We present a novel approach enabling interactive visualization of volumetric Locally Refined B-splines (LR-splines). To this end we propose a highly efficient algorithm for direct visualization of scalar and vector fields given by an LR-spline. For the case of scalar fields a volume rendering approach is designed, along with methods for the necessary adaptive sampling distance, on-the-fly trimming with a surface geometry given by a STereoLithography (STL)-file, and local volume illumination based on on-the-fly evaluation of the derivative of the underlying LR-spline function. For vector fields we design a two-stage algorithm consisting of the computation of stream lines with adaptive step size and their rendering with tubes. In both cases, the common basic ingredient to achieve interactive frame rates is an acceleration structure based on a k-d forest together with suitable data structures. The algorithms are designed to fully utilize modern graphics processing unit (GPU) capabilities. Important applications where LR-spline volumes emerge are given for instance by approximation of large-scale simulation and sensor data, and Isogeometric Analysis (IGA). For the first case -- approximation of large three dimensional point clouds with an associated field -- we provide an extension of the multilevel B-spline approximation (MBA) algorithm to the case of volumetric LR-splines. We showcase interactive rendering achieved by our approach on different representative use cases, stemming from simulations of wind flow around a telescope, Magnetic Resonance (MR) imaging of a human brain, and simulations of a fluidized bed used for mixing and coating particles in industrial processes.
 The application of volume-rendering techniques to the display of surfaces from sampled scalar functions of three spatial dimensions is discussed. It is not necessary to fit geometric primitives to the sampled data; images are formed by directly shading each sample and projecting it onto the picture plane. Surface-shading calculations are performed at every voxel with local gradient vectors serving as surface normals. In a separate step, surface classification operators are applied to compute a partial opacity of every voxel. Operators that detect isovalue contour surfaces and region boundary surfaces are examined. The technique is simple and fast, yet displays surfaces exhibiting smooth silhouettes and few other aliasing artifacts. The use of selective blurring and supersampling to further improve image quality is described. Examples from molecular graphics and medical imaging are given. > We propose a new approach to efficiently render large volumetric data sets. The system achieves interactive to real-time rendering performance for several billion voxels. Our solution is based on an adaptive data representation depending on the current view and occlusion information, coupled to an efficient ray-casting rendering algorithm. One key element of our method is to guide data production and streaming directly based on information extracted during rendering. Our data structure exploits the fact that in CG scenes, details are often concentrated on the interface between free space and clusters of density and shows that volumetric models might become a valuable alternative as a rendering primitive for real-time applications. In this spirit, we allow a quality performance trade-off and exploit temporal coherence. We also introduce a mipmapping-like process that allows for an increased display rate and better quality through high quality filtering. To further enrich the data set, we create additional details through a variety of procedural methods. We demonstrate our approach in several scenarios, like the exploration of a 3D scan (81923 resolution), of hypertextured meshes (163843 virtual resolution), or of a fractal (theoretically infinite resolution). All examples are rendered on current generation hardware at 20--90 fps and respect the limited GPU memory budget.