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<p><b>Abstract</b>—The purpose of this paper is to present a ray-tracing isosurface rendering algorithm for spectral/<tmath>hp</tmath> (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/<tmath>hp</tmath> 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 <it>pixel-exact</it> image at a rate far faster than sampling the spectral/<tmath>hp</tmath> element solution and applying classic low-order visualization techniques such as marching cubes.</p>
Spectral/hp elements, high-order finite elements, ray-tracing, isosurface rendering, fluid flow visualization, error budget.

R. M. Kirby and B. Nelson, "Ray-Tracing Polymorphic Multidomain Spectral/hp Elements for Isosurface Rendering," in IEEE Transactions on Visualization & Computer Graphics, vol. 12, no. , pp. 114-125, 2006.
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