The Closest Point Method (CPM) is a method for numerically solving partial differential equations (PDEs) on arbitrary surfaces, independent of the existence of a surface parametrization. The CPM uses a closest point representation of the surface, to solve the unmodified Cartesian version of a surface PDE in a 3D volume embedding, using simple and well‐understood techniques. In this paper, we present the numerical solution of the wave equation and the incompressible Navier‐Stokes equations on surfaces via the CPM, and we demonstrate surface appearance and shape variations in real‐time using this method. To fully exploit the potential of the CPM, we present a novel GPU realization of the entire CPM pipeline. We propose a surface‐embedding adaptive 3D spatial grid for efficient representation of the surface, and present a high‐performance approach using CUDA for converting surfaces given by triangulations into this representation. For real‐time performance, CUDA is also used for the numerical procedures of the CPM. For rendering the surface (and the PDE solution) directly from the closest point representation without the need to reconstruct a triangulated surface, we present a GPU ray‐casting method that works on the adaptive 3D grid.

Fig. 1. Visualizations of structures in 1024 3 turbulence data sets on 1024 × 1024 viewports, directly from the turbulent motion field. Left: Close-up of iso-surfaces of the ∆ Chong invariant with direct volume rendering of vorticity direction inside the vortex tubes. Middle: Direct volume rendering of color-coded vorticity direction. Right: Close-up of direct volume rendering of R S . The visualizations are generated by our system in less than 5 seconds on a desktop PC equipped with 12 GB of main memory and an NVIDIA GeForce GTX 580 graphics card with 1.5 GB of video memory.Abstract-Despite the ongoing efforts in turbulence research, the universal properties of the turbulence small-scale structure and the relationships between small-and large-scale turbulent motions are not yet fully understood. The visually guided exploration of turbulence features, including the interactive selection and simultaneous visualization of multiple features, can further progress our understanding of turbulence. Accomplishing this task for flow fields in which the full turbulence spectrum is well resolved is challenging on desktop computers. This is due to the extreme resolution of such fields, requiring memory and bandwidth capacities going beyond what is currently available. To overcome these limitations, we present a GPU system for feature-based turbulence visualization that works on a compressed flow field representation. We use a wavelet-based compression scheme including run-length and entropy encoding, which can be decoded on the GPU and embedded into brick-based volume ray-casting. This enables a drastic reduction of the data to be streamed from disk to GPU memory. Our system derives turbulence properties directly from the velocity gradient tensor, and it either renders these properties in turn or generates and renders scalar feature volumes. The quality and efficiency of the system is demonstrated in the visualization of two unsteady turbulence simulations, each comprising a spatio-temporal resolution of 1024 4 . On a desktop computer, the system can visualize each time step in 5 seconds, and it achieves about three times this rate for the visualization of a scalar feature volume.

Figure 1: A terrain field of over 300 gigasamples (left). Direct editing using a paint and displacement brush (right) and simultaneous rendering of the resulting changes is performed at 60 fps on a 1920×1080 viewport using our approach. AbstractPrevious terrain rendering approaches have addressed the aspect of data compression and fast decoding for rendering, but applications where the terrain is repeatedly modified and needs to be buffered on disk have not been considered so far. Such applications require both decoding and encoding to be faster than disk transfer. We present a novel approach for editing gigasample terrain fields at interactive rates and high quality. To achieve high decoding and encoding throughput, we employ a compression scheme for height and pixel maps based on a sparse wavelet representation. On recent GPUs it can encode and decode up to 270 and 730 MPix/s of color data, respectively, at compression rates and quality superior to JPEG, and it achieves more than twice these rates for lossless height field compression. The construction and rendering of a height field triangulation is avoided by using GPU ray-casting directly on the regular grid underlying the compression scheme. We show the efficiency of our method for interactive editing and continuous level-of-detail rendering of terrain fields comprised of several hundreds of gigasamples.

The augmentation of objects by textual annotations provides a powerful means for visual data exploration. Especially in interactive scenarios, where the view on the objects and, thus, the preferred placement of annotations changes continually, efficient labeling procedures are required. As identified by a preliminary study for this paper, these procedures have to consider a number of requirements for achieving an optimal readability, e.g. cartographic principles, visual association and temporal coherence. In this paper, we present a force-based labeling algorithm for 2D and 3D scenes, which can compute the placements of annotations at very high speed and fulfills the identified requirements. The efficient labeling of several hundred annotations is achieved by computing their layout in parallel on the GPU. This allows for a real-time and collision-free arrangement of both dynamically changing and static information. We demonstrate that our method supports a large variety of applications, e.g. geographical information systems, automotive navigation systems, and scientific or information visualization systems. We conclude the paper with an expert study which confirms the enhancements brought by our algorithm with respect to visual association and readability.

Abstract-Interactive and high-quality visualization of spatially continuous 3D fields represented by scattered distributions of billions of particles is challenging. One common approach is to resample the quantities carried by the particles to a regular grid and to render the grid via volume ray-casting. In large-scale applications such as astrophysics, however, the required grid resolution can easily exceed 10K samples per spatial dimension, letting resampling approaches appear unfeasible. In this paper we demonstrate that even in these extreme cases such approaches perform surprisingly well, both in terms of memory requirement and rendering performance. We resample the particle data to a multiresolution multiblock grid, where the resolution of the blocks is dictated by the particle distribution. From this structure we build an octree grid, and we then compress each block in the hierarchy at no visual loss using wavelet-based compression. Since decompression can be performed on the GPU, it can be integrated effectively into GPU-based out-of-core volume ray-casting. We compare our approach to the perspective grid approach which resamples at run-time into a view-aligned grid. We demonstrate considerably faster rendering times at high quality, at only a moderate memory increase compared to the raw particle set.