Implementing intersection calculations of the ray tracing algorithm with systolic arrays

Ray tracing is one technique that has been used to synthesize realistic images with a computer. Unfortunately, this technique, when implemented in software, is slow and expensive. The trend in computer graphics has been toward the use of special purpose hardware, to speed up the calculations, and, hence, the generation of the synthesized image. This paper describes the design and the operation of a systolic based architecture, tailored to speed up the intersection calculations, that must be performed as a part of the ray tracing algorithm

Procedural function-based modelling of volumetric microstructures

We propose a new approach to modelling heterogeneous objects containing internal volumetric structures with size of details orders of magnitude smaller than the overall size of the object. The proposed function-based procedural representation provides compact, precise, and arbitrarily parameterised models of coherent microstructures, which can undergo blending, deformations, and other geometric operations, and can be directly rendered and fabricated without generating any auxiliary representations (such as polygonal meshes and voxel arrays). In particular, modelling of regular lattices and cellular microstructures as well as irregular porous media is discussed and illustrated. We also present a method to estimate parameters of the given model by fitting it to microstructure data obtained with magnetic resonance imaging and other measurements of natural and artificial objects. Examples of rendering and digital fabrication of microstructure models are presented

ConTesse: Accurate Occluding Contours for Subdivision Surfaces

This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when a sampled occluding contour is valid, that is, when it may be assigned consistent visibility. Previous methods do not guarantee these conditions, which helps explain why smooth contour visibility has been such a challenging problem in the past. The paper then proposes an algorithm that, given a subdivision surface, finds sampled contours satisfying these conditions, and then generates a new triangle mesh matching the given occluding contours. The contours of the output triangle mesh may then be rendered with standard non-photorealistic rendering algorithms, using the mesh for visibility computation. The method can be applied to any triangle mesh, by treating it as the base mesh of a subdivision surface.Comment: Accepted to ACM Transactions on Graphics (TOG

Vertex classification for non-uniform geometry reduction.

Complex models created from isosurface extraction or CAD and highly accurate 3D models produced from high-resolution scanners are useful, for example, for medical simulation, Virtual Reality and entertainment. Often models in general require some sort of manual editing before they can be incorporated in a walkthrough, simulation, computer game or movie. The visualization challenges of a 3D editing tool may be regarded as similar to that of those of other applications that include an element of visualization such as Virtual Reality. However the rendering interaction requirements of each of these applications varies according to their purpose. For rendering photo-realistic images in movies computer farms can render uninterrupted for weeks, a 3D editing tool requires fast access to a model's fine data. In Virtual Reality rendering acceleration techniques such as level of detail can temporarily render parts of a scene with alternative lower complexity versions in order to meet a frame rate tolerable for the user. These alternative versions can be dynamic increments of complexity or static models that were uniformly simplified across the model by minimizing some cost function. Scanners typically have a fixed sampling rate for the entire model being scanned, and therefore may generate large amounts of data in areas not of much interest or that contribute little to the application at hand. It is therefore desirable to simplify such models non-uniformly. Features such as very high curvature areas or borders can be detected automatically and simplified differently to other areas without any interaction or visualization. However a problem arises when one wishes to manually select features of interest in the original model to preserve and create stand alone, non-uniformly reduced versions of large models, for example for medical simulation. To inspect and view such models the memory requirements of LoD representations can be prohibitive and prevent storage of a model in main memory. Furthermore, although asynchronous rendering of a base simplified model ensures a frame rate tolerable to the user whilst detail is paged, no guarantees can be made that what the user is selecting is at the original resolution of the model or of an appropriate LoD owing to disk lag or the complexity of a particular view selected by the user. This thesis presents an interactive method in the con text of a 3D editing application for feature selection from any model that fits in main memory. We present a new compression/decompression of triangle normals and colour technique which does not require dedicated hardware that allows for 87.4% memory reduction and allows larger models to fit in main memory with at most 1.3/2.5 degrees of error on triangle normals and to be viewed interactively. To address scale and available hardware resources, we reference a hierarchy of volumes of different sizes. The distances of the volumes at each level of the hierarchy to the intersection point of the line of sight with the model are calculated and these distances sorted. At startup an appropriate level of the tree is automatically chosen by separating the time required for rendering from that required for sorting and constraining the latter according to the resources available. A clustered navigation skin and depth buffer strategy allows for the interactive visualisation of models of any size, ensuring that triangles from the closest volumes are rendered over the navigation skin even when the clustered skin may be closer to the viewer than the original model. We show results with scanned models, CAD, textured models and an isosurface. This thesis addresses numerical issues arising from the optimisation of cost functions in LoD algorithms and presents a semi-automatic solution for selection of the threshold on the condition number of the matrix to be inverted for optimal placement of the new vertex created by an edge collapse. We show that the units in which a model is expressed may inadvertently affect the condition of these matrices, hence affecting the evaluation of different LoD methods with different solvers. We use the same solver with an automatically calibrated threshold to evaluate different uniform geometry reduction techniques. We then present a framework for non-uniform reduction of regular scanned models that can be used in conjunction with a variety of LoD algorithms. The benefits of non-uniform reduction are presented in the context of an animation system. (Abstract shortened by UMI.)

