| Even if Computer-Aided Geometric Design modelers are now based on powerful mathematical models for curves and surfaces, there are important needs for tools to create, analyze and modify these objects. Designing product shapes with free-form curves and surfaces is still a tedious task and modifying the shape obtained is even more difficult and, most of the time, needs recreating a part up to the entire model. Moreover, designers prefer to concentrate on design objectives, expressed in terms of functionalities and constraints related to engineering topics and technical matters rather than being forced to spend time on mathematical and geometric parameters of a model, which is not very meaningful for them. Firstly, the aim of this paper is to analyze the problem of constraint modeling of curves and surfaces and to propose a survey of the main results achieved in the area of geometric constraint specification for 3D objects incorporating free-form curves and surfaces. Secondly, a list of major scientific difficulties to overcome is proposed that relates free-form shapes to their use in the context of engineering design. |
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