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Smooth trivariate splines on uniform tetrahedral partitions are well suited for high-quality visualization of isosurfaces from scalar volumetric data. We propose a novel rendering approach based on spline patches with low total degree, for which ray-isosurface intersections are computed using efficient root finding algorithms. Smoothly varying surface normals are directly extracted from the underlying spline representation. Our approach is using a combined CUDA and graphics pipeline and yields two key advantages over previous work. First, we can interactively vary the isovalues since all required processing steps are performed on the GPU. Second, we employ instancing in order to reduce shader complexity and to minimize overall memory usage. In particular, this allows to compute the spline coefficients on-the-fly in real-time on the GPU.

We develop an approach for hardware-accelerated, high-quality rendering of volume data using trivariate splines. The proposed quasi-interpolating schemes are realtime reconstructions. The low total degrees provide several advantages for our GPU implementation. In particular, intersecting rays with spline isosurfaces for direct Phong illumination is performed by simple root finding algorithms (analytic and iterative), while the necessary normals result from blossoming. Since visualizations are on a fragment base, our renderer for isosurfaces includes an automatic level of detail. While we use well-known spatial data structures in the CPU part of the algorithm for hierarchical view frustum culling and memory reduction, our GPU implementations have to take the highly complex structure of the splines into account. These include an appropriate organization of the data streams, i.e. we develop an advanced encoding scheme for the spline coefficients, as well as an implicit scheme for bounding geometry retrieval. In addition, we propose an elaborated clipping procedure to be performed in the fragment shader. These features essentially reduce bus traffic, memory consumption, and data access on the GPU leading to interactive frame rates for renderings of high visual quality. Compared with pure CPU implementations and existing GPU implementations for trivariate polynomials frame rates increase by factors between 10 and 100.

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