Constraint Modeling for Curves and Surfaces in CAGD: a Survey

Computer-Aided Geometric Design modelers are now based on powerful mathematical curve and surface models, but there is still a considerable need for efficient tools to handle, analyze and modify these objects. Designing product shapes using geometric operations on free-form curves and surfaces is still a tedious task. Moreover, designers would prefer to use meaningful tools to concentrate on design objectives expressed in terms of functionalities and constraints related to engineering topics and technical matters. This explains why constraint modeling in CAGD is an important challenge for the forthcoming years and the paper aims at setting up some of its foundations. The corresponding global modeling approaches already proposed in CAD are first exposed. The specific existing techniques for handling constraints on curves and surfaces are then surveyed. A synthesis of these techniques and our current studies allows us to suggest a classification of the different constraints which ought to be taken into account in a constraint based modeling CAGD software. Open issues in the context of engineering design are finally emphasized.