3D-POLY: A Robot Vision System for Recognizing Objects in Occluded Environments

The two factors that determine the time complexity associated with model-driven interpretation of range maps are: I) the particular strategy used for the generation of object hypotheses; and 2) the manner in which both the model and the sensed data are organized, data organization being a primary determinant of the efficiency of verification of a given hypothesis. In this report, we present 3D-POLY, a working system for recognizing objects in the presence of occlusion and against cluttered backgrounds. The time complexity of this system is only O(n2) for single object recognition, where n is the number of features on the object. The most novel aspect of this system is the manner in which the feature data are organized for the models. We use a data structure called the feature sphere for the purpose. We will present efficient algorithms for assigning a feature to its proper place on a feature sphere, and for extracting the neighbors of a given feature from the feature sphere representation. For hypothesis generation, we use local feature sets, a notion similar to those used before us by Bolles, Shirai and others. The combination of the feature sphere idea for streamlining verification and the local feature sets for hypothesis generation results in a system whose time complexity has a polynomial bound. In addition to recognizing objects in occluded environments, 3D-POLY also possesses model learning capability. Model learning consists of looking at a model object from different views and integrating the resulting information. The 3D-POLY system also contains utilities for range image segmentation and classification of scene surfaces

Free-form deformation of solid models in CSR.

Lai Chi-fai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 98-99).Abstracts in English and Chinese.Chapter 1. --- INTRODUCTION --- p.7Chapter 1.1 --- Motivations and objectives --- p.7Chapter 1.2 --- Thesis Organization --- p.10Chapter 2. --- related works --- p.11Chapter 2.1 --- Deformation Techniques --- p.11Chapter 2.1.1 --- Deformation techniques requiring a deformation tool --- p.11Chapter 2.1.2 --- Directly specified deformation techniques --- p.14Chapter 2.1.3 --- Comparison on Different Deformation Technique --- p.15Chapter 2.2 --- Application of Deformation --- p.16Chapter 2.2.1 --- Deforming superquadrics --- p.16Chapter 2.2.2 --- Volume wraping --- p.16Chapter 2.2.3 --- Deforming linear object --- p.17Chapter 2.2.4 --- FFD for animation synthesis --- p.17Chapter 2.2.5 --- Using FFD on feature-based Surface --- p.18Chapter 2.2.6 --- NURBS-BASED Free-Form Deformation (NFFD) --- p.18Chapter 2.3 --- Algebraic Patch Techniques --- p.20Chapter 2.3.1 --- Dahmen's scheme --- p.20Chapter 2.3.2 --- Lodha and Warren's technique --- p.20Chapter 2.3.3 --- Guo's method --- p.21Chapter 3. --- BACKGROUND THEORIES --- p.22Chapter 3.1 --- Algebraic Patches --- p.22Chapter 3.1.1 --- Bernstein-Bezier representation of a single patch --- p.22Chapter 3.1.2 --- Constructing free-form objects --- p.29Chapter 3.1.2.1 --- Bounding volumes for quadric patches --- p.29Chapter 3.1.2.2 --- Filling two-sided gaps --- p.31Chapter 3.2 --- Constructive Shell Representation --- p.35Chapter 3.2.1 --- Properties of quadric patches and its construction tetrahedron and trunctets --- p.38Chapter 3.3 --- Free-Form Deformation --- p.40Chapter 3.3.1 --- Formulating free-form deformation --- p.40Chapter 4. --- FREE-FORM DEFORMATION OF CSR SOLID MODELS --- p.43Chapter 4.1 --- Determination of Lattice Structure --- p.43Chapter 4.2 --- "Relation between weights, normals and shape of a trunctet" --- p.46Chapter 4.3 --- Applying FFD on CSR solid models --- p.49Chapter 4.3.1 --- Deforming normal at vertices --- p.52Chapter 4.3.2 --- Using vertices' neighborhoods --- p.54Chapter 4.4 --- Free-Form Deformation of CSR objects by Surface Fitting --- p.57Chapter 4.4.1 --- Deforming a single surface patch --- p.57Chapter 4.4.1.1 --- Locating surface points --- p.59Chapter 4.4.1.2 --- Conversion between barycentric and Cartesian coordinates --- p.61Chapter 4.4.1.3 --- Evaluating the deformed surface patch --- p.62Chapter 4.4.1.4 --- Saddle shape trunctet --- p.64Chapter 4.4.1.5 --- Using double tetrahedrons --- p.66Chapter 4.4.1.6 --- Surface subdivision --- p.69Chapter 4.4.2 --- Deforming Entire Solid Model --- p.72Chapter 4.4.3 --- Comparison on different approaches --- p.75Chapter 4.5 --- Conversion of CSG solid Models into CSR --- p.76Chapter 4.5.1 --- Converting halfspaces into CSR objects --- p.77Chapter 5. --- IMPLEMENTATION AND RESULTS --- p.82Chapter 5.1 --- Implementation --- p.82Chapter 5.2 --- Experimental Results --- p.84Chapter 6. --- CONCLUSION AND SUGGESTIONS FOR FURTHER WORK --- p.93Chapter 6.1 --- Conclusion --- p.93Chapter 6.2 --- Suggestions for further work --- p.9

