By Tor Dokken, Bert Jüttler

ISBN-10: 3642062334

ISBN-13: 9783642062339

The papers incorporated during this quantity offer an summary of the cutting-edge in approximative implicitization and numerous similar subject matters, together with either the theoretical foundation and the prevailing computational techniques.The novel suggestion of approximate implicitization has bolstered the present hyperlink among laptop Aided Geometric layout and classical algebraic geometry. there's a starting to be curiosity from researchers and execs either in CAGD and Algebraic Geometry, to satisfy andcombine wisdom and ideas,with the purpose to enhance the fixing of industrial-type demanding situations, in addition to to start up new instructions for uncomplicated study. This quantity will help this trade of rules among a few of the groups.

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**Extra resources for Computational Methods for Algebraic Spline Surfaces. ESF Exploratory Workshop**

**Example text**

Connect the remaining points in Vj0 to c, by segments. If there is a x-critical point of C in Li , exchange the role of Li and Li+1 in the previous steps. Proposition 17. Assume that we are in a generic position. Then the topology of the curve above the segment [αi , αi+1 ] is the same as the set of segments produced by the algorithm 16. Topology of Three-Dimensional Algebraic Curves 39 Proof. Since we are in a generic position, by theorem 15, the algorithm 16 produces the only way the arcs of the curve C above [αi , αi+1 ] connect the points of Li to the points of Li+1 .

B0 (x, y) with ad1 (x, y) = 0 and bd2 (x, y) = 0. Then, the resultant polynomial G(x, y) = Resz (P1 , P2 ) vanishes on the projection of the curve C on the plane (x, y). Conversely, by the resultant theorem [8], G(x, y) = 0 deﬁnes exactly the projection C of the curve C if ad1 (x, y) and bd2 (x, y) do not vanish simultaneously on a component of dimension 1 of C , that is, if the gcd c(x, y) of ad1 (x, y) and bd2 (x, y) in [x, y] is 1. If it’s not the case, G is a non-trivial multiple of the implicit equation of C .

Intersection between a blend surface and its mother Fig. 11. Tangential intersection with singularities 25 26 V. Skytt References 1. E. Tracing surface intersections. Computer Aided Geometric Design 5 (1988) 285-307 2. E. N. Surface/surface intersection. Computer Aided Geometric Design 20 (1986) 18-36. 3. E. N. A marching method for parametric surface/surface intersection. Computer Aided Geometry Design 7 (1990) 257-280 4. Dokken T. Aspects of Intersection Algorithms and Approximation, Doctor thesis.

### Computational Methods for Algebraic Spline Surfaces. ESF Exploratory Workshop by Tor Dokken, Bert Jüttler

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