published_or_final_version / Computer Science and Information Systems / Master / Master of Philosophy

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Recent advances in the computer graphics of woven images on surfaces in 3-space motivate the development of weavings for arbitrary genus surfaces. We present herein a general framework for weaving structures on general surfaces in 3-space, and through it, we demonstrate how weavings on such surfaces are inducible from connected graph imbeddings on the same surfaces. The necessary and sufficient conditions to identify the inducible weavings in our framework are also given. For low genus surfaces, like plane and torus, we extend our framework to the weavings which are inducible from disconnected imbedded graphs. In particular, we show all weavings on a plane are inducible in our framework, including most Celtic Knots. Moreover, we study different weaving structures on general surfaces in 3-space based on our framework. We show that any weaving inducible in our framework can be converted into an alternating weaving by appropriately changing the strand orders at some crossings. By applying a topological surgery operation, called doubling operation, we can refine a weaving or convert certain non-twillable weavings into twillable weavings on the same surfaces. Interestingly, two important subdivision algorithms on graphs imbeddings, the Catmull-Clark and Doo-Sabin algorithms, correspond nicely to our doubling operation on induced weavings. Another technique we used in studying weaving structures is repetitive patterns. A weaving that can be converted into a twillable weaving by our doubling operation has a highly-symmetric structure, which consists of only two repetitive patterns. An extension of the symmetric structure leads to Quad-Pattern Coverable meshes, which can be seamlessly covered with only one periodic pattern. Both of these two topological structures can be represented with simple Permutation Voltage graphs. A considerable advantage of our model is that it is topological. This permits the graphic designer to superimpose strand colors and geometric attributes — distances, angles, and curvatures — that conform to manufacturing or artistic criteria. We also give a software example for plane weaving construction. A benefit of the software is that it supports plane weaving reconstructions from an image of a plane weaving, which could be useful for recording and modifying existing weavings in real life.

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This work investigates methods to provide clinically useful visualisations of the data produced by an X-ray/CT scanner. Specifically, it examines the use of perceptual depth cues (PDCs) and perceptual depth cue theory to create effective visualisations. Two visualisation systems are explored: one to display X-ray data and the other to display volumetric data. The systems are enhanced using stereoscopic and motion PDCs. The presented analyses show that these are the only possible enhancements common to both systems. The theoretical and practical aspects of implementing these enhancements are presented. Volume rendering techniques are explored to find an approach which gracefully handles poorly sampled data and provides the interactive rendering needed for motion cues. A low cost real time volume rendering system is developed and a novel stereo volume rendering technique is presented. The developed system uses commodity graphics hardware and Open-GL. To evaluate the visualisation systems a task-based user test is designed and implemented. The test requires the subjects to be observed while they complete a 3D diagnostic task using each system. The speed and accuracy with which the task is performed are used as metrics. The experimental results are used to compare the effectiveness of the augmented perceptual depth cues and to cross-compare the systems. The experiments show that the user performance in the visualisation systems are statistically equivalent. This suggests that the enhanced X-ray visualisation can be used in place of CT data for some tasks. The benefits of this are two fold: a decrease in the patient's exposure to radiation and a reduction in the data acquisition time.

