Objetivo 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. Ámbito científico natural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programa(s) FP5-IST - Programme for research, technological development and demonstration on a "User-friendly information society, 1998-2002" Tema(s) 1.1.2.-6.1.1 - FET O: Open domain Convocatoria de propuestas Data not available Régimen de financiación CSC - Cost-sharing contracts Coordinador SINTEF - STIFTELSEN FOR INDUSTRIELL OG TEKNISK FORSKNING VED NORGES TEKNISKE HOEGSKOLE Aportación de la UE Sin datos Dirección STRINDVEIEN 4 7034 TRONDHEIM Noruega Ver en el mapa Coste total Sin datos Participantes (6) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE Francia Aportación de la UE Sin datos Dirección 3, RUE MICHEL-ANGE 75794 PARIS CEDEX 16 Ver en el mapa Coste total Sin datos JOHANNES KEPLER UNIVERSITAET LINZ - INSTITUT FUER ANALYSIS Austria Aportación de la UE Sin datos Dirección ALTENBERGERSTRASSE 69 4040 LINZ Ver en el mapa Coste total Sin datos THINK3 Francia Aportación de la UE Sin datos Dirección 55 AVENUE GALLINE 69100 VILLEURBANNE Ver en el mapa Coste total Sin datos UNIVERSIDAD DE CANTABRIA España Aportación de la UE Sin datos Dirección AVENIDA DE LOS CASTROS S/N 39005 CANTABRIA Ver en el mapa Coste total Sin datos UNIVERSITE DE NICE - SOPHIA ANTIPOLIS Francia Aportación de la UE Sin datos Dirección 28 AV. DE VALROSE - PARC VALROSE 06108 NICE - CEDEX 2 Ver en el mapa Coste total Sin datos UNIVERSITETET I OSLO Noruega Aportación de la UE Sin datos Dirección PROBLEMVEIEN 5-7 0316 OSLO Ver en el mapa Coste total Sin datos