Ray-tracing polymorphic multidomain spectral/hp elements for isosurface rendering

The purpose of this paper is to present a ray-tracing isosurface rendering algorithm for spectral/hp (high-order finite) element methods in which the visualization error is both quantified and minimized. Determination of the ray-isosurface intersection is accomplished by classic polynomial root-finding applied to a polynomial approximation obtained by projecting the finite element solution over element-partitioned segments along the ray. Combining the smoothness properties of spectral/hp elements with classic orthogonal polynomial approximation theory, we devise an adaptive scheme which allows the polynomial approximation along a ray-segment to be arbitrarily close to the true solution. The resulting images converge toward a pixel-exact image at a rate far faster than sampling the spectral/hp element solution and applying classic low-order visualization techniques such as marching cubes.

1 Introduction

The use of simulation science [1] as a means of scientific inquiry is increasing at a tremendous rate. The process of mathematically modeling physical phenomena, experimentally estimating important key modeling parameters, numerically approximating the solution of the mathematical model, and computationally solving the resulting algorithm has inundated the scientific and engineering worlds, allowing for rapid advances in our modern understanding and utilization of the world around us.