Interval methods for constructive geometric constraint solving problems

In advanced computer-aided design systems, an object is defined by a collection of geometric elements along with a set of geometric constraints between them. Given the values assigned to the constraint parameters, solving the geometric problem consists of computing the coordinates of the points of t...

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Detalles Bibliográficos
Autores: Joan Arinyo, Robert|||0000-0002-1896-2940, Mata, Núria, Soto Riera, Antoni|||0000-0002-6136-1964
Tipo de recurso: informe técnico
Fecha de publicación:2002
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/97580
Acceso en línea:https://hdl.handle.net/2117/97580
Access Level:acceso abierto
Palabra clave:Computer-aided design systems
Interval methods
Constructive geometric constraint solving problems
CAD
CAM
Àrees temàtiques de la UPC::Informàtica
Descripción
Sumario:In advanced computer-aided design systems, an object is defined by a collection of geometric elements along with a set of geometric constraints between them. Given the values assigned to the constraint parameters, solving the geometric problem consists of computing the coordinates of the points of the geometric elements defining the object. Traditionally, constraint parameters have been considered to be exact values. In many applications, however, it is more realistic to consider that some dimensions of the object may take values in given intervals. As a result, the coordinates of the points are also intervals. In this situation, known geometric constraint solving techniques cannot solve directly the geometric problem. In this paper, we report on an interval-based method to solve geometric problems with interval parameters. We assume that we are given a construction plan for a geometric problem, and an assignment of interval values to the constraint parameters. We present an algorithm that computes precise and rigorous intervals for the coordinates of the points. We illustrate the performance of the algorithm with a case study.