By Mohamed Elkadi (Editor), Bernard Mourrain (Editor), Ragni Piene (Editor)
This ebook spans the space among algebraic descriptions of geometric gadgets and the rendering of electronic geometric shapes in line with algebraic types. those contrasting issues of view motivate an intensive research of the most important demanding situations and the way they're met. The articles specialise in vital sessions of difficulties: implicitization, category, and intersection. Combining illustrative snap shots, computations and evaluation articles this ebook is helping the reader achieve an organization sensible seize of those topics.
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Additional info for Algebraic Geometry and Geometric Modeling (Mathematics and Visualization)
76 sec. 16 sec. 2 MB 10 sec. 9 sec. 7 sec. 8 sec. 6 MB 12 sec. 3 sec. 7 sec. 9 sec. 52 sec. 70 sec. 35 sec. 77 sec. 91 sec. 34 sec. 28 sec. 29 sec. 64 sec. 01 sec. 6 sec. 99 sec. 2 sec. 99 sec. 38 sec. 14 sec. 25 sec. 035 failed failed Table 1. Result for the academic (upper part) and industrial (lower part) surfaces. F. Shalaby et al. 72 sec. 96 sec. 005170 216 46 Example (#Points for PPL) Piecewise approximate implicitization: experiments using industrial data 47 3) are used. For both algorithms, the implicitization is performed in reasonable time, with reasonable memory usage, and with relatively small error.
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. Goldman and R. Krasauskas, AMS Contemporary Mathematics, Vol.
In the case of PPL, this was achieved by introducing an additional tension term. It is possible to develop (semi–) automatic techniques for adjusting the inﬂuence of this term. 2 Avoiding unwanted branches and the reproduction of singularities All methods may produce unwanted branches of the surfaces, and possible additional singularities. The latter ones can be detected by analyzing the singular points of the implicitly deﬁned surface, along the parametric surface.