Chinese Journal of Computers   Full Text
Title	The method of Grbner basis for constructing algebraic blending surfaces
Authors	LOU Wen-ping/FENG Yu-yu/CHEN Fa-lai/DENG Jian-song
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Year	2002
Issue	No.6(599-605)
Abstract &   Background	A new method using Grbner basis in algebraic geometry combined with techniques in CAGD for constructing algebraic blending surfaces is introduced. At first a theorem characterized all elements in an ideal which the degree of them is not greater than m using Grbner basis with Graded Lex order is proved. According to this theorem all algebraic blending surfaces which satisfy the given conditions can be obtained, furthermore, the lowest degree blending surfaces also can be found. Based on geometric continuous condition between algebraic surfaces, a general algorithm for constructing algebraic surfaces to blend several given surfaces with GCk continuity is given, and the algorithm is very efficient to find low-degree algebraic blending surfaces.In order to control the shape of blending algebraic surface, It is written in the Bernstein-Beziér form. Most of B-B coefficients can be determined by solving a linear system of equations according to continuous conditions. Some coefficients as free parameters are remained, and can be used to control the shape of algebraic blending surfaces. An example is given to illustrate the method and efficiency. Finally, this paper presents a solid modeling of a teapot by eight piecewise algebraic surfaces. The lid is constructed by three piecewise algebraic surfaces of degree four with GC2 continuity. The body is combined by two piecewise quadratic algebraic surfaces with GC1 continuity. The spout is made of two piecewise cubic algebraic surfaces with GC1 continuity, and the handle is a single quartic algebraic surface. keywords Algebraic blending surface, Grbner basis, free parameter, shape control