Unstructured mesh generation for mesh improvement techniques and contour meshing.

This thesis will investigate surface mesh generation and develop ideas to improve the quality of surface meshes that are currently produced. Surface geometries are represented by a CAD definition, but the CAD definition does not necessarily guarantee that the surface geometry is acceptable for mesh generation. CAD geometries will often contain a number of detailed features which will need to be improved by processes such as CAD repair before mesh generation can take place. Even then the geometries can still contain problems in the features such as, small sliver surface patches and sliver edges. These features cause major difficulties when meshed, as they generate small distorted elements. Here we will look to improve the meshes by merging together neighboring surface patches to create a super patch and then generate the mesh on this one surface. The merging of surfaces is controlled by the angle between surface patches. Another method that will be investigated involves the re-meshing of the geometry based on a prescribed metric. In addition to looking at this problem of CAD representation we will also look at the growing area of medical imaging. Here we will look to produce a 3D mesh from a set of contours. From this the mesh produced will be remeshed using the previous ideas to produce a mesh that can be used for analysis

High-Quality Simplification and Repair of Polygonal Models

Because of the rapid evolution of 3D acquisition and modelling methods, highly complex and detailed polygonal models with constantly increasing polygon count are used as three-dimensional geometric representations of objects in computer graphics and engineering applications. The fact that this particular representation is arguably the most widespread one is due to its simplicity, flexibility and rendering support by 3D graphics hardware. Polygonal models are used for rendering of objects in a broad range of disciplines like medical imaging, scientific visualization, computer aided design, film industry, etc. The handling of huge scenes composed of these high-resolution models rapidly approaches the computational capabilities of any graphics accelerator. In order to be able to cope with the complexity and to build level-of-detail representations, concentrated efforts were dedicated in the recent years to the development of new mesh simplification methods that produce high-quality approximations of complex models by reducing the number of polygons used in the surface while keeping the overall shape, volume and boundaries preserved as much as possible. Many well-established methods and applications require "well-behaved" models as input. Degenerate or incorectly oriented faces, T-joints, cracks and holes are just a few of the possible degenaracies that are often disallowed by various algorithms. Unfortunately, it is all too common to find polygonal models that contain, due to incorrect modelling or acquisition, such artefacts. Applications that may require "clean" models include finite element analysis, surface smoothing, model simplification, stereo lithography. Mesh repair is the task of removing artefacts from a polygonal model in order to produce an output model that is suitable for further processing by methods and applications that have certain quality requirements on their input. This thesis introduces a set of new algorithms that address several particular aspects of mesh repair and mesh simplification. One of the two mesh repair methods is dealing with the inconsistency of normal orientation, while another one, removes the inconsistency of vertex connectivity. Of the three mesh simplification approaches presented here, the first one attempts to simplify polygonal models with the highest possible quality, the second, applies the developed technique to out-of-core simplification, and the third, prevents self-intersections of the model surface that can occur during mesh simplification

Virtual reality based creation of concept model designs for CAD systems

This work introduces a novel method to overcome most of the drawbacks in traditional methods for creating design models. The main innovation is the use of virtual tools to simulate the natural physical environment in which freeform. Design models are created by experienced designers. Namely, the model is created in a virtual environment by carving a work piece with tools that simulate NC milling cutters. Algorithms have been developed to support the approach, in which the design model is created in a Virtual Reality (VR) environment and selection and manipulation of tools can be performed in the virtual space. The desianer\u27s hand movements generate the tool trajectories and they are obtained by recording the position and orientation of a hand mounted motion tracker. Swept volumes of virtual tools are generated from the geometry of the tool and its trajectories. Then Boolean operations are performed on the swept volumes and the initial virtual stock (work piece) to create the design model. Algorithms have been developed as a part of this work to integrate the VR environment with a commercial CAD/CAM system in order to demonstrate the practical applications of the research results. The integrated system provides a much more efficient and easy-to-implement process of freeform model creation than employed in current CAD/CAM software. It could prove to be the prototype for the next-generation CAD/CAM system