Chapter 8Geometric Modeling: Examples
This chapter uses various examples to illustrate most of the methods described in Chapter 7 and what they allow us to obtain. These examples will give us an occasion to see that there are many fields of application for the methods of geometric modeling, in the sense that we use it. These fields of application cover, notably, computer graphics (visualization), CAD (isometric parametrization, moving from continuous to discrete and discrete to continuous), reverse engineering (with respect, in particular, to solid mechanics, formation by stamping via a reverse approach and, in geology, the reconstitution of the history of geological layers), virtual reality by simplification or reduction (from a very dense discrete model, such as is often seen in 3D reconstruction), virtual reality by 3D reconstruction (from a point cloud raised on an object or in an environment), etc.
We will thus explore, in this order, examples for the application of:
- – discrete modeling of surfaces made up of parametric patches;
- – the extraction of characteristic lines from a discrete surface;
- – the isometric unfolding of a discrete surface;
- – the discrete 3D reconstruction of a digitized object or environment.
These examples are the link between a continuous model and its discrete version and, in this role and because of their generic character, are representative of the situations encountered in most geometric modeling problems. These examples were realized with the ...