Fast and Exact Fiber Surfaces for Tetrahedral Meshes

Isosurfaces are fundamental geometrical objects for the analysis and visualization of volumetric scalar fields. Recent work has generalized them to bivariate volumetric fields with fiber surfaces, the pre-image of polygons in range space. However, the existing algorithm for their computation is approximate, and is limited to closed polygons. Moreover, its runtime performance does not allow instantaneous updates of the fiber surfaces upon user edits of the polygons. Overall, these limitations prevent a reliable and interactive exploration of the space of fiber surfaces. This paper introduces the first algorithm for the exact computation of fiber surfaces in tetrahedral meshes. It assumes no restriction on the topology of the input polygon, handles degenerate cases and better captures sharp features induced by polygon bends. The algorithm also allows visualization of individual fibers on the output surface, better illustrating their relationship with data features in range space. To enable truly interactive exploration sessions, we further improve the runtime performance of this algorithm. In particular, we show that it is trivially parallelizable and that it scales nearly linearly with the number of cores. Further, we study acceleration data-structures both in geometrical domain and range space and we show how to generalize interval trees used in isosurface extraction to fiber surface extraction. Experiments demonstrate the superiority of our algorithm over previous work, both in terms of accuracy and running time, with up to two orders of magnitude speedups. This improvement enables interactive edits of range polygons with instantaneous updates of the fiber surface for exploration purpose. A VTK-based reference implementation is provided as additional material to reproduce our results

The Topology ToolKit

This system paper presents the Topology ToolKit (TTK), a software platform designed for topological data analysis in scientific visualization. TTK provides a unified, generic, efficient, and robust implementation of key algorithms for the topological analysis of scalar data, including: critical points, integral lines, persistence diagrams, persistence curves, merge trees, contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots, Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due to a tight integration with ParaView. It is also easily accessible to developers through a variety of bindings (Python, VTK/C++) for fast prototyping or through direct, dependence-free, C++, to ease integration into pre-existing complex systems. While developing TTK, we faced several algorithmic and software engineering challenges, which we document in this paper. In particular, we present an algorithm for the construction of a discrete gradient that complies to the critical points extracted in the piecewise-linear setting. This algorithm guarantees a combinatorial consistency across the topological abstractions supported by TTK, and importantly, a unified implementation of topological data simplification for multi-scale exploration and analysis. We also present a cached triangulation data structure, that supports time efficient and generic traversals, which self-adjusts its memory usage on demand for input simplicial meshes and which implicitly emulates a triangulation for regular grids with no memory overhead. Finally, we describe an original software architecture, which guarantees memory efficient and direct accesses to TTK features, while still allowing for researchers powerful and easy bindings and extensions. TTK is open source (BSD license) and its code, online documentation and video tutorials are available on TTK's website

Doctor of Philosophy

dissertationDespite the progress that has been made since the inception of the finite element method, the field of biomechanics has generally relied on software tools that were not specifically designed to target this particular area of application. Software designed specifically for the field of computational biomechanics does not appear to exist. To overcome this limitation, FEBio was developed, an acronym for “Finite Elements for Biomechanics”, which provided an open-source framework for developing finite element software that is tailored to the specific needs of the biomechanics and biophysics communities. The proposed work added an extendible framework to FEBio that greatly facilitates the implementation of novel features and provides an ideal platform for exploring novel computational approaches. This framework supports plugins, which simplify the process of adding new features even more since plugins can be developed independently from the main source code. Using this new framework, this work extended FEBio in two important areas of interest in biomechanics. First, as tetrahedral elements continue to be the preferred modeling primitive for representing complex geometries, several tetrahedral formulations were investigated in terms of their robustness and accuracy for solving problems in computational biomechanics. The focus was on the performance of quadratic tetrahedral formulations in large deformation contact analyses, as this is an important area of application in biomechanics. Second, the application of prestrain to computational models has been recognized as an important component in simulations of biological tissues in order to accurately predict the mechanical response. As this remains challenging to do in existing software packages, a general computational framework for applying prestrain was incorporated in the FEBio software. The work demonstrated via several examples how plugins greatly simplify the development of novel features. In addition, it showed that the quadratic tetrahedral formulations studied in this work are viable alternatives for contact analyses. Finally, it demonstrated the newly developed prestrain plugin and showed how it can be used in various applications of prestrain

