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.

Show description

Read or Download Algebraic Geometry and Geometric Modeling (Mathematics and Visualization) PDF

Best geometry and topology books

Geometry, mechanics, and dynamics: volume in honor of the 60th birthday of J.E. Marsden

Jerry Marsden, one of many world’s pre-eminent mechanicians and utilized mathematicians, celebrated his sixtieth birthday in August 2002. the development used to be marked by way of a workshop on “Geometry, Mechanics, and Dynamics”at the Fields Institute for study within the Mathematical Sciences, of which he wasthefoundingDirector.

Additional info for Algebraic Geometry and Geometric Modeling (Mathematics and Visualization)

Sample text

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.

Download PDF sample

Rated 4.02 of 5 – based on 16 votes