Doctor of Philosophy

dissertationIn this dissertation, we advance the theory and practice of verifying visualization algorithms. We present techniques to assess visualization correctness through testing of important mathematical properties. Where applicable, these techniques allow us to distinguish whether anomalies in visualization features can be attributed to the underlying physical process or to artifacts from the implementation under verification. Such scientific scrutiny is at the heart of verifiable visualization - subjecting visualization algorithms to the same verification process that is used in other components of the scientific pipeline. The contributions of this dissertation are manifold. We derive the mathematical framework for the expected behavior of several visualization algorithms, and compare them to experimentally observed results in the selected codes. In the Computational Science & Engineering community CS&E, this technique is know as the Method of Manufactured Solution (MMS). We apply MMS to the verification of geometrical and topological properties of isosurface extraction algorithms, and direct volume rendering. We derive the convergence of geometrical properties of isosurface extraction techniques, such as function value and normals. For the verification of topological properties, we use stratified Morse theory and digital topology to design algorithms that verify topological invariants. In the case of volume rendering algorithms, we provide the expected discretization errors for three different error sources. The results of applying the MMS is another important contribution of this dissertation. We report unexpected behavior for almost all implementations tested. In some cases, we were able to find and fix bugs that prevented the correctness of the visualization algorithm. In particular, we address an almost 2 0 -year-old bug with the core disambiguation procedure of Marching Cubes 33, one of the first algorithms intended to preserve the topology of the trilinear interpolant. Finally, an important by-product of this work is a range of responses practitioners can expect to encounter with the visualization technique under verification

Interactive isosurface ray tracing of large octree volumes

Journal ArticleWe present a technique for ray tracing isosurfaces of large compressed structured volumes. Data is first converted into a losslesscompression octree representation that occupies a fraction of the original memory footprint. An isosurface is then dynamically rendered by tracing rays through a min/max hierarchy inside interior octree nodes. By embedding the acceleration tree and scalar data in a single structure and employing optimized octree hash schemes, we achieve competitive frame rates on common multicore architectures, and render large time-variant data that could not otherwise be accomodated

A fast voxelization algorithm for trilinearly interpolated isosurfaces

International audienceIn this work we propose a new method for a fast incremental voxelization of isosurfaces obtained by the trilinear interpolation of 3D data. Our objective consists in the fast generation of subvoxelized iso-surfaces extracted by a point-based technique similar to the Dividing Cubes algorithm. Our technique involves neither an exhaustive scan search process nor a graph-based search approach when generating iso-surface points. Instead an optimized incremental approach is adopted here for a rapid isosurface extraction. With a sufficient sampling subdivision criteria around critical points, the extracted isosurface is both correct and topologically consistent with respect to the piece-wise trilinear interpolant. Furthermore, the discretiza-tion scheme used in our method ensures obtaining thin-one voxel width-isosurfaces as compared to the given by the Dividing Cubes algorithm. The resultant sub-voxelized isosurfaces are efficiently tested against all possible configurations of the trilinear interpolant and real-world datasets

Lattice cleaving: a multimaterial tetrahedral meshing algorithm with guarantees

pre-printWe introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, to reduce element counts in regions of homogeneity. Additionally, we provide proofs showing that both element quality and geometric fidelity are bounded using this approach

Doctor of Philosophy

dissertationOne of the fundamental building blocks of many computational sciences is the construction and use of a discretized, geometric representation of a problem domain, often referred to as a mesh. Such a discretization enables an otherwise complex domain to be represented simply, and computation to be performed over that domain with a finite number of basis elements. As mesh generation techniques have become more sophisticated over the years, focus has largely shifted to quality mesh generation techniques that guarantee or empirically generate numerically well-behaved elements. In this dissertation, the two complementary meshing subproblems of vertex placement and element creation are analyzed, both separately and together. First, a dynamic particle system achieves adaptivity over domains by inferring feature size through a new information passing algorithm. Second, a new tetrahedral algorithm is constructed that carefully combines lattice-based stenciling and mesh warping to produce guaranteed quality meshes on multimaterial volumetric domains. Finally, the ideas of lattice cleaving and dynamic particle systems are merged into a unified framework for producing guaranteed quality, unstructured and adaptive meshing of multimaterial volumetric domains

Animating physical phenomena with embedded surface meshes

Accurate computational representations of highly deformable surfaces are indispensable in the fields of computer animation, medical simulation, computer vision, digital modeling, and computational physics. The focus of this dissertation is on the animation of physics-based phenomena with highly detailed deformable surfaces represented by triangle meshes. We first present results from an algorithm that generates continuum mechanics animations with intricate surface features. This method combines a finite element method with a tetrahedral mesh generator and a high resolution surface mesh, and it is orders of magnitude more efficient than previous approaches. Next, we present an efficient solution for the challenging problem of computing topological changes in detailed dynamic surface meshes. We then introduce a new physics-inspired surface tracking algorithm that is capable of preserving arbitrarily thin features and reproducing realistic fine-scale topological changes like Rayleigh-Plateau instabilities. This physics-inspired surface tracking technique also opens the door for a unique coupling between surficial finite element methods and volumetric finite difference methods, in order to simulate liquid surface tension phenomena more efficiently than any previous method. Due to its dramatic increase in computational resolution and efficiency, this method yielded the first computer simulations of a fully developed crown splash with droplet pinch off.Ph.D.Committee Chair: Turk, Greg; Committee Member: Essa, Irfan; Committee Member: Liu, Karen; Committee Member: Mucha, Peter J.; Committee Member: Rossignac, Jare

