Direct visualization of piecewise polynomial data

Abstract

High order methods are regarded as a primary means to significantly improve the efficiency of numerical techniques. While the particular high order methods can be very distinct, most have in common that their solution is represented by piecewise polynomials. However, since high order methods evolved only recently, most of the present visualization techniques are not suited for the needs of resulting simulation data; they are predominantly based on tensor product linear interpolation and applying them to high order data is nowadays accomplished by static resampling, involving prohibitive storage and computation costs, and providing at most sufficient results. In this paper, we describe two of our existing visualization approaches and discuss some of the involved problems and concepts, and exemplify them using different high order simulation results.