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

Fully anisotropic split-tree adaptive refinement mesh generation using tetrahedral mesh stitching

Due to the myriad of geometric topologies that modern computational fluid dynamicists desire to mesh and run solutions on, the need for a robust Cartesian Mesh Generation algorithm is paramount. Not only do Cartesian meshes require less elements and often help resolve flow features but they also allow the grid generator to have a great deal of control in so far as element aspect ratio, size, and gradation. Fully Anisotropic Split-Tree Adaptive Refinement (FASTAR) is a code that allows the user to exert a great deal of control and ultimately generate a valid, geometry conforming mesh. Due to the split-tree nature and the use of volumetric pixels (voxels), non-unit aspect ratio meshing is easily achieved. Nodes are not generated until the end which mitigates tolerance issues. The tree is retained coherently, and viscous layers may be inserted in the space between the geometry and the Cartesian mesh before it is tetrahedralized. FASTAR uses tree traversal to determine neighbors robustly, and with the tetrahedralization of only a small amount of space around the geometry, sliver cells and inverted elements are avoided. The code uses Riemannian Metric Tensors to generate geometry-appropriate spacing and is capable of adaptive meshing from a spacing field generated either by the user or from solution data. FASTAR is a robust, general mesh generator that allows maximum flexibility with minimal post-processing

Volumetric rendering techniques for scientific visualization

Ankara : The Department of Computer Engineering and The Graduate School of Engineering and Science of Bilkent University, 2014.Thesis (Ph.D.) -- Bilkent University, 2014.Includes bibliographical references leaves 80-86.Direct volume rendering is widely used in many applications where the inside of a transparent or a partially transparent material should be visualized. We have explored several aspects of the problem. First, we proposed a view-dependent selective refinement scheme in order to reduce the high computational requirements without affecting the image quality significantly. Then, we explored the parallel implementations of direct volume rendering: both on GPU and on multi-core systems. Finally, we used direct volume rendering approaches to create a tool, MaterialVis, to visualize amorphous and/or crystalline materials. Visualization of large volumetric datasets has always been an important problem. Due to the high computational requirements of volume-rendering techniques, achieving interactive rates is a real challenge. We present a selective refinement scheme that dynamically refines the mesh according to the camera parameters. This scheme automatically determines the impact of different parts of the mesh on the output image and refines the mesh accordingly, without needing any user input. The viewdependent refinement scheme uses a progressive mesh representation that is based on an edge collapse-based tetrahedral mesh simplification algorithm. We tested our view-dependent refinement framework on an existing state-of-the-art volume renderer. Thanks to low overhead dynamic view-dependent refinement, we achieve interactive frame rates for rendering common datasets at decent image resolutions. Achieving interactive rates for direct volume rendering of large unstructured volumetric grids is a challenging problem, but parallelizing direct volume rendering algorithms can help achieve this goal. Using Compute Unified Device Architecture (CUDA), we propose a GPU-based volume rendering algorithm that itself is based on a cell projection-based ray-casting algorithm designed for CPU implementations. We also propose a multi-core parallelized version of the cell-projection algorithm using OpenMP. In both algorithms, we favor image quality over rendering speed. Our algorithm has a low memory footprint, allowing us to render large datasets. Our algorithm support progressive rendering. We compared the GPU implementation with the serial and multi-core implementations. We observed significant speed-ups, that, together with progressive rendering, enabling reaching interactive rates for large datasets. Visualization of materials is an indispensable part of their structural analysis. We developed a visualization tool for amorphous as well as crystalline structures, called MaterialVis. Unlike the existing tools, MaterialVis represents material structures as a volume and a surface manifold, in addition to plain atomic coordinates. Both amorphous and crystalline structures exhibit topological features as well as various defects. MaterialVis provides a wide range of functionality to visualize such topological structures and crystal defects interactively. Direct volume rendering techniques are used to visualize the volumetric features of materials, such as crystal defects, which are responsible for the distinct fingerprints of a specific sample. In addition, the tool provides surface visualization to extract hidden topological features within the material. Together with the rich set of parameters and options to control the visualization, MaterialVis allows users to visualize various aspects of materials very efficiently as generated by modern analytical techniques such as the Atom Probe Tomography.Okuyan, ErhanPh.D

Tracing Analytic Ray Curves for Light and Sound Propagation in Non-Linear Media

The physical world consists of spatially varying media, such as the atmosphere and the ocean, in which light and sound propagates along non-linear trajectories. This presents a challenge to existing ray-tracing based methods, which are widely adopted to simulate propagation due to their efficiency and flexibility, but assume linear rays. We present a novel algorithm that traces analytic ray curves computed from local media gradients, and utilizes the closed-form solutions of both the intersections of the ray curves with planar surfaces, and the travel distance. By constructing an adaptive unstructured mesh, our algorithm is able to model general media profiles that vary in three dimensions with complex boundaries consisting of terrains and other scene objects such as buildings. Our analytic ray curve tracer with the adaptive mesh improves the efficiency considerably over prior methods. We highlight the algorithm's application on simulation of visual and sound propagation in outdoor scenes

La marche céleste: une marche oublieuse dans les subdivisions convexes à terminaison garantie

We present a new oblivious walking strategy for convex subdivisions. Our walk isfaster than the straight walk and more generally applicable than the visiblity walk. To provetermination of our walk we use a novel monotonically decreasing distance measure.Nous présentons une nouvelle stratégie de marche pour les subdivisions convexes.Cette stratégie est oublieuse, c’est à dire que la prochaine cellule visitée ne dépends pas des cellulesvisitées précédemment. Notre marche est plus rapide que la marche rectiligne et s’applique à dessubdivisions plus générales que la marche par visibilité. La démonstration de terminaison reposesur la décroissance monotone d’une nouvelle distance mesurant le progrès de la march

Texture-Based Segmentation and Finite Element Mesh Generation for Heterogeneous Biological Image Data

The design, analysis, and control of bio-systems remain an engineering challenge. This is mainly due to the material heterogeneity, boundary irregularity, and nonlinear dynamics associated with these systems. The recent developments in imaging techniques and stochastic upscaling methods provides a window of opportunity to more accurately assess these bio-systems than ever before. However, the use of image data directly in upscaled stochastic framework can only be realized by the development of certain intermediate steps. The goal of the research presented in this dissertation is to develop a texture-segmentation method and a unstructured mesh generation for heterogeneous image data. The following two new techniques are described and evaluated in this dissertation: 1. A new texture-based segmentation method, using the stochastic continuum concepts and wavelet multi-resolution analysis, is developed for characterization of heterogeneous materials in image data. The feature descriptors are developed to efficiently capture the micro-scale heterogeneity of macro-scale entities. The materials are then segmented at a representative elementary scale at which the statistics of the feature descriptor stabilize. 2. A new unstructured mesh generation technique for image data is developed using a hierarchical data structure. This representation allows for generating quality guaranteed finite element meshes. The framework for both the methods presented in this dissertation, as such, allows them for extending to higher dimensions. The experimental results using these methods conclude them to be promising tools for unifying data processing concepts within the upscaled stochastic framework across biological systems. These are targeted for inclusion in decision support systems where biological image data, simulation techniques and artificial intelligence will be used conjunctively and uniformly to assess bio-system quality and design effective and appropriate treatments that restore system health

Efficient Light and Sound Propagation in Refractive Media with Analytic Ray Curve Tracer

Refractive media is ubiquitous in the natural world, and light and sound propagation in refractive media leads to characteristic visual and acoustic phenomena. Those phenomena are critical for engineering applications to simulate with high accuracy requirements, and they can add to the perceived realism and sense of immersion for training and entertainment applications. Existing methods can be roughly divided into two categories with regard to their handling of propagation in refractive media; first category of methods makes simplifying assumption about the media or entirely excludes the consideration of refraction in order to achieve efficient propagation, while the second category of methods accommodates refraction but remains computationally expensive. In this dissertation, we present algorithms that achieve efficient and scalable propagation simulation of light and sound in refractive media, handling fully general media and scene configurations. Our approaches are based on ray tracing, which traditionally assumes homogeneous media and rectilinear rays. We replace the rectilinear rays with analytic ray curves as tracing primitives, which represent closed-form trajectory solutions based on assumptions of a locally constant media gradient. For general media profiles, the media can be spatially decomposed into explicit or implicit cells, within which the media gradient can be assumed constant, leading to an analytic ray path within that cell. Ray traversal of the media can therefore proceed in segments of ray curves. The first source of speedup comes from the fact that for smooth media, a locally constant media gradient assumption tends to stay valid for a larger area than the assumption of a locally constant media property. The second source of speedup is the constant-cost intersection computation of the analytic ray curves with planar surfaces. The third source of speedup comes from making the size of each cell and therefore each ray curve segment adaptive to the magnitude of media gradient. Interactions with boundary surfaces in the scene can be efficiently handled within this framework in two alternative approaches. For static scenes, boundary surfaces can be embedded into the explicit mesh of tetrahedral cells, and the mesh can be traversed and the embedded surfaces intersected with by the analytic ray curve in a unified manner. For dynamic scenes, implicit cells are used for media traversal, and boundary surface intersections can be handled separately by constructing hierarchical acceleration structures adapted from rectilinear ray tracer. The efficient handling of boundary surfaces is the fourth source of speedup of our propagation path computation. We demonstrate over two orders-of-magnitude performance improvement of our analytic ray tracing algorithms over prior methods for refractive light and sound propagation. We additionally present a complete sound-propagation simulation solution that matches the path computation efficiency achieved by the ray curve tracer. We develop efficient pressure computation algorithm based on analytic evaluations and combine our algorithm with the Gaussian beam for fast acoustic field computation. We validate the accuracy of the simulation results on published benchmarks, and we show the application of our algorithms on complex and general three-dimensional outdoor scenes. Our algorithms enable simulation scenarios that are simply not feasible with existing methods, and they have the potential of being extended and complementing other propagation methods for capability beyond handling refractive media.Doctor of Philosoph