By Dangming Wang, Falai Chen

This ebook comprises educational surveys and unique study contributions in geometric computing, modeling, and reasoning. Highlighting the function of algebraic computation, it covers: floor mixing, implicitization, and parametrization; computerized deduction with Clifford algebra and in genuine geometry; and designated geometric computation. easy ideas, complicated equipment, and new findings are provided coherently, with many examples and illustrations. utilizing this ebook the reader will simply move the frontiers of symbolic computation, laptop aided geometric layout, and automatic reasoning. The booklet can be a important reference for individuals operating in different suitable components, similar to medical computing, special effects, and synthetic intelligence.

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1994). A Survey of Blending Methods Using Parametric Surfaces. Computer Aided Design vol. 26, pp. 341-365. 65. Wang D. (2003). Implicitization and Offsetting via Regular Systems. , Wang D. ), pp. 156-176. World Scientific, Singapore New Jersey. 66. Warren J. (1986). On Algebraic Surfaces Meeting with Geometric Continuity. D. thesis, Cornell University, USA. 67. Warren J. (1989). Blending Algebraic Surfaces. ACM Transactions on Graphics vol. 8, no. 4, pp. 263-278. CHAPTER 2 CONSTRUCTING PIECEWISE ALGEBRAIC SURFACES BLENDING Yuyu Feng, Falai Chen, Jiansong Deng, Changsong Chen, and Xing Tang Department of Mathematics University of Science and Technology of China Hefei, Anhui 230026, P.

Notations and Preliminaries In this section, we introduce some notations and recall a few basic concepts from computational algebraic geometry. Two good references are the books 10 ' 11 by Cox and others. 2, the definition of geometric continuity is introduced. As for the details of geometric continuity, please refer to the paper 17 by Garrity and Warren. 36 Feng et al. 1. Monomial Orders and Grobner Bases Let K[x] := K[xi,... , xn] denote the ring of polynomials in X\,... ,xn over some field K.

The body is composed of two quadratic algebraic surfaces and the spout consists of two cubic algebraic surfaces with G 1 continuity. Finally, one quartic algebraic surface is taken for the handle. The details can be found in the master thesis 22 of Lou. Figure 11 shows the teapot model. In summary, the method of Grobner bases provides a powerful tool for the construction of blending surfaces of lowest degree. All the blending surfaces are expressed with several free parameters. These free parameters can be determined by interpolating or least-square approximation to a set of points.