Peter L. Williams

Fast Polyhedral Cell Sorting for Interactive Rendering of Unstructured Grids

Direct volume rendering based on projective methods works by projecting, in visibility order, the polyhedral cells of a mesh onto the image plane, and incrementally compositing the cell’s color and opacity into the final image. Crucial to this method is the computation of a visibility ordering of the cells. If the mesh is “well‐behaved” (acyclic and convex), then the MPVO method of Williams provides a very fast sorting algorithm; however, this method only computes an approximate ordering in general datasets, resulting in visual artifacts when rendered. A recent method of Silva et al. removed the assumption that the mesh is convex, by means of a sweep algorithm used in conjunction with the MPVO method; their algorithm is substantially faster than previous exact methods for general meshes.

A Functional Gene Array for Detection of Bacterial Virulence Elements

Emerging known and unknown pathogens create profound threats to public health. Platforms for rapid detection and characterization of microbial agents are critically needed to prevent and respond to disease outbreaks. Available detection technologies cannot provide broad functional information about known or novel organisms. As a step toward developing such a system, we have produced and tested a series of high-density functional gene arrays to detect elements of virulence and antibiotic resistance mechanisms. Our first generation array targets genes from Escherichia coli strains K12 and CFT073, Enterococcus faecalis and Staphylococcus aureus. We determined optimal probe design parameters for gene family detection and discrimination. When tested with organisms at varying phylogenetic distances from the four target strains, the array detected orthologs for the majority of targeted gene families present in bacteria belonging to the same taxonomic family. In combination with whole-genome amplification, the array detects femtogram concentrations of purified DNA, either spiked in to an aerosol sample background, or in combinations from one or more of the four target organisms. This is the first report of a high density NimbleGen microarray system targeting microbial antibiotic resistance and virulence mechanisms. By targeting virulence gene families as well as genes unique to specific biothreat agents, these arrays will provide important data about the pathogenic potential and drug resistance profiles of unknown organisms in environmental samples.

Image-space visibility ordering for cell projection volume rendering of unstructured data

Projection methods for volume rendering unstructured data work by projecting, in visibility order, the polyhedral cells of the mesh onto the image plane, and incrementally compositing each cells color and opacity into the final image. Normally, such methods require an algorithm to determine a visibility order of the cells. The meshed polyhedra visibility order (MPVO) algorithm can provide such an order for convex meshes by considering the implications of local ordering relations between cells sharing a common face. However, in nonconvex meshes, one must also consider ordering relations along viewing rays which cross empty space between cells. In order to include these relations, the algorithm described in this paper, the scanning exact meshed polyhedra visibility ordering (SXMPVO) algorithm, scan-converts the exterior faces of the mesh and saves the ray-face intersections in an A-buffer data structure which is then used for retrieving the extra ordering relations. The image which SXMPVO produces is the same as would be produced by ordering the cells exactly, even though SXMPVO does not compute an exact visibility ordering. This is because the image resolution used for computing the visibility ordering relations is the same as that which is used for the actual volume rendering and we choose our A-buffer rays at the same sample points that are used to establish a polygons pixel coverage during hardware scan conversion. Thus, the algorithm is image-space correct. The SXMPVO algorithm has several desirable features; among them are speed, simplicity of implementation, and no extra (i.e., with respect to MPVO) preprocessing.

Tera-Scalable Algorithms for Variable-Density Elliptic Hydrodynamics with Spectral Accuracy

We describe Miranda, a massively parallel spectral/compact solver for variabledensity incompressible flow, including viscosity and species diffusivity effects. Miranda utilizes FFTs and band-diagonal matrix solvers to compute spatial derivatives to at least 10th-order accuracy. We have successfully ported this communicationintensive application to BlueGene/L and have explored both direct block parallel and transpose-based parallelization strategies for its implicit solvers. We have discovered a mapping strategy which results in virtually perfect scaling of the transpose method up to 65,536 processors of the BlueGene/L machine. Sustained global communication rates in Miranda typically run at 85% of the theoretical peak speed of the BlueGene/L torus network, while sustained communication plus computation speeds reach 2.76 TeraFLOPS. This effort represents the first time that a high-order variable-density incompressible flow solver with species diffusion has demonstrated sustained performance in the TeraFLOPS range.

Volume rendering for curvilinear and unstructured grids

We discuss two volume rendering methods developed at Lawrence Livermore National Laboratory. The first, cell projection, renders the polygons in the projection of each cell. It requires a global visibility sort in order to composite the cells in back to front order, and we discuss several different algorithms for this sort. The second method uses regularly spaced slice planes perpendicular to the X, Y, or Z axes, which slice the cells into polygons. Both methods are supplemented with antialiasing techniques to deal with small cells that might fall between pixel samples or slice planes, and both have been parallelized.

Multiplex primer prediction software for divergent targets

We describe a Multiplex Primer Prediction (MPP) algorithm to build multiplex compatible primer sets to amplify all members of large, diverse and unalignable sets of target sequences. The MPP algorithm is scalable to larger target sets than other available software, and it does not require a multiple sequence alignment. We applied it to questions in viral detection, and demonstrated that there are no universally conserved priming sequences among viruses and that it could require an unfeasibly large number of primers (∼3700 18-mers or ∼2000 10-mers) to generate amplicons from all sequenced viruses. We then designed primer sets separately for each viral family, and for several diverse species such as foot-and-mouth disease virus (FMDV), hemagglutinin (HA) and neuraminidase (NA) segments of influenza A virus, Norwalk virus, and HIV-1. We empirically demonstrated the application of the software with a multiplex set of 16 short (10 nt) primers designed to amplify the Poxviridae family to produce a specific amplicon from vaccinia virus.

Approximate Volume Rendering for Curvilinear and Unstructured Grids by Hardware-Assisted Polyhedron Projection

A hardware polygon rendering pipeline can be used with hardware compositing to volume render arbitrary unstructured grids composed of convex polyhedral cells. This technique is described, together with the global sorting necessary for back‐to‐front compositing, and the modifications that must be made to approximate curvilinear cells, whose faces may not be planar.© 2000 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 11, 53–61, 2000

Cell Projection of Meshes With Non-Planar Faces

We review the cell projection method of volume rendering, discussing back-to-front cell sorting, and approximations involved in hardware color computation and interpolation. We describe how the method accommodates cells with non-planar faces using view dependent subdivision into tetrahedra.

Parallelizing a high accuracy hardware-assisted volume renderer for meshes with arbitrary polyhedra

Discusses our efforts to improve the performance of the high-accuracy (HIAC) volume rendering system, based on cell projection, which is used to display unstructured, scientific data sets for analysis. The parallelization of HIAC, using Pthreads and MPI APIs, resulted in significant speedup, but interactive frame rates are not yet attainable for very large data sets.

Metrics and generation specifications for comparing volume-rendered images

The goal of this paper is to lay a foundation for objectively comparing volume-rendered images, leading to objective evaluation of their accuracy and quality. The key elements of the foundation are: (1) a rigorous specification of all the input and parameters that need to be specified to define the conditions under which a volume-rendered image is generated; and (2) the basis for a methodology for difference classification, including a suite of functions or metrics to quantify and classify the difference between two volume-rendered images that will support an analysis of the relative importance of particular differences. The results of this method can be used to study the changes caused by modifying particular parameter values, to compare and quantify changes between images of similar data sets rendered in the same way, and to detect errors in the design, implementation or modification of a volume-rendering system. If a benchmark image is available, for example one created by a high-accuracy volume-rendering system, the method can be used to evaluate the accuracy of a given image. The key contribution of this paper is the separation of the difference into noise, bias and structured difference components. Copyright