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

机译:射线追踪多态多域光谱/ hp元素,用于等值面渲染

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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.
机译:本文的目的是为光谱/ hp(高阶有限元)方法提供一种射线追踪等值面渲染算法,其中可视化误差既可以量化也可以最小化。射线等值面相交的确定是通过将​​经典有限项根查找应用于多项式近似而完成的,该多项式近似是通过将有限元解投影到沿射线的元素划分的分段上而获得的。结合光谱/ hp元素的平滑特性与经典正交多项式逼近理论,我们设计了一种自适应方案,该方案允许沿射线段的多项式逼近任意接近真实解。生成的图像以比采样光谱/ hp元素解决方案和应用经典的低阶可视化技术(例如行进立方体)快得多的速度收敛到精确像素图像。

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