Jacobi Fiber Surfaces for Bivariate Reeb Space Computation

This paper presents an efficient algorithm for the computation of the Reeb space of an input bivariate piecewise linear scalar function f defined on a tetrahedral mesh. By extending and generalizing algorithmic concepts from the univariate case to the bivariate one, we report the first practical, output-sensitive algorithm for the exact computation of such a Reeb space. The algorithm starts by identifying the Jacobi set of f , the bivariate analogs of critical points in the univariate case. Next, the Reeb space is computed by segmenting the input mesh along the new notion of Jacobi Fiber Surfaces, the bivariate analog of critical contours in the univariate case. We additionally present a simplification heuristic that enables the progressive coarsening of the Reeb space. Our algorithm is simple to implement and most of its computations can be trivially parallelized. We report performance numbers demonstrating orders of magnitude speedups over previous approaches, enabling for the first time the tractable computation of bivariate Reeb spaces in practice. Moreover, unlike range-based quantization approaches (such as the Joint Contour Net), our algorithm is parameter-free. We demonstrate the utility of our approach by using the Reeb space as a semi-automatic segmentation tool for bivariate data. In particular, we introduce continuous scatterplot peeling, a technique which enables the reduction of the cluttering in the continuous scatterplot, by interactively selecting the features of the Reeb space to project. We provide a VTK-based C++ implementation of our algorithm that can be used for reproduction purposes or for the development of new Reeb space based visualization techniques

Direct Multifield Volume Ray Casting of Fiber Surfaces

Multifield data are common in visualization. However, reducing these data to comprehensible geometry is a challenging problem. Fiber surfaces, an analogy of isosurfaces to bivariate volume data, are a promising new mechanism for understanding multifield volumes. In this work, we explore direct ray casting of fiber surfaces from volume data without any explicit geometry extraction. We sample directly along rays in domain space, and perform geometric tests in range space where fibers are defined, using a signed distance field derived from the control polygons. Our method requires little preprocess, and enables real-time exploration of data, dynamic modification and pixel-exact rendering of fiber surfaces, and support for higher-order interpolation in domain space. We demonstrate this approach on several bivariate datasets, including analysis of multi-field combustion data

3D FEM model development from 3D optical measurement technique applied to corroded steel bars

Understanding the mechanical effects of the corrosion pits on the steel surface requires an accurate definition of their geometry and distribution along the rebar. 3D optical measurement technique is used to obtain the outer geometry of artificially corroded bars tested under cyclic or monotonic loads. 3D FEM model development from the 3D scanning results were carried out in order to investigate the failure process and local effects on the pits, which are responsible of the variation of the mechanical properties in corroded steel reinforcement. In addition, a validation of a simplified model, which allows the mechanical steel properties determination given an estimated corrosion level, is presented. 3D models were convenient to observe and measure the local effects on the pits.Peer ReviewedPostprint (author's final draft

Assumed Strain Finite Element Formulations and Stabilization Techniques

The design of any engineering component requires robust analysis using numerical methods like the Finite Element Method. Of paramount importance is to develop convergent formulations that can achieve accurate estimates for the solution at cheaper computational costs.We investigate a method for improving the accuracy of the stress predicted from models using the mean-strain finite elements recently proposed by Krysl and collaborators [IJNME 2016, 2017]. In state-of-the-art finite element programs, the stress values at the integration points are commonly post-processed to obtain nodal stresses. The mean stresses are element-wise constant, and hence the nodal values obtained from the mean stresses tend to be less accurate. The proposed method post-processes the uniform stress in each element in combination with a linearly-varying stabilization stress field to compute more accurate nodal stresses. Selected examples are presented to demonstrate improvements achievable with the proposed methodology for hexahedral and quadratic tetrahedral mean-strain finite elements. The nodally integrated formulations exhibit spuriousness in dynamic analyses (such as in modal analysis). Previously proposed methods involved a heuristic stabilization factor, which may not work for a large range of problems, and a uniform stabilization was used over all the finite elements in the mesh. The method proposed herein makes use of energy-sampling stabilization. The stabilization factor depends on the shape of the element and appears in the definition of the properties of a stabilization material. The stabilization factor is non-uniform over the mesh, and can be computed to alleviate shear locking, which directly depends on the aspect ratios ofthe finite elements. The nodal stabilization factor is then computed by volumetric averaging of the element-based stabilization factors. Energy-sampling stabilized nodally integrated elements (ESNICE) tetrahedral and hexahedral are proposed. We demonstrate on examples that the proposed procedure effectively removes spurious (unphysical) modes both at lower and at higher ends of the frequency spectrum. The examples shown demonstrate the reliability of energy-sampling in stabilizing the nodally integrated formulations in vibration problems, just sufficient to eliminate spuriousness while imparting minimal excessive stiffness to the structure. We also show by the numerical inf-sup test that the formulation is coercive and locking-free