Overview

Mesh generation for surfaces representing the boundaries of a three-dimensional domain is, undoubtedly, a crucial point, especially for the computational schemes in finite element methods. As well as this field of application, the construction of surface meshes is also an important feature in applications such as visualization, virtual reality, animation, etc.

In this chapter, we discuss some methods that make it possible to construct the mesh of a segment or a curve traced on a surface, as well as the mesh of a surface itself. As in the previous chapter, there are two possible approaches to dealing with this meshing problem, depending on the definition of the geometric model. In practical terms, the problem is of a different nature, depending on whether a CAD type definition is known or the sole data available corresponds to a discretization (i.e., a polyhedral approximation) of the given surface. The first case leads rather to envisaging the development of appropriate mesh generation methods, while in the second case, mesh modification methods will be preferred.

First, we briefly discuss curve meshing (already mentioned in Chapter 14), in the particular case where they are traced onto a surface (or along a side of a patch).

Then, by means of examples, we illustrate the different types of surface meshes that can be constructed, a priori These examples allow us to specify the nature of the given problem and to indicate the various possible approaches. We will see that there exists a direct approach (where the...