Character animation is the process of modelling and rendering a mobile character in a virtual world. It has numerous applications both off-line, such as virtual actors in films, and real-time, such as in games and other virtual environments. There are a number of algorithms for determining the appearance of an animated character, with different trade-offs between quality, ease of control, and computational cost. We introduce a new method, animation space, which provides a good balance between the ease-of-use of very simple schemes and the quality of more complex schemes, together with excellent performance. It can also be integrated into a range of existing computer graphics algorithms. Animation space is described by a simple and elegant linear equation. Apart from making it fast and easy to implement, linearity facilitates mathematical analysis. We derive two metrics on the space of vertices (the “animation space”), which indicate the mean and maximum distances between two points on an animated character. We demonstrate the value of these metrics by applying them to the problems of parametrisation, level-of-detail (LOD) and frustum culling. These metrics provide information about the entire range of poses of an animated character, so they are able to produce better results than considering only a single pose of the character, as is commonly done. In order to compute parametrisations, it is necessary to segment the mesh into charts. We apply an existing algorithm based on greedy merging, but use a metric better suited to the problem than the one suggested by the original authors. To combine the parametrisations with level-of-detail, we require the charts to have straight edges. We explored a heuristic approach to straightening the edges produced by the automatic algorithm, but found that manual segmentation produced better results. Animation space is nevertheless beneficial in flattening the segmented charts; we use least squares conformal maps (LSCM), with the Euclidean distance metric replaced by one of our animation-space metrics. The resulting parametrisations have significantly less overall stretch than those computed based on a single pose. Similarly, we adapt appearance preserving simplification (APS), a progressive mesh-based LOD algorithm, to apply to animated characters by replacing the Euclidean metric with an animation-space metric. When using the memoryless form of APS (in which local rather than global error is considered), the use of animation space for computations reduces the geometric errors introduced by LOD decomposition, compared to simplification based on a single pose. User tests, in which users compared video clips of the two, demonstrated a statistically significant preference for the animation-space simplifications, indicating that the visual quality is better as well. While other methods exist to take multiple poses into account, they are based on a sampling of the pose space, and the computational cost scales with the number of samples used. In contrast, our method is analytic and uses samples only to gather statistics. The quality of LOD approximations by improved further by introducing a novel approach to LOD, influence simplification, in which we remove the influences of bones on vertices, and adjust the remaining influences to approximate the original vertex as closely as possible. Once again, we use an animation-space metric to determine the approximation error. By combining influence simplification with the progressive mesh structure, we can obtain further improvements in quality: for some models and at some detail levels, the error is reduced by an order of magnitude relative to a pure progressive mesh. User tests showed that for some models this significantly improves quality, while for others it makes no significant difference. Animation space is a generalisation of skeletal subspace deformation (SSD), a popular method for real-time character animation. This means that there is a large existing base of models that can immediately benefit from the modified algorithms mentioned above. Furthermore, animation space almost entirely eliminates the well-known shortcomings of SSD (the so-called “candy-wrapper” and “collapsing elbow” effects). We show that given a set of sample poses, we can fit an animation-space model to these poses by solving a linear least-squares problem. Finally, we demonstrate that animation space is suitable for real-time rendering, by implementing it, along with level-of-detail rendering, on a PC with a commodity video card. We show that although the extra degrees of freedom make the straightforward approach infeasible for complex models, it is still possible to obtain high performance; in fact, animation space requires fewer basic operations to transform a vertex position than SSD. We also consider two methods of lighting LOD-simplified models using the original normals: tangent-space normal maps, an existing method that is fast to render but does not capture dynamic structures such as wrinkles; and tangent maps, a novel approach that encodes animation-space tangent vectors into textures, and which captures dynamic structures. We compare the methods both for performance and quality, and find that tangent-space normal maps are at least an order of magnitude faster, while user tests failed to show any perceived difference in quality between them.

The field of Procedural Generation is being increasingly used in modern content generation for its ability to significantly decrease the cost and time involved. One such area of Procedural Generation is Shape Grammars, a type of formal grammar that operates on geometric shapes instead of symbols. Conventional shape grammar implementations use mesh representations of shapes, but this has two significant drawbacks. Firstly, mesh representations make Boolean geometry operations on shapes difficult to accomplish. Boolean geometry operations allow us to combine shapes using Boolean operators (and, or, not), producing complex, composite shapes. A second drawback is that sub-, or trans-shape detailing is challenging to achieve. To address these two problems with conventional mesh-based shape grammars, we present a novel extension to shape grammars, in which a voxel representation of the generated shapes is used. We outline a five stage algorