Computational Methods for Algebraic Spline Surfaces
ESF Exploratory Workhshop Schloß Weinberg at Kefermarkt, Austria 2003. Revised Papers
(Sprache: Englisch)
This volume contains revised papers that were presented at the international workshop entitled Computational Methods for Algebraic Spline Surfaces ("COMPASS"), which was held from September 29 to October 3, 2003, at Schloß Weinberg, Kefermarkt (A- tria)....
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This volume contains revised papers that were presented at the international workshop entitled Computational Methods for Algebraic Spline Surfaces ("COMPASS"), which was held from September 29 to October 3, 2003, at Schloß Weinberg, Kefermarkt (A- tria). The workshop was mainly devoted to approximate algebraic geometry and its - plications. The organizers wanted to emphasize the novel idea of approximate implici- zation, that has strengthened the existing link between CAD / CAGD (Computer Aided Geometric Design) and classical algebraic geometry. The existing methods for exact implicitization (i. e. , for conversion from the parametric to an implicit representation of a curve or surface) require exact arithmetic and are too slow and too expensive for industrial use. Thus the duality of an implicit representation and a parametric repres- tation is only used for low degree algebraic surfaces such as planes, spheres, cylinders, cones and toroidal surfaces. On the other hand, this duality is a very useful tool for - veloping ef?cient algorithms. Approximate implicitization makes this duality available for general curves and surfaces. The traditional exact implicitization of parametric surfaces produce global rep- sentations, which are exact everywhere. The surface patches used in CAD, however, are always de?ned within a small box only; they are obtained for a bounded parameter domain (typically a rectangle, or - in the case of "trimmed" surface patches - a subset of a rectangle). Consequently, a globally exact representation is not really needed in practice.
Inhaltsverzeichnis zu „Computational Methods for Algebraic Spline Surfaces “
- Approximate Parametrisation of Confidence Sets (Zbynek Sír)- Challenges in surface-surface intersections (Vibeke Skytt)
- Computing the topology of three-dimensional algebraic curves (G. Gatellier, A. Labrouzy, B. Mourrain, J.P. Técourt)
- Distance Properties of Points on Algebraic Curves (Sonia Pérez-Díaz, Juana Sendra, J.Rafael Sendra)
- Distance Separation Measures Between Parametric Curves and Surfaces Toward Intersection and Collision Detection Applications (Gershon Elber)
- Elementary Theory of Del Pezzo Surfaces (Josef Schicho)
- The Geometry of the Tangent Developable (Pal Hermunn Johansen)
- Numerical and algebraic properties (Joab R. Winkler)
- Polynomial C2 spline surfaces guided by rational multisided patches (Kestutis Karciauskas, Jörg Peters)
- A Recursive Taylor Method for Algebraic Curves and Surfaces (Huahao Shou, Ralph Martin, Guojin Wang, Adrian Bowyer, Irina Voiculescu)
- Self-intersection problems and approximate implicitization (Jan B. Thomassen)
- Singularities of some projective rational surfaces (Ragni Piene)
- On the Shape Effect of a Control Point Experimenting with NURBS Surfaces (Panagiotis Kaklis, Spyridon Dellas)
- Third Order Invariants of Surfaces (Jens Gravesen)
- Universal Rational Parametrizations and Spline Curves on Toric Surfaces (Rimvydas Krasauskas, Margarita Kazakeviciute)
- Panel discussion.
Bibliographische Angaben
- Autoren: Tor Dokken , Bert Juttler
- 2005, 238 Seiten, Maße: 16,1 x 24,1 cm, Gebunden, Englisch
- Herausgegeben:Dokken, Tor; Jüttler, Bert
- Verlag: Springer
- ISBN-10: 3540232745
- ISBN-13: 9783540232742
- Erscheinungsdatum: 10.12.2004
Sprache:
Englisch
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