Kalbe, ThomasZeilfelder, Frank2015-02-212015-02-2120081467-8659https://doi.org/10.1111/j.1467-8659.2008.01130.xWe 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 100.10.1111/j.1467-8659.2008.01130.x331-340