Cel Dual parametric and implicit representations are central in algorithms for low degree (typically 1 or 2) algebraic surfaces. Although available in theory, exact implicit representations of sculptured CAD-type surfaces are not useful in practice, as they are computationally too expensive. This is due to the high degrees and the exploding number of coefficients. Since the advent of approximate implicitisation, new methods are within reach. A previous FET assessment project verified that self-intersection algorithms work with approximate implicit of total degree as low as 4. Intersection algorithms are the most complex part of 3D CAD kernels, and the source of many problems in advanced CAD model exchange and use. Approximate implicitisation opens a bridge to algebraic geometry. By combining results from different branches of mathematics, we plan to investigate the use of approximate algebraic geometry in surface intersection algorithms.DESCRIPTION OF WORK1. Singularities: Classification, detection and localisation. The partners believe that Computer Aided Geometric Design will benefit from algebraic geometry. The project will address both real and classical algebraic geometry to achieve a better understanding of intersection problems and identify results that can improve intersection algorithms.2. Representation: Different methods for finding algebraic representations exist. We will examine in more detail the resultant types, further investigate approximate methods and address piecewise algebraic methods. Topics of special interest are approximation with parametrical implicit curves/ surfaces and classes of algebraic surfaces governed by a small numbers of parameters.3. Intersection: As the main objective is intersection algorithms, we will examine how the approximate algebraic approach complements state-of-the-art methods, and develop prototype integration. More accurate methods and compact representations for intersection tracks will also be in focus. The results will be demonstrated in an industrial prototype.4. Applications: The assessment project resulted in a number of open issues that will be addressed. Some applications have already been identified, such as detection of loops on curves and ray tracing for graphics; others are foreseen. When a complex geometric constellation arises, a local approximate algebraic geometry is a tool to gain more insight and sort out the solution. As the project will benefit from industrial feedback from a larger industrial audience, the GAIA users club will invite industrial companies interested in influencing new CAD-type technology. Dziedzina nauki natural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Program(-y) FP5-IST - Programme for research, technological development and demonstration on a "User-friendly information society, 1998-2002" Temat(-y) 1.1.2.-6.1.1 - FET O: Open domain Zaproszenie do składania wniosków Data not available System finansowania CSC - Cost-sharing contracts Koordynator SINTEF - STIFTELSEN FOR INDUSTRIELL OG TEKNISK FORSKNING VED NORGES TEKNISKE HOEGSKOLE Wkład UE Brak danych Adres STRINDVEIEN 4 7034 TRONDHEIM Norwegia Zobacz na mapie Koszt całkowity Brak danych Uczestnicy (6) Sortuj alfabetycznie Sortuj według wkładu UE Rozwiń wszystko Zwiń wszystko CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE Francja Wkład UE Brak danych Adres 3, RUE MICHEL-ANGE 75794 PARIS CEDEX 16 Zobacz na mapie Koszt całkowity Brak danych JOHANNES KEPLER UNIVERSITAET LINZ - INSTITUT FUER ANALYSIS Austria Wkład UE Brak danych Adres ALTENBERGERSTRASSE 69 4040 LINZ Zobacz na mapie Koszt całkowity Brak danych THINK3 Francja Wkład UE Brak danych Adres 55 AVENUE GALLINE 69100 VILLEURBANNE Zobacz na mapie Koszt całkowity Brak danych UNIVERSIDAD DE CANTABRIA Hiszpania Wkład UE Brak danych Adres AVENIDA DE LOS CASTROS S/N 39005 CANTABRIA Zobacz na mapie Koszt całkowity Brak danych UNIVERSITE DE NICE - SOPHIA ANTIPOLIS Francja Wkład UE Brak danych Adres 28 AV. DE VALROSE - PARC VALROSE 06108 NICE - CEDEX 2 Zobacz na mapie Koszt całkowity Brak danych UNIVERSITETET I OSLO Norwegia Wkład UE Brak danych Adres PROBLEMVEIEN 5-7 0316 OSLO Zobacz na mapie Koszt całkowity Brak danych