use the characteristic set method to solve it. We will give several examples to show how to solve the surface fitting problem by the characteristic set method and give the necessary and sufficient conditions for the suitable surface fitting.
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