Volume Rendering on Non-regular Grids

Abstract

In this article we present the principle methods for volumerendering of non-regular grids as used in the Finite Element Method or the Method of Control Volumes. Besides linear element types, the methods discussed here also cover the handling of commonly used non-linear element types but little considered in the Computer Graphics community. The very basic operation in the whole rendering process, namely the interpolation of the geometry and function values is fully based on the element type specific shape functions, ensuring a consistent mathematical treatment of the object in the sense of the underlying numerical simulation. We discuss the implications of this approach and propose optimizations justified by general assumptions on the qualify of the simulation model.