Abstract—Visualization algorithms can have a large number of parameters, making the space of possible rendering results rather high-dimensional. Only a systematic analysis of the perceived quality can truly reveal the optimal setting for each such parameter. However, an exhaustive search in which all possible parameter permutations are presented to each user within a study group would be infeasible to conduct. Additional complications may result from possible parameter co-dependencies. Here, we will introduce an efficient user study design and analysis strategy that is geared to cope with this problem. The user feedback is fast and easy to obtain and does not require exhaustive parameter testing. To enable such a framework we have modified a preference measuring methodology, conjoint analysis, that originated in psychology and is now also widely used in market research. We demonstrate our framework by a study that measures the perceived quality in volume rendering within the context of large parameter spaces.

cranium modelled as interval volume isosurface modelled as interval volume standard DVR isosurface modelled as interval volume standard DVR Fig. 1. Volume visualization of the head data set. The orange isosurface at the skin level is modeled as an infinitesimally thin interval volume with scale-invariant opacity. Soft tissue (green), brain (red), and dentin (blue) are classified with standard direct volume rendering (DVR). Left: the cranium (white) is also visualized with standard DVR. Opacity depends on the physical length of the ray segments, e.g. the brain area is almost transparent whereas the silhouette of the cranium is opaque. Furthermore, the tooth enamel is not visible at all. Right: the cranium (white) is modeled as an interval volume. Opacity does not depend on physical dimensions. The finite extent of the interval volume is apparent at the semi-transparent silhouette. The surface-like structures of the cranium are visible and the enamel is classified properly. An increase of the extinction coefficient in the left image could remedy these deficiencies but only at the cost of a completely opaque cranium. Abstract—We extend direct volume rendering with a unified model for generalized isosurfaces, also called interval volumes, allowing a wider spectrum of visual classification. We generalize the concept of scale-invariant opacity—typical for isosurface rendering— to semi-transparent interval volumes. Scale-invariant rendering is independent of physical space dimensions and therefore directly facilitates the analysis of data characteristics. Our model represents sharp isosurfaces as limits of interval volumes and combines them with features of direct volume rendering. Our objective is accurate rendering, guaranteeing that all isosurfaces and interval volumes are visualized in a crack-free way with correct spatial ordering. We achieve simultaneous direct and interval volume rendering by extending preintegration and explicit peak finding with data-driven splitting of ray integration and hybrid computation in physical and data domains. Our algorithm is suitable for efficient parallel processing for interactive applications as demonstrated by our CUDA implementation.

Higher-order finite element methods have emerged as an important discretization scheme for simulation. They are increasingly used in contemporary numerical solvers, generating a new class of data that must be analyzed by scientists and engineers. Currently available visualization tools for this type of data are either batch oriented or limited to certain cell types and polynomial degrees. Other approaches approximate higher-order data by resampling resulting in trade-offs in interactivity and quality. To overcome these limitations, we have developed a distributed visualization system which allows for interactive exploration of non-conforming unstructured grids, resulting from space-time discontinuous Galerkin simulations, in which each cell has its own higher-order polynomial solution. Our system employs GPU-based raycasting for direct volume rendering of complex grids which feature non-convex, curvilinear cells with varying polynomial degree. Frequency-based adaptive sampling accounts for the high variations along rays. For distribution across a GPU cluster, the initial object-space partitioning is determined by cell characteristics like the polynomial degree and is adapted at runtime by a load balancing mechanism. The performance and utility of our system is evaluated for different aeroacoustic simulations involving the propagation of shock fronts.