Volume MLS Ray Casting

The method of Moving Least Squares (MLS) is a popular framework for reconstructing continuous functions from scattered data due to its rich mathematical properties and well-understood theoretical foundations. This paper applies MLS to volume rendering, providing a unified mathematical framework for ray casting of scalar data stored over regular as well as irregular grids. We use the MLS reconstruction to render smooth isosurfaces and to compute accurate derivatives for high-quality shading effects. We also present a novel, adaptive preintegration scheme to improve the efficiency of the ray casting algorithm by reducing the overall number of function evaluations, and an efficient implementation of our framework exploiting modern graphics hardware. The resulting system enables high-quality volume integration and shaded isosurface rendering for regular and irregular volume data.Engineering and Applied Science

Single-Strip Triangulation of Manifolds with Arbitrary Topology

Triangle strips have been widely used for efficient rendering. It is NP-complete to test whether a given triangulated model can be represented as a single triangle strip, so many heuristics have been proposed to partition models into few long strips. In this paper, we present a new algorithm for creating a single triangle loop or strip from a triangulated model. Our method applies a dual graph matching algorithm to partition the mesh into cycles, and then merges pairs of cycles by splitting adjacent triangles when necessary. New vertices are introduced at midpoints of edges and the new triangles thus formed are coplanar with their parent triangles, hence the visual fidelity of the geometry is not changed. We prove that the increase in the number of triangles due to this splitting is 50% in the worst case, however for all models we tested the increase was less than 2%. We also prove tight bounds on the number of triangles needed for a single-strip representation of a model with holes on its boundary. Our strips can be used not only for efficient rendering, but also for other applications including the generation of space filling curves on a manifold of any arbitrary topology.Comment: 12 pages, 10 figures. To appear at Eurographics 200

Tools for Analysis and Visualization of Large Time-Varying CFD Data Sets

In the second year, we continued to built upon and improve our scanline-based direct volume renderer that we developed in the first year of this grant. This extremely general rendering approach can handle regular or irregular grids, including overlapping multiple grids, and polygon mesh surfaces. It runs in parallel on multi-processors. It can also be used in conjunction with a k-d tree hierarchy, where approximate models and error terms are stored in the nodes of the tree, and approximate fast renderings can be created. We have extended our software to handle time-varying data where the data changes but the grid does not. We are now working on extending it to handle more general time-varying data. We have also developed a new extension of our direct volume renderer that uses automatic decimation of the 3D grid, as opposed to an explicit hierarchy. We explored this alternative approach as being more appropriate for very large data sets, where the extra expense of a tree may be unacceptable. We also describe a new approach to direct volume rendering using hardware 3D textures and incorporates lighting effects. Volume rendering using hardware 3D textures is extremely fast, and machines capable of using this technique are becoming more moderately priced. While this technique, at present, is limited to use with regular grids, we are pursuing possible algorithms extending the approach to more general grid types. We have also begun to explore a new method for determining the accuracy of approximate models based on the light field method described at ACM SIGGRAPH '96. In our initial implementation, we automatically image the volume from 32 equi-distant positions on the surface of an enclosing tessellated sphere. We then calculate differences between these images under different conditions of volume approximation or decimation. We are studying whether this will give a quantitative measure of the effects of approximation. We have created new tools for exploring the differences between images produced by various rendering methods. Images created by our software can be stored in the SGI RGB format. Our idtools software reads in pair of images and compares them using various metrics. The differences of the images using the RGB, HSV, and HSL color models can be calculated and shown. We can also calculate the auto-correlation function and the Fourier transform of the image and image differences. We will explore how these image differences compare in order to find useful metrics for quantifying the success of various visualization approaches. In general, progress was consistent with our research plan for the second year of the grant

TetSplat: Real-time Rendering and Volume Clipping of Large Unstructured Tetrahedral Meshes

