# Computer Graphics and Mathematics by Maharaj Mukherjee, George Nagy, Shashank Mehta (auth.),

By Maharaj Mukherjee, George Nagy, Shashank Mehta (auth.), Bianca Falcidieno, Ivan Herman, Caterina Pienovi (eds.)

Since its very life as a separate box inside of laptop technology, special effects needed to make large use of non-trivial arithmetic, for instance, projective geometry, sturdy modelling, and approximation concept. This interaction of arithmetic and machine technology is fascinating, but in addition makes it tough for college kids and researchers to assimilate or continue a view of the mandatory arithmetic. the chances provided by means of an interdisciplinary technique are nonetheless no longer totally applied. This booklet provides a variety of contributions to a workshop held close to Genoa, Italy, in October 1991, the place a bunch of mathematicians and machine scientists accrued to discover methods of extending the cooperation among arithmetic and computing device graphics.

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12. Part of a torus as a cyclide patch. 13. The offset patches of a cyclide patch. 4. ::... :l. :~<. 14. A cyclide patch for which some weights of its control points are modified . ~::..... ~ .... 15. Two cyclide patches which are connected with el continuity. " ,,/" ~""':':::::::::i:, ,I .... ::~ .... FIGURE 4,16. A cyclide patch and a NUBRS patch which are connected with el continuity. 7 References [1] W. Boehm. On de Boor-like AIgorithms and Blossoming. Computer Aided Geometric Design, 5:pp.

Computer-Aided Geom. Design, 5:81-86, 1988. -P. Seidel. A new multiaffine approach to B-splines. Computer-Aided Geom. Design, 6:23-32, 1989. -P. Seidel. Polar forms and triangular B-Spline surfaees. 52, ACM SIGGRAPH, 1991. -P. Seidel. Symmetric recursive algorithms for surfaees: B-patches and the de Boor algorithm for polynomials over triangles. Constr. , 7:257-279, 1991. 4 Representing and Modeling of Cyclide Patches using NURBS X iaolin Zhou ABSTRACT In this paper we introduce a method to represent cyclide patches using NURBS.

Bi,j+a,k Bijk (2u, 2v - 1, 2w) Ea. b i ,j,k+aBijk(2u, 2v, 2w - 1) Ea. 6} is called the Bezier net of b with respeet to the triangulation T. There are efficient and numerically stable algorithms, so called subdivision or refinement algorithms, to compute it [2, 6]. 3 Initial approximation From the subdivision technique described in the previous section one can derive an interpolation method which generates a patch P with a prescribed boundary and cross boundary derivatives, Le. p is the interpolant.