CAD : Geometrical modelling

CAD is essentially based on one or more geometric models. Historically, different choices have been made, depending not only on the business in question, but also on the capabilities of the technology. The models currently in use are based on a number of fundamental approaches that emerged in the 1960s-1970s. The very foundations of the models are thus derived from work that has led to a number of preferred representations over the last forty years.

Since then, a number of important developments have taken place. It is therefore essential to understand the basic elements on which the modelers were developed, as well as more recent contributions. Last but not least, it's interesting to see that some of the original proposals offer new potentialities.

After introducing the concept of modeling, this article presents the fundamentals of the two main families of geometric modeling: solid (or volume) models and surface models. In particular, we show the important differences between these two approaches and how they can be integrated into a single modeler. The approach used in volume modeling is fairly easy to grasp, but the diversity of models implies consequences for CAD use that users need to make their own. The consequences of the choices made in surface modeling are trickier to master. Curves and surfaces are based on mathematical models that need to be managed by computer models and algorithms. It is therefore necessary to be familiar with a number of concepts (surface decomposition, continuities, etc.). Insofar as interesting developments are underway, a sufficiently precise vision of the new avenues being explored is of interest. We need to take into account certain limitations linked to a historical approach, in order to obtain surfaces of controlled quality.

In the article [H 3 752] , we show how these geometric models can be integrated into applications and evolve into functional systems.

A glossary of terms is provided at the end of the article.