We present a novel approach to interactive visualization and exploration of large unstructured tetrahedral meshes. These massive 3D meshes are used in mission-critical CFD and structural mechanics simulations, and typically sample multiple field values on several millions of unstructured grid points. Our method relies on the pre-processing of the tetrahedral mesh to partition it into non-convex boundaries and internal fragments that are subsequently encoded into compressed multi-resolution data representations. These compact hierarchical data structures are then adaptively rendered and probed in real-time on a commodity PC. Our point-based rendering algorithm, which is inspired by QSplat, employs a simple but highly efficient splatting technique that guarantees interactive frame-rates regardless of the size of the input mesh and the available rendering hardware. It furthermore allows for real-time probing of the volumetric data-set through constructive solid geometry operations as well as interactive editing of color transfer functions for an arbitrary number of field values. Thus, the presented visualization technique allows end-users for the first time to interactively render and explore very large unstructured tetrahedral meshes on relatively inexpensive hardware

Parzsweep: A Novel Parallel Algorithm for Volume Rendering of Regular Datasets

The sweep paradigm for volume rendering has previously been successfully applied with irregular grids. This thesis describes a parallel volume rendering algorithm called PARZSweep for regular grids that utilizes the sweep paradigm. The sweep paradigm is a concept where a plane sweeps the data volume parallel to the viewing direction. As the sweeping proceeds in the increasing order of z, the faces incident on the vertices are projected onto the viewing volume to constitute to the image. The sweeping ensures that all faces are projected in the correct order and the image thus obtained is very accurate in its details. PARZSweep is an extension of a serial algorithm for regular grids called RZSweep. The hypothesis of this research is that a parallel version of RZSweep can be designed and implemented which will utilize multiple processors to reduce rendering times. PARZSweep follows an approach called image-based task scheduling or tiling. This approach divides the image space into tiles and allocates each tile to a processor for individual rendering. The sub images are composite to form a complete final image. PARZSweep uses a shared memory architecture in order to take advantage of inherent cache coherency for faster communication between processor. Experiments were conducted comparing RZSweep and PARZSweep with respect to prerendering times, rendering times and image quality. RZSweep and PARZSweep have approximately the same prerendering costs, produce exactly the same images and PARZSweep substantially reduced rendering times. PARZSweep was evaluated for scalability with respect to the number of tiles and number of processors. Scalability results were disappointing due to uneven data distribution

Rzsweep: A New Volume-Rendering Technique for Uniform Rectilinear Datasets

A great challenge in the volume-rendering field is to achieve high-quality images in an acceptable amount of time. In the area of volume rendering, there is always a trade-off between speed and quality. Applications where only high-quality images are acceptable often use the ray-casting algorithm, but this method is computationally expensive and typically achieves low frame rates. The work presented here is RZSweep, a new volume-rendering algorithm for uniform rectilinear datasets, that gives high-quality images in a reasonable amount of time. In this algorithm a plane sweeps the vertices of the implicit grid of regular datasets in depth order, projecting all the implicit faces incident on each vertex. This algorithm uses the inherent properties of a rectilinear datasets. RZSweep is an object-order, back-toront, direct volume rendering, face projection algorithm for rectilinear datasets using the cell approach. It is a single processor serial algorithm. The simplicity of the algorithm allows the use of the graphics pipeline for hardware-assisted projection, and also, with minimum modification, a version of the algorithm that is graphics-hardware independent. Lighting, color and various opacity transfer functions are implemented for giving realism to the final resulting images. Finally, an image comparison is done between RZSweep and a 3D texture-based method for volume rendering using standard image metrics like Euclidian and geometric differences

Real-time tessellation of terrain on graphics hardware

Synthetic terrain is a key element in many applications, which can lessen the sense of realism if it is not handled correctly. We propose a new technique for visualizing terrain surfaces by tessellating them on the GPU. The presented algorithm introduces a new adaptive tessellation scheme for managing the level of detail of the terrain mesh, avoiding the appearance of t-vertices that can produce visually disturbing artifacts. Previous solutions exploited the geometry shader's capabilities to tessellate meshes from scratch. In contrast, we reuse the already calculated data to minimize the operations performed in the shader units. This feature allows us to increase performance through smart refining and coarsening. Finally, we also propose a framework to manage large DEMs as height maps.This work has been supported by the Spanish Ministry of Science and Technology (projects TIN2009-14103-C03-03, TSI-020400-2009-0133 and TIN2010-21089-C03-03), by the Generalitat Valenciana (project PROMETEO/2010/028), by Bancaja (project P1 1B2010-08) and by ITEA2 (project IP08009