By Mohamed Elkadi (Editor), Bernard Mourrain (Editor), Ragni Piene (Editor)

This booklet spans the space among algebraic descriptions of geometric items and the rendering of electronic geometric shapes in response to algebraic versions. those contrasting issues of view encourage a radical research of the most important demanding situations and the way they're met. The articles specialize in very important periods of difficulties: implicitization, category, and intersection. Combining illustrative portraits, computations and evaluation articles this booklet is helping the reader achieve a company sensible snatch of those matters.

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3, 3) The surface is generated by sweeping a circular section along a curve. It consists of 2310 bicubic patches connected with C 2 continuity. (3, 3) The surface is a general sweeping surface. It is obtained by sweeping a curve (drive) along another curve (boundary). It consists of 1824 bicubic patches connected with C 2 continuity. Fig. 2. Industrial test surfaces (data courtesy of think3) Piecewise approximate implicitization: experiments using industrial data 45 The quoted time is an approximation of the processor time used by the program, and similarly for the memory.

Sarraga, R. (1983), Algebraic methods for intersections of quadric surfaces in GMSOLID, Computer Vision, Graphics and Image Processing, Vol. 22, pp. 222-238. 49. Sederberg, T. and Chen, F. (1995), Implicitization using moving curves and surfaces, Proceedings of Siggraph‘95. 50. , and Anderson, D. (1984), Implicit representation of parametric curves and surfaces, Computer Vision, Graphics, and Image Processing, Vol. 28, pp. 72-84. 51. , and Du, H. (1997), Implicitizing rational curves by the method of moving algebraic curves, Journal of Symbolic Computation, Vol.

282-292. 32. Hoffmann, C. (1989), Geometric and Solid Modeling: An Introduction, Morgan Kaufmann. 33. Juettler, B. and Wurm, E. (2003), Approximate implicitization via curve fitting, in L. Kobbelt, P. Schroder, H. ), Symposium on Geometry Processing, Eurographics/ACM Siggraph, New York, pp. 240-247. 34. Kakie, K. (1976), The resultant of several homogeneous polynomials in two indeterminates, Proceedings of AMS, Vol. 54, pp. 1-7. 35. Karciauskas, K. (2003), Rational M-patches and tensor border patches, in Topics in Algebraic Geometry and Geometric Modeling, edited by R.

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