Volume meshing amounts to subdivide a given three-dimensional domain into a collection of simple cells. Many exist-ing volume meshing algorithms have major weaknesses which often depend on the choice of using floating point arith-metic rather than exact number representations. We consider two different problems: (1) meshing domains with "de-fects" and (2) computing Constrained Delaunay Tetrahedrizations (CDT) of well-formed domains. Algorithms that ro-bustly solve the former problem exist, but they are too slow for a widespread use. Conversely, tools that quickly com-pute the CDT exist but are not robust. For both the problems, we have re-designed state-of-the-art methods by integrat-ing implicit points and indirect predicates: this approach made it possible, for the first time, to combine and guarantee both robustness and efficiency.

Mesh Models, Volume Meshing, Numeric Robustness and Representability