A new isosurface extraction method on arbitrary grids

The development of interface-capturing methods (such as level-set, phase-field or volume of fluid (VOF) methods) for arbitrary 3D grids has further highlighted the need for more accurate and efficient interface reconstruction procedures. In this work, we propose a new method for the extraction of isosurfaces on arbitrary polyhedra that can be used with advantage for this purpose. The isosurface is extracted from volume fractions by a general polygon tracing procedure, which is valid for convex or non-convex geometries, even with non-planar faces. The proposed method, which can be considered as an extension of the marching cubes technique, produces consistent results even for ambiguous situations in polyhedra of arbitrary shape. To show the reproducibility of the results presented in this work, we provide the open source library isoap, which has been developed to implement the proposed method and includes test programs to demonstrate the successful extraction of isosurfaces on several grids with polyhedral cells of different types. We present results obtained not only for isosurface extraction from discrete volume fractions resulting from a volume of fluid method, but also from data sets obtained from implicit mathematical functions and signed distances to scanned surfaces. The improvement provided by the proposed method for the extraction of isosurfaces in arbitrary grids will also be very useful in other fields, such as CFD visualization or medical imaging.The authors gratefully acknowledge the support of the Spanish Ministerio de Ciencia, Innovación y Universidades - Agencia Estatal de Investigación and FEDER through projects DPI2017-87826-C2-1-P and DPI2017-87826-C2-2-P

Homeomorphic Tetrahedralization of Multi-material Images with Quality and Fidelity Guarantees

We present a novel algorithm for generating three-dimensional unstructured tetrahedral meshes of multi-material images. The algorithm produces meshes with high quality since it provides a guaranteed dihedral angle bound of up to 19.47° for the output tetrahedra. In addition, it allows for user-specified guaranteed bounds on the two-sided Hausdorff distance between the boundaries of the mesh and the boundaries of the materials. Moreover, the mesh boundary is proved to be homeomorphic to the object surface. The algorithm is fast and robust, it produces a sufficiently small number of mesh elements that comply with these guarantees, as compared to other software. The theory and effectiveness of our method are illustrated with the experimental evaluation on synthetic and real medical data

Graphical Computing Solution for Industrial Plant Engineering

When preparing an engineering operation on an industrial plant, reliable and updated models of the plant must be available for correct decisions and planning. However, especially in the case of offshore oil and gas installations, it can hazardous and expensive to send an engineering party to assess and update the model of the plant. To reduce the cost and risk of modelling the plant, there are methods for quickly generating a 3D representation, such as LiDAR and stereoscopic reconstruction. However, these methods generate large files with no inherit cohesion. To address this, we propose to find a solution to efficiently transform point clouds from stereoscopic reconstruction into small mesh files that can be streamed or shared across teams. With that in mind, different techniques for treating point clouds and generating meshes were tested independently to measure their performance and effectiveness on an artifact-rich data set, such as the ones this work is aimed for. Afterwards, the techniques were combined into pipelines and compared with each other in terms of efficiency, file size output, and quality. With all results in place, the best solution from the ones tested was identified and validated with large real-world data sets.Master's Thesis in InformaticsINF39

Topology verification for isosurface extraction

Journal ArticleThe broad goals of verifiable visualization rely on correct algorithmic implementations. We extend a framework for verification of isosurfacing implementations to check topological properties. Specifically, we use stratified Morse theory and digital topology to design algorithms which verify topological invariants. Our extended framework reveals unexpected behavior and coding mistakes in popular publicly available isosurface codes

Warping cubes: better triangles from marching cubes

National Science Foundatio

GPU-friendly marching cubes.

Xie, Yongming.Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.Includes bibliographical references (leaves 77-85).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Isosurfaces --- p.1Chapter 1.2 --- Graphics Processing Unit --- p.2Chapter 1.3 --- Objective --- p.3Chapter 1.4 --- Contribution --- p.3Chapter 1.5 --- Thesis Organization --- p.4Chapter 2 --- Marching Cubes --- p.5Chapter 2.1 --- Introduction --- p.5Chapter 2.2 --- Marching Cubes Algorithm --- p.7Chapter 2.3 --- Triangulated Cube Configuration Table --- p.12Chapter 2.4 --- Summary --- p.16Chapter 3 --- Graphics Processing Unit --- p.18Chapter 3.1 --- Introduction --- p.18Chapter 3.2 --- History of Graphics Processing Unit --- p.19Chapter 3.2.1 --- First Generation GPU --- p.20Chapter 3.2.2 --- Second Generation GPU --- p.20Chapter 3.2.3 --- Third Generation GPU --- p.20Chapter 3.2.4 --- Fourth Generation GPU --- p.21Chapter 3.3 --- The Graphics Pipelining --- p.21Chapter 3.3.1 --- Standard Graphics Pipeline --- p.21Chapter 3.3.2 --- Programmable Graphics Pipeline --- p.23Chapter 3.3.3 --- Vertex Processors --- p.25Chapter 3.3.4 --- Fragment Processors --- p.26Chapter 3.3.5 --- Frame Buffer Operations --- p.28Chapter 3.4 --- GPU CPU Analogy --- p.31Chapter 3.4.1 --- Memory Architecture --- p.31Chapter 3.4.2 --- Processing Model --- p.32Chapter 3.4.3 --- Limitation of GPU --- p.33Chapter 3.4.4 --- Input and Output --- p.34Chapter 3.4.5 --- Data Readback --- p.34Chapter 3.4.6 --- FramebufFer --- p.34Chapter 3.5 --- Summary --- p.35Chapter 4 --- Volume Rendering --- p.37Chapter 4.1 --- Introduction --- p.37Chapter 4.2 --- History of Volume Rendering --- p.38Chapter 4.3 --- Hardware Accelerated Volume Rendering --- p.40Chapter 4.3.1 --- Hardware Acceleration Volume Rendering Methods --- p.41Chapter 4.3.2 --- Proxy Geometry --- p.42Chapter 4.3.3 --- Object-Aligned Slicing --- p.43Chapter 4.3.4 --- View-Aligned Slicing --- p.45Chapter 4.4 --- Summary --- p.48Chapter 5 --- GPU-Friendly Marching Cubes --- p.49Chapter 5.1 --- Introduction --- p.49Chapter 5.2 --- Previous Work --- p.50Chapter 5.3 --- Traditional Method --- p.52Chapter 5.3.1 --- Scalar Volume Data --- p.53Chapter 5.3.2 --- Isosurface Extraction --- p.53Chapter 5.3.3 --- Flow Chart --- p.54Chapter 5.3.4 --- Transparent Isosurfaces --- p.56Chapter 5.4 --- Our Method --- p.56Chapter 5.4.1 --- Cell Selection --- p.59Chapter 5.4.2 --- Vertex Labeling --- p.61Chapter 5.4.3 --- Cell Indexing --- p.62Chapter 5.4.4 --- Interpolation --- p.65Chapter 5.5 --- Rendering Translucent Isosurfaces --- p.67Chapter 5.6 --- Implementation and Results --- p.69Chapter 5.7 --- Summary --- p.74Chapter 6 --- Conclusion --- p.76Bibliography --- p.7

Diamond-based models for scientific visualization

Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains including scientific visualization, finite element analysis and shape modeling and analysis. A popular class of such approaches is based on the regular simplex bisection operator, which bisects simplices (e.g. line segments, triangles, tetrahedra) along the midpoint of a predetermined edge. Regular simplex bisection produces adaptive simplicial meshes of high geometric quality, while simplifying the extraction of crack-free, or conforming, approximations to the original dataset. Efficient multiresolution representations for such models have been achieved in 2D and 3D by clustering sets of simplices sharing the same bisection edge into structures called diamonds. In this thesis, we introduce several diamond-based approaches for scientific visualization. We first formalize the notion of diamonds in arbitrary dimensions in terms of two related simplicial decompositions of hypercubes. This enables us to enumerate the vertices, simplices, parents and children of a diamond. In particular, we identify the number of simplices involved in conforming updates to be factorial in the dimension and group these into a linear number of subclusters of simplices that are generated simultaneously. The latter form the basis for a compact pointerless representation for conforming meshes generated by regular simplex bisection and for efficiently navigating the topological connectivity of these meshes. Secondly, we introduce the supercube as a high-level primitive on such nested meshes based on the atomic units within the underlying triangulation grid. We propose the use of supercubes to associate information with coherent subsets of the full hierarchy and demonstrate the effectiveness of such a representation for modeling multiresolution terrain and volumetric datasets. Next, we introduce Isodiamond Hierarchies, a general framework for spatial access structures on a hierarchy of diamonds that exploits the implicit hierarchical and geometric relationships of the diamond model. We use an isodiamond hierarchy to encode irregular updates to a multiresolution isosurface or interval volume in terms of regular updates to diamonds. Finally, we consider nested hypercubic meshes, such as quadtrees, octrees and their higher dimensional analogues, through the lens of diamond hierarchies. This allows us to determine the relationships involved in generating balanced hypercubic meshes and to propose a compact pointerless representation of such meshes. We also provide a local diamond-based triangulation algorithm to generate high-quality conforming simplicial meshes

Volume Ray casting with peak finding and differential sampling

Journal ArticleDirect volume rendering and isosurfacing are ubiquitous rendering techniques in scientific visualization, commonly employed in imaging 3D data from simulation and scan sources. Conventionally, these methods have been treated as separate modalities, necessitating different sampling strategies and rendering algorithms. In reality, an isosurface is a special case of a transfer function, namely a Dirac impulse at a given isovalue. However, artifact-free rendering of discrete isosurfaces in a volume rendering framework is an elusive goal, requiring either infinite sampling or smoothing of the transfer function. While preintegration approaches solve the most obvious deficiencies in handling sharp transfer functions, artifacts can still result, limiting classification. In this paper, we introduce a method for rendering such features by explicitly solving for isovalues within the volume rendering integral. In addition, we present a sampling strategy inspired by ray differentials that automatically matches the frequency of the image plane, resulting in fewer artifacts near the eye and better overall performance. These techniques exhibit clear advantages over standard uniform ray casting with and without preintegration, and allow for high-quality interactive volume rendering with sharp C0 transfer functions

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