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

Real-time Photorealistic Visualisation of Large-scaleMultiresolution Terrain Models

Height field terrain rendering is an important aspect of GIS, outdoor virtual reality applicationssuch as flight simulation, 3-D games, etc. A polygonal model of very large terrain data requiresa large number of triangles. So, even most high-performance graphics workstations have greatdifficulty to display even moderately sized height fields at interactive frame rates. To bringphotorealism in visualisation, it is required to drape corresponding high-resolution satellite oraerial phototexture over 3-D digital terrain and also to place multiple collections of point-location-based static objects such as buildings, trees, etc and to overlay polyline vector objects suchas roads on top of the terrain surface. It further complicates the requirement of interactive framerates while navigation over the terrain. This paper describes a novel approach for objects andterrain visualisation by combination of two algorithms, one for terrain data and the other forobjects. The terrain rendering is accomplished by an efficient dynamic multiresolution view-dependent level-of-detail mesh simplification algorithm. It is augmented with out-of-corevisualisation of large-height geometry and phototexture terrain data populated with 3-D/2-Dstatic objects as well as vector overlays without extensive memory load. The proposedmethodology provides interactive frame rates on a general-purpose desktop PC with OpenGL-enabled graphics hardware. The software TREND has been successfully tested on different real-world height maps and satellite phototextures of sizes up to 16K*16K coupled with thousandsof static objects and polyline vector overlays

Scalable Realtime Rendering and Interaction with Digital Surface Models of Landscapes and Cities

Interactive, realistic rendering of landscapes and cities differs substantially from classical terrain rendering. Due to the sheer size and detail of the data which need to be processed, realtime rendering (i.e. more than 25 images per second) is only feasible with level of detail (LOD) models. Even the design and implementation of efficient, automatic LOD generation is ambitious for such out-of-core datasets considering the large number of scales that are covered in a single view and the necessity to maintain screen-space accuracy for realistic representation. Moreover, users want to interact with the model based on semantic information which needs to be linked to the LOD model. In this thesis I present LOD schemes for the efficient rendering of 2.5d digital surface models (DSMs) and 3d point-clouds, a method for the automatic derivation of city models from raw DSMs, and an approach allowing semantic interaction with complex LOD models. The hierarchical LOD model for digital surface models is based on a quadtree of precomputed, simplified triangle mesh approximations. The rendering of the proposed model is proved to allow real-time rendering of very large and complex models with pixel-accurate details. Moreover, the necessary preprocessing is scalable and fast. For 3d point clouds, I introduce an LOD scheme based on an octree of hybrid plane-polygon representations. For each LOD, the algorithm detects planar regions in an adequately subsampled point cloud and models them as textured rectangles. The rendering of the resulting hybrid model is an order of magnitude faster than comparable point-based LOD schemes. To automatically derive a city model from a DSM, I propose a constrained mesh simplification. Apart from the geometric distance between simplified and original model, it evaluates constraints based on detected planar structures and their mutual topological relations. The resulting models are much less complex than the original DSM but still represent the characteristic building structures faithfully. Finally, I present a method to combine semantic information with complex geometric models. My approach links the semantic entities to the geometric entities on-the-fly via coarser proxy geometries which carry the semantic information. Thus, semantic information can be layered on top of complex LOD models without an explicit attribution step. All findings are supported by experimental results which demonstrate the practical applicability and efficiency of the methods

**FULL TITLE** ASP Conference Series, Vol. **VOLUME**, **YEAR OF PUBLICATION** **NAMES OF EDITORS** Visualization of Scalar Adaptive Mesh Refinement Data

Abstract. Adaptive Mesh Refinement (AMR) is a highly effective computation method for simulations that span a large range of spatiotemporal scales, such as astrophysical simulations, which must accommodate ranges from interstellar to sub-planetary. Most mainstream visualization tools still lack support for AMR grids as a first class data type and AMR code teams use custom built applications for AMR visualization. The Department of Energy's (DOE's) Science Discovery through Advanced Computing (SciDAC) Visualization and Analytics Center for Enabling Technologies (VACET) is currently working on extending VisIt, which is an open source visualization tool that accommodates AMR as a first-class data type. These efforts will bridge the gap between generalpurpose visualization applications and highly specialized AMR visual analysis applications. Here, we give an overview of the state of the art in AMR scalar data visualization research

