Triangle meshes have been longtime used in computer
graphics and polygonal geometric modeling, and a large body of data
structures and geometry processing algorithms based on them has been
developed in the literature. Yet, in recent years, quadrilateral meshes seem
to be preferred for many applications, and a burst of research is being
carried on them.
In this talk, we will outline the advantages and disadvantages of modeling approaches based on these two types of meshes, with respect to applications, algorithms and data structures. In particular, we will briefly explore issues concerning surface analysis and mesh quality, mesh conversion, simplification and parametrization, and remeshing. We will also discuss contrasting issues such as mesh regularity, adaptiveness, and alignment with line fields.