Doctor of Philosophy

dissertationShape analysis is a well-established tool for processing surfaces. It is often a first step in performing tasks such as segmentation, symmetry detection, and finding correspondences between shapes. Shape analysis is traditionally employed on well-sampled surfaces where the geometry and topology is precisely known. When the form of the surface is that of a point cloud containing nonuniform sampling, noise, and incomplete measurements, traditional shape analysis methods perform poorly. Although one may first perform reconstruction on such a point cloud prior to performing shape analysis, if the geometry and topology is far from the true surface, then this can have an adverse impact on the subsequent analysis. Furthermore, for triangulated surfaces containing noise, thin sheets, and poorly shaped triangles, existing shape analysis methods can be highly unstable. This thesis explores methods of shape analysis applied directly to such defect-laden shapes. We first study the problem of surface reconstruction, in order to obtain a better understanding of the types of point clouds for which reconstruction methods contain difficulties. To this end, we have devised a benchmark for surface reconstruction, establishing a standard for measuring error in reconstruction. We then develop a new method for consistently orienting normals of such challenging point clouds by using a collection of harmonic functions, intrinsically defined on the point cloud. Next, we develop a new shape analysis tool which is tolerant to imperfections, by constructing distances directly on the point cloud defined as the likelihood of two points belonging to a mutually common medial ball, and apply this for segmentation and reconstruction. We extend this distance measure to define a diffusion process on the point cloud, tolerant to missing data, which is used for the purposes of matching incomplete shapes undergoing a nonrigid deformation. Lastly, we have developed an intrinsic method for multiresolution remeshing of a poor-quality triangulated surface via spectral bisection

New Algorithmic Techniques for Large Scale Volumetric Data Visualization on Parallel Architectures

Volume visualization is widely used as an effective approach for the visual exploration, computational analysis, and manipulation of volumetric datasets. Due to the dramatic advances in imaging instruments and computing technologies, such datasets are now appearing at a very fast rate with increasingly larger sizes in many engineering, science and medical applications. Isosurface and direct volume rendering(DVR) are two of the most widely used techniques to render such datasets. This dissertation introduces novel techniques for rendering isosurfaces and volumes, and extends these techniques to multiprocessor architectures. We first focus on cluster-based techniques for isosurface extraction and rendering using polygonal approximation. We present a new simple indexing scheme and data layout approach, which enable scalable and efficient isosurface generation. This algorithm is the first known parallel algorithm to achieve provable load balancing on multiprocessor systems. We also develop an algorithm to generate isosurfaces using ray-casting on multi-core processors. Our method is based on a hybrid strategy that begins with an object order traversal of the data followed by ray-casting on ordered sets of an adaptive number of subcubes, one set for each small group of pixels on the image. We develop a multithreaded implementation, which uses new dynamic load balancing techniques that start with an image partitioning for the initial stage and then perform dynamic allocation of groups of ray-casting tasks among the different threads. The strategy ensures almost equal loads among the cores while maintaining spatial data locality. This scheme is extended to perform direct volume rendering and is shown to achieve similar improvements in terms of overall performance, load balancing, and scalability. We conduct a large number of tests for all our algorithms on the University of Maryland Visualization Cluster and on the 8-core Clovertown platform using a wide variety of datasets such as Richtmyer-Meshkov Instability dataset (7.5GB for each time step) and Visible Human dataset (~1GB). We obtain results that consistently validate the efficiency and the scalability of our algorithms. In particular, the overall performance of our hybrid ray-casting scheme achieves an interactive rendering rate on high resolution (1024x1024) screens for all the datasets tested

New Models for High-Quality Surface Reconstruction and Rendering

The efficient reconstruction and artifact-free visualization of surfaces from measured real-world data is an important issue in various applications, such as medical and scientific visualization, quality control, and the media-related industry. The main contribution of this thesis is the development of the first efficient GPU-based reconstruction and visualization methods using trivariate splines, i.e., splines defined on tetrahedral partitions. Our methods show that these models are very well-suited for real-time reconstruction and high-quality visualizations of surfaces from volume data. We create a new quasi-interpolating operator which for the first time solves the problem of finding a globally C1-smooth quadratic spline approximating data and where no tetrahedra need to be further subdivided. In addition, we devise a new projection method for point sets arising from a sufficiently dense sampling of objects. Compared with existing approaches, high-quality surface triangulations can be generated with guaranteed numerical stability. Keywords. Piecewise polynomials; trivariate splines; quasi-interpolation; volume data; GPU ray casting; surface reconstruction; point set surface