Intelligent Computational Transportation

Transportation is commonplace around our world. Numerous researchers dedicate great efforts to vast transportation research topics. The purpose of this dissertation is to investigate and address a couple of transportation problems with respect to geographic discretization, pavement surface automatic examination, and traffic ow simulation, using advanced computational technologies. Many applications require a discretized 2D geographic map such that local information can be accessed efficiently. For example, map matching, which aligns a sequence of observed positions to a real-world road network, needs to find all the nearby road segments to the individual positions. To this end, the map is discretized by cells and each cell retains a list of road segments coincident with this cell. An efficient method is proposed to form such lists for the cells without costly overlapping tests. Furthermore, the method can be easily extended to 3D scenarios for fast triangle mesh voxelization. Pavement surface distress conditions are critical inputs for quantifying roadway infrastructure serviceability. Existing computer-aided automatic examination techniques are mainly based on 2D image analysis or 3D georeferenced data set. The disadvantage of information losses or extremely high costs impedes their effectiveness iv and applicability. In this study, a cost-effective Kinect-based approach is proposed for 3D pavement surface reconstruction and cracking recognition. Various cracking measurements such as alligator cracking, traverse cracking, longitudinal cracking, etc., are identified and recognized for their severity examinations based on associated geometrical features. Smart transportation is one of the core components in modern urbanization processes. Under this context, the Connected Autonomous Vehicle (CAV) system presents a promising solution towards the enhanced traffic safety and mobility through state-of-the-art wireless communications and autonomous driving techniques. Due to the different nature between the CAVs and the conventional Human- Driven-Vehicles (HDVs), it is believed that CAV-enabled transportation systems will revolutionize the existing understanding of network-wide traffic operations and re-establish traffic ow theory. This study presents a new continuum dynamics model for the future CAV-enabled traffic system, realized by encapsulating mutually-coupled vehicle interactions using virtual internal and external forces. A Smoothed Particle Hydrodynamics (SPH)-based numerical simulation and an interactive traffic visualization framework are also developed

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

Spatial Decompositions for Geometric Interpolation and Efficient Rendering

Interpolation is fundamental in many applications that are based on multidimensional scalar or vector fields. In such applications, it is possible to sample points from the field, for example, through the numerical solution of some mathematical model. Because point sampling may be computationally intensive, it is desirable to store samples in a data structure and estimate the values of the field at intermediate points through interpolation. We present methods based on building dynamic spatial data structures in which the samples are computed on-demand, and adaptive strategies are used to avoid oversampling. We first show how to apply this approach to accelerate realistic rendering through ray-tracing. Ray-tracing can be formulated as a sampling and reconstruction problem, where rays in 3-space are modeled as points in a 4-dimensional parameter space. Sample rays are associated with various geometric attributes, which are then used in rendering. We collect and store a relatively sparse set of sampled rays, and use inexpensive interpolation methods to approximate the attribute values for other rays. We present two data structures: (1) the <i>ray interpolant tree (RI-tree)</i>, which is based on a kd-tree-like subdivision of space, and (2) the <i>simplex decomposition tree (SD-tree)</i>, which is based on a hierarchical regular simplicial mesh, and improves the functionality of the RI-tree by guaranteeing continuity. For compact storage as well as efficient neighbor computation in the mesh, we present a pointerless representation of the SD-tree. An essential element of this approach is the development of a location code that enables efficient access and navigation of the data structure. For this purpose we introduce a location code, called an LPTcode, that uniquely encodes the geometry of each simplex of the hierarchy. We present rules to compute the neighbors of a given simplex efficiently through the use of this code. We show how to traverse the associated tree and how to answer point location and interpolation queries. Our algorithms work in arbitrary dimensions. We also demonstrate the use of the SD-tree for rendering atmospheric effects. We present empirical evidence that our methods can produce renderings of good quality significantly faster than simple ray-tracing

Appearance Preserving Rendering of Out-of-Core Polygon and NURBS Models

In Computer Aided Design (CAD) trimmed NURBS surfaces are widely used due to their flexibility. For rendering and simulation however, piecewise linear representations of these objects are required. A relatively new field in CAD is the analysis of long-term strain tests. After such a test the object is scanned with a 3d laser scanner for further processing on a PC. In all these areas of CAD the number of primitives as well as their complexity has grown constantly in the recent years. This growth is exceeding the increase of processor speed and memory size by far and posing the need for fast out-of-core algorithms. This thesis describes a processing pipeline from the input data in the form of triangular or trimmed NURBS models until the interactive rendering of these models at high visual quality. After discussing the motivation for this work and introducing basic concepts on complex polygon and NURBS models, the second part of this thesis starts with a review of existing simplification and tessellation algorithms. Additionally, an improved stitching algorithm to generate a consistent model after tessellation of a trimmed NURBS model is presented. Since surfaces need to be modified interactively during the design phase, a novel trimmed NURBS rendering algorithm is presented. This algorithm removes the bottleneck of generating and transmitting a new tessellation to the graphics card after each modification of a surface by evaluating and trimming the surface on the GPU. To achieve high visual quality, the appearance of a surface can be preserved using texture mapping. Therefore, a texture mapping algorithm for trimmed NURBS surfaces is presented. To reduce the memory requirements for the textures, the algorithm is modified to generate compressed normal maps to preserve the shading of the original surface. Since texturing is only possible, when a parametric mapping of the surface - requiring additional memory - is available, a new simplification and tessellation error measure is introduced that preserves the appearance of the original surface by controlling the deviation of normal vectors. The preservation of normals and possibly other surface attributes allows interactive visualization for quality control applications (e.g. isophotes and reflection lines). In the last part out-of-core techniques for processing and rendering of gigabyte-sized polygonal and trimmed NURBS models are presented. Then the modifications necessary to support streaming of simplified geometry from a central server are discussed and finally and LOD selection algorithm to support interactive rendering of hard and soft shadows is described