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

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

Numerical studies of flow in porous media using an unstructured approach

Flow and transport in porous media is relevant to many areas of engineering and science including groundwater hydrology and the recovery of oil and gas. Porous materials are characterized by the unique shape and connectivity of the internal void structures which give rise to a large range in macroscopic transport properties. Historically an inability to accurately describe the internal pore-structure has prevented detailed study of the role of pore structure on transport. In recent decades however, the combination of high resolution imaging technologies with computational modeling has seen the development of fundamental pore-scale techniques for studying flow in porous media. Image-based pore-scale modeling of transport phenomena has become an important tool for understanding the complicated relationships between pore structure and measurable macroscopic properties, including permeability and formation factor. This has commonly been achieved by a network-based approach where the pore space is idealized as a series of pores connected by throats, or by a grid-based approach where the voxels of a 3D image represent structured quadrilateral elements or nodal locations. In this work however, image-based unstructured meshing techniques are used to represent voxelised pore spaces by grids comprising entirely of tetrahedral elements. These unstructured tetrahedral grids are used in finite element models to calculate permeability and formation factor. Solutions to the Stokes equations governing creeping, or Darcy flow, are used to validate the finite element approach employed in this work, and to assess the impact of different image-based unstructured meshing strategies on predicted permeability. Testing shows that solutions to the Stokes equations by a P2P1 tetrahedral element are significantly more accurate than solutions based on a P1P1 element, while permeability is shown to be sensitive to structural changes to the pore space induced by different meshing approaches. The modeling approach is also used to investigate the relationship of an electric and hydraulic definition of tortuosity to the Carman-Kozeny equation. The results of simulations using a number of computer generated porous structures indicate that an electrical tortuosity based on computed formation factor is well correlated with the tortuosity suggested by the Carman-Kozeny equation

Doctor of Philosophy

dissertationDataflow pipeline models are widely used in visualization systems. Despite recent advancements in parallel architecture, most systems still support only a single CPU or a small collection of CPUs such as a SMP workstation. Even for systems that are specifically tuned towards parallel visualization, their execution models only provide support for data-parallelism while ignoring taskparallelism and pipeline-parallelism. With the recent popularization of machines equipped with multicore CPUs and multi-GPU units, these visualization systems are undoubtedly falling further behind in reaching maximum efficiency. On the other hand, there exist several libraries that can schedule program executions on multiple CPUs and/or multiple GPUs. However, due to differences in executing a task graph and a pipeline along with their APIs being considerably low-level, it still remains a challenge to integrate these run-time libraries into current visualization systems. Thus, there is a need for a redesigned dataflow architecture to fully support and exploit the power of highly parallel machines in large-scale visualization. The new design must be able to schedule executions on heterogeneous platforms while at the same time supporting arbitrarily large datasets through the use of streaming data structures. The primary goal of this dissertation work is to develop a parallel dataflow architecture for streaming large-scale visualizations. The framework includes supports for platforms ranging from multicore processors to clusters consisting of thousands CPUs and GPUs. We achieve this in our system by introducing the notion of Virtual Processing Elements and Task-Oriented Modules along with a highly customizable scheduler that controls the assignment of tasks to elements dynamically. This creates an intuitive way to maintain multiple CPU/GPU kernels yet still provide coherency and synchronization across module executions. We have implemented these techniques into HyperFlow which is made of an API with all basic dataflow constructs described in the dissertation, and a distributed run-time library that can be used to deploy those pipelines on multicore, multi-GPU and cluster-based platforms

Deformable Simplicial Complexes

In this dissertation we present a novel method for deformable interface tracking in 2D and 3D|deformable simplicial complexes (DSC). Deformable interfaces are used in several applications, such as fluid simulation, image analysis, reconstruction or structural optimization. In the DSC method, the interface (curve in 2D; surface in 3D) is represented explicitly as a piecewise linear curve or surface. However, the domain is also subject to discretization: triangulation in 2D; tetrahedralization in 3D. This way, the interface can be alternatively represented as a set of edges/triangles separating triangles/tetrahedra marked as outside from those marked as inside. Such an approach allows for robust topological adaptivity. Among other advantages of the deformable simplicial complexes there are: space adaptivity, ability to handle and preserve sharp features, possibility for topology control. We demonstrate those strengths in several applications. In particular, a novel, DSC-based fluid dynamics solver has been developed during the PhD project. A special feature of this solver is that due to the fact that DSC maintains an explicit interface representation, surface tension is more easily dealt with. One particular advantage of DSC is the fact that as an alternative to topology adaptivity, topology control is also possible. This is exploited in the construction of cut loci on tori where a front expands from a single point on a torus and stops when it self-intersects