Interactive direct volume rendering of curvilinear and unstructured data

Methods for interactive volume rendering of nonrectilinear 3D scientific data sets, such as those generated by the finite element method, are investigated. We focus on the use of projection methods, in particular splatting algorithms, for volume rendering curvilinear and irregular data. The data is rendered without interpolating it to a rectilinear mesh. The goal is interactive performance even when the data sets are very large. To achieve this, we investigate parallelization, graphics hardware support, a suite of splatting approximations, and mesh filtration. Using these techniques, we have generated images of nonrectilinear data sets with over 1,000,000 cells interactively (in less than 15-30 seconds). Using filtering methods this performance is possible for even larger data sets. Various optical models are discussed as a theoretical basis for volume rendering. A new theoretical model for interactive volume rendering is introduced. An algorithm is presented that generates a visibility ordering of an acyclic convex set of meshed convex polyhedra. This algorithm takes time linear in the size of the mesh. Modifications to this algorithm and/or preprocessing techniques are described which permit nonconvex cells, nonconvex meshes (meshes with cavities and/or voids), meshes with cycles, and sets of disconnected meshes to be ordered. It is shown how the ordering algorithms can be used for domain decomposition of finite element meshes for parallel processing, and how the data structures used by these algorithms can be used to solve the spatial point location problem. The effects of cyclically obstructing polyhedra are discussed, and methods for their elimination are described,including the use of the Delaunay triangulation. Methods for converting nonconvex meshes into convex meshes are described. A suite of splatting approximations are presented, which along with other more accurate methods discussed, form a hierarchy of rendering methods that tradeoff image accuracy/quality and generation time. Parallel volume rendering algorithms that include visibility ordering for both convex and nonconvex irregular meshes are investigated and results are given for several versions of parallel algorithms. A performance analysis of one of these algorithms on a high performance MIMD 3D graphics workstation is presented.