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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.
Visualization and Computer Graphics, IEEE Transactions on (Volume:12 , Issue: 1 )
Date of Publication: Jan.-Feb. 2006