Modeling Multiresolution 3D Scalar Fields through Regular Simplex Bisection

We review modeling techniques for multiresolution three-dimensional scalar fields based on a dis-cretization of the field domain into nested tetrahedral meshes generated through regular simplex
bisection. Such meshes are described through hierarchical data structures and their representa-
tion is characterized by the modeling primitive used. The primary conceptual distinction among
the different approaches proposed in the literature is whether they treat tetrahedra or clusters
of tetrahedra, called diamonds, as the modeling primitive. We first focus on representations for
the modeling primitive and for nested meshes. Next, we survey the applications of these meshes
to modeling multiresolution 3D scalar fields, with an emphasis on interactive visualization. We
also consider the relationship of such meshes to octrees. Finally, we discuss directions for further
research