Download PDF by Dongming Wang: Geometric Computation (Lecture Notes Series on Computing

By Dongming Wang

ISBN-10: 9812387994

ISBN-13: 9789812387998

ISBN-10: 9812794832

ISBN-13: 9789812794833

This ebook includes instructional surveys and unique study contributions in geometric computing, modeling, and reasoning. Highlighting the position of algebraic computation, it covers: floor mixing, implicitization, and parametrization; automatic deduction with Clifford algebra and in genuine geometry; and targeted geometric computation. simple ideas, complicated equipment, and new findings are provided coherently, with many examples and illustrations. utilizing this publication the reader will simply go the frontiers of symbolic computation, machine aided geometric layout, and automatic reasoning. The e-book is additionally a worthwhile reference for individuals operating in different proper parts, reminiscent of medical computing, special effects, and synthetic intelligence.

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SIAM, Philadelphia. 45. Hong H. (1996). An Efficient Method for Analyzing the Topology of Plane Real Algebraic Curves. Mathematics and Computers in Simulation vol. 42, nos. 4-6, pp. 571-582. 46. , Lasser D. (1993). Fundamentals of Computer Aided Geometric Design. K. , Ltd. 47. Kalkbrener M. (1991). Implicitization of Rational Parametric Curves and Surfaces. Proc. AAECC-8, Lecture Notes in Computer Science, pp. 249-259. 48. Kotsireas I. S. (2003). Panorama of Methods for Exact Implicitization of Algebraic Curves and Surfaces.

3. , Sendra J. R. (1997). Parametric Generalized Offsets to Hypersurfaces. Journal of Symbolic Computation vol. 23, pp. 267-285. 4. , Sendra J. R. (1999). Genus Formula for Generalized Offset Curves, Journal of Pure and Applied Algebra vol. 136, no. 3, pp. 199209. 5. Bajaj C. (1993). The Emergence of Algebraic Curves and Surfaces in Geometric Design. Directions in Geometric Computing, R. ), pp. 1-29. Information Geometers Press, Winchester, UK. 6. Bajaj C. ) (1994). Algebraic Geometry and its Applications.

H Mi e K[t, ft] and gcd(ft(ft - l)(ft - 2)(ft - 3), M{) = 1. Another interesting problem in this context is the computation and characterization of existence of polynomial parametric solutions because they avoid the unstable numerical behavior of the denominators when tracing the surface. In this situation, one may state the result analogous to Theorem 9 for the polynomial case (see the paper 53 by Perez-Diaz and Sendra). T h e o r e m 13: Let 7^Pol(*,ft) be a particular polynomial solution of the parametric blending problem.

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Geometric Computation (Lecture Notes Series on Computing Vol. 11) by Dongming Wang

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