Read e-book online Geometric Computation PDF

By Dangming Wang, Falai Chen

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 function of algebraic computation, it covers: floor mixing, implicitization, and parametrization; automatic deduction with Clifford algebra and in actual geometry; and distinct geometric computation. uncomplicated suggestions, complicated tools, and new findings are awarded coherently, with many examples and illustrations. utilizing this publication the reader will simply move the frontiers of symbolic computation, desktop aided geometric layout, and automatic reasoning. The e-book can also be a worthy reference for individuals operating in different correct components, reminiscent of medical computing, special effects, and synthetic intelligence.

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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. , Wang D. ), pp. 126-155. World Scientific, Singapore New Jersey. Using Algebraic Methods in CAGD 33 49. Lii W. (1995). Offset-Rational Parametric Plane Curves, Computer Aided Geometric Design vol.

Solutions of P A S . Solving the system of equations, we obtain the following expressions for the PAS g = 0: {9i=7ifi+PiF*+1=0, 92 = li fi + A ^ + 1 + ai7r* +1 = 0, 93='Y2f2+foF*+1 =0, 94 = 72/2 + p2F%+1 + a 3 7r£ +1 = 0, P5=^/3+i83i;,3*+1=0, . 06 = 73/3 + PsF*+1 + a 5 % * + 1 = 0. As an example, we take n = 4, A? ht = h2 = h% = - , n r 2 rr: 7*3 5" Then there are three free parameters in the solution, and one solution is shown in Fig. 5. Fig. 5. Blending three cylinders (from two different views) D e t e r m i n a t i o n of free p a r a m e t e r s .

2001). Algebraic Methods for Sectioning Parametric Surfaces. Computer Algebra in Scientific Computing CASC-01, Lectures Notes in Computer Science XII, pp. 283-295. SpringerVerlag, Berlin Heidelberg. , Necula I. (2002). An Algorithm for the Approximate Conversion of Rational B-spline Curves/Surfaces to Integral Bspline Curves/Surfaces and its Implementation. Preprint, Universidad de Cantabria, Spain. , Necula I. (2001). A Symbolic/Numeric Toolbox for Computer Aided Geometric Design. To appear in the Annals of the University of Timisoara, Mathematics and Computer Science Series.

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Geometric Computation by Dangming Wang, Falai Chen

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