Decal-Lenses: Interactive Lenses on Surfaces for Multivariate Visualization.

We present decal-lenses, a new interaction technique that extends the concept of magic lenses to augment and manage multivariate visualizations on arbitrary surfaces. Our object-space lenses follow the surface geometry and allow the user to change the point of view during data exploration while maintaining a spatial reference to positions where one or more lenses were placed. Each lens delimits specific regions of the surface where one or more attributes can be selected or combined. Similar to 2D lenses, the user interacts with our lenses in real-time, switching between different attributes within the lens context. The user can also visualize the surface data representations from the point of view of each lens by using local cameras. To place lenses on surfaces of intricate geometry, such as the human brain, we introduce the concept of support surfaces for designing interaction techniques. Support surfaces provide a way to place and interact with the lenses while avoiding holes and occluded regions during data exploration. We further extend decal-lenses to arbitrary regions using brushing and lassoing operations. We discuss the applicability of our technique and present several examples where our lenses can be useful to create a customized exploration of multivariate data on surfaces.

Toward high-quality gradient estimation on regular lattices.

In this paper, we present two methods for accurate gradient estimation from scalar field data sampled on regular lattices. The first method is based on the multidimensional Taylor series expansion of the convolution sum and allows us to specify design criteria such as compactness and approximation power. The second method is based on a Hilbert space framework and provides a minimum error solution in the form of an orthogonal projection operating between two approximation spaces. Both methods lead to discrete filters, which can be combined with continuous reconstruction kernels to yield highly accurate estimators as compared to the current state of the art. We demonstrate the advantages of our methods in the context of volume rendering of data sampled on Cartesian and Body-Centered Cubic lattices. Our results show significant qualitative and quantitative improvements for both synthetic and real data, while incurring a moderate preprocessing and storage overhead.

Gradient estimation revitalized.

We investigate the use of a Fourier-domain derivative error kernel to quantify the error incurred while estimating the gradient of a function from scalar point samples on a regular lattice. We use the error kernel to show that gradient reconstruction quality is significantly enhanced merely by shifting the reconstruction kernel to the centers of the principal lattice directions. Additionally, we exploit the algebraic similarities between the scalar and derivative error kernels to design asymptotically optimal gradient estimation filters that can be factored into an infinite impulse response interpolation prefilter and a finite impulse response directional derivative filter. This leads to a significant performance gain both in terms of accuracy and computational efficiency. The interpolation prefilter provides an accurate scalar approximation and can be re-used to cheaply compute directional derivatives on-the-fly without the need to store gradients. We demonstrate the impact of our filters in the context of volume rendering of scalar data sampled on the Cartesian and Body-Centered Cubic lattices. Our results rival those obtained from other competitive gradient estimation methods while incurring no additional computational or storage overhead.

The Lattice-Boltzmann method on optimal sampling lattices.

In this paper, we extend the single relaxation time Lattice-Boltzmann Method (LBM) to the 3D body-centered cubic (BCC) lattice. We show that the D3bQ15 lattice defined by a 15 neighborhood connectivity of the BCC lattice is not only capable of more accurately discretizing the velocity space of the continuous Boltzmann equation as compared to the D3Q15 Cartesian lattice, it also achieves a comparable spatial discretization with 30 percent less samples. We validate the accuracy of our proposed lattice by investigating its performance on the 3D lid-driven cavity flow problem and show that the D3bQ15 lattice offers significant cost savings while maintaining a comparable accuracy. We demonstrate the efficiency of our method and the impact on graphics and visualization techniques via the application of line-integral convolution on 2D slices as well as the extraction of streamlines of the 3D flow. We further study the benefits of our proposed lattice by applying it to the problem of simulating smoke and show that the D3bQ15 lattice yields more detail and turbulence at a reduced computational cost.