Interactive visualization of large higher-order tetrahedral data.

摘要

Computational simulations frequently generate solutions defined over very large tetrahedral volume meshes containing many millions of elements. Furthermore, solutions over these meshes may often be expressed using non-linear basis functions. Certain solution techniques, such as discontinuous Galerkin finite element methods, may even produce non-conforming meshes. Such data is difficult to visualize interactively, as it is far too large to fit in memory and many common data reduction techniques, such as mesh simplification, cannot be applied to non-conforming meshes. Common linear interpolation method cannot faithfully and accurately evaluate the non-linear solutions.;In this dissertation we propose novel algorithms to accurately, interactively, and efficiently visualize large higher-order volumetric data sets with non-conforming meshes and discontinuous solution fields, which is an uncovered field so far. Our algorithms include accurate pixel-exact surface rendering, interactive point-based volume visualization and efficient feature-based visualization. This dissertation presents our techniques can efficiently render volumes on the order of 20 million tetrahedra with cubic-order polynomial solution data at interactive rates. Our methods are not limited to higher-order tetrahedral data, they can be generalized to other non-linear or linear volumetric data sets as sell.