An exact general remeshing scheme applied to physically conservative voxelization

We present an exact general remeshing scheme to compute analytic integrals of polynomial functions over the intersections between convex polyhedral cells of old and new meshes. In physics applications this allows one to ensure global mass, momentum, and energy conservation while applying higher-order polynomial interpolation. We elaborate on applications of our algorithm arising in the analysis of cosmological N-body data, computer graphics, and continuum mechanics problems. We focus on the particular case of remeshing tetrahedral cells onto a Cartesian grid such that the volume integral of the polynomial density function given on the input mesh is guaranteed to equal the corresponding integral over the output mesh. We refer to this as "physically conservative voxelization". At the core of our method is an algorithm for intersecting two convex polyhedra by successively clipping one against the faces of the other. This algorithm is an implementation of the ideas presented abstractly by Sugihara (1994), who suggests using the planar graph representations of convex polyhedra to ensure topological consistency of the output. This makes our implementation robust to geometric degeneracy in the input. We employ a simplicial decomposition to calculate moment integrals up to quadratic order over the resulting intersection domain. We also address practical issues arising in a software implementation, including numerical stability in geometric calculations, management of cancellation errors, and extension to two dimensions. In a comparison to recent work, we show substantial performance gains. We provide a C implementation intended to be a fast, accurate, and robust tool for geometric calculations on polyhedral mesh elements.Comment: Code implementation available at https://github.com/devonmpowell/r3

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

Ambient occlusion and shadows for molecular graphics

Computer based visualisations of molecules have been produced as early as the 1950s to aid researchers in their understanding of biomolecular structures. An important consideration for Molecular Graphics software is the ability to visualise the 3D structure of the molecule in a clear manner. Recent advancements in computer graphics have led to improved rendering capabilities of the visualisation tools. The capabilities of current shading languages allow the inclusion of advanced graphic effects such as ambient occlusion and shadows that greatly improve the comprehension of the 3D shapes of the molecules. This thesis focuses on finding improved solutions to the real time rendering of Molecular Graphics on modern day computers. The methods of calculating ambient occlusion and both hard and soft shadows are examined and implemented to give the user a more complete experience when navigating large molecular structures

Gap Processing for Adaptive Maximal Poisson-Disk Sampling

In this paper, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or have their radius changed. We build on the concepts of the regular triangulation and the power diagram. Third, we will show how our analysis can make a contribution to the state-of-the-art in surface remeshing.Comment: 16 pages. ACM Transactions on Graphics, 201

VoroCrust: Voronoi Meshing Without Clipping

Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting arbitrarily curved boundaries and sharp features. In addition, the power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous formulations. The VoroCrust algorithm is the first provably-correct algorithm for conforming polyhedral Voronoi meshing for non-convex and non-manifold domains with guarantees on the quality of both surface and volume elements. A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface circumventing the need for clipping and avoiding its many drawbacks. The algorithm has the flexibility of filling the interior by either structured or random samples, while preserving all sharp features in the output mesh. We demonstrate the capabilities of the algorithm on a variety of models and compare against state-of-the-art polyhedral meshing methods based on clipped Voronoi cells establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf. Supplemental materials available on https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd

Multiple dataset visualization (MDV) framework for scalar volume data

Many applications require comparative analysis of multiple datasets representing different samples, conditions, time instants, or views in order to develop a better understanding of the scientific problem/system under consideration. One effective approach for such analysis is visualization of the data. In this PhD thesis, we propose an innovative multiple dataset visualization (MDV) approach in which two or more datasets of a given type are rendered concurrently in the same visualization. MDV is an important concept for the cases where it is not possible to make an inference based on one dataset, and comparisons between many datasets are required to reveal cross-correlations among them. The proposed MDV framework, which deals with some fundamental issues that arise when several datasets are visualized together, follows a multithreaded architecture consisting of three core components, data preparation/loading, visualization and rendering. The visualization module - the major focus of this study, currently deals with isosurface extraction and texture-based rendering techniques. For isosurface extraction, our all-in-memory approach keeps datasets under consideration and the corresponding geometric data in the memory. Alternatively, the only-polygons- or points-in-memory only keeps the geometric data in memory. To address the issues related to storage and computation, we develop adaptive data coherency and multiresolution schemes. The inter-dataset coherency scheme exploits the similarities among datasets to approximate the portions of isosurfaces of datasets using the isosurface of one or more reference datasets whereas the intra/inter-dataset multiresolution scheme processes the selected portions of each data volume at varying levels of resolution. The graphics hardware-accelerated approaches adopted for MDV include volume clipping, isosurface extraction and volume rendering, which use 3D textures and advanced per fragment operations. With appropriate user-defined threshold criteria, we find that various MDV techniques maintain a linear time-N relationship, improve the geometry generation and rendering time, and increase the maximum N that can be handled (N: number of datasets). Finally, we justify the effectiveness and usefulness of the proposed MDV by visualizing 3D scalar data (representing electron density distributions in magnesium oxide and magnesium silicate) from parallel quantum mechanical simulation

A survey of techniques and technologies for web-based real-time interactive rendering

When exploring a virtual environment, realism depends mainly on two factors: realistic images and real-time feedback (motions, behaviour etc.). In this context, photo realism and physical validity of computer generated images required by emerging applications, such as advanced e-commerce, still impose major challenges in the area of rendering research whereas the complexity of lighting phenomena further requires powerful and predictable computing if time constraints must be attained. In this technical report we address the state-of-the-art on rendering, trying to put the focus on approaches, techniques and technologies that might enable real-time interactive web-based clientserver rendering systems. The focus is on the end-systems and not the networking technologies used to interconnect client(s) and server(s).Siemens; Bertelsmann mediaSystems GmbH; Eptron Multimedia; Instituto Politécnico do Porto - ISEP-IPP; Institute Laboratory for Mixed Realities at the Academy of Media Arts Cologne, LMR; Mälardalen Real-Time Research Centre (MRTC) at Mälardalen University in Västerås; Q-Systems

On Volumetric Shape Reconstruction from Implicit Forms

International audienceIn this paper we report on the evaluation of volumetric shape reconstruction methods that consider as input implicit forms in 3D. Many visual applications build implicit representations of shapes that are converted into explicit shape representations using geometric tools such as the Marching Cubes algorithm. This is the case with image based reconstructions that produce point clouds from which implicit functions are computed, with for instance a Poisson reconstruction approach. While the Marching Cubes method is a versatile solution with proven efficiency, alternative solutions exist with different and complementary properties that are of interest for shape modeling. In this paper, we propose a novel strategy that builds on Centroidal Voronoi Tessellations (CVTs). These tessellations provide volumetric and surface representations with strong regularities in addition to provably more accurate approximations of the implicit forms considered. In order to compare the existing strategies, we present an extensive evaluation that analyzes various properties of the main strategies for implicit to explicit volumetric conversions: Marching cubes, Delaunay refinement and CVTs, including accuracy and shape quality of the resulting shape mesh

Fast Exact Booleans for Iterated CSG using Octree-Embedded BSPs

We present octree-embedded BSPs, a volumetric mesh data structure suited for performing a sequence of Boolean operations (iterated CSG) efficiently. At its core, our data structure leverages a plane-based geometry representation and integer arithmetics to guarantee unconditionally robust operations. These typically present considerable performance challenges which we overcome by using custom-tailored fixed-precision operations and an efficient algorithm for cutting a convex mesh against a plane. Consequently, BSP Booleans and mesh extraction are formulated in terms of mesh cutting. The octree is used as a global acceleration structure to keep modifications local and bound the BSP complexity. With our optimizations, we can perform up to 2.5 million mesh-plane cuts per second on a single core, which creates roughly 40-50 million output BSP nodes for CSG. We demonstrate our system in two iterated CSG settings: sweep volumes and a milling simulation