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.
Nelson
Blake
B
School of Computing and Scientific Computing and Imaging Institute, University of Utah, Salt Lake City 84112, USA. bnelson@cs.utah.edu
Kirby
Robert M
RM
D000465:Algorithms; D003196:Computer Graphics; D003198:Computer Simulation; D020342:Finite Element Analysis; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008962:Models, Theoretical; D014584:User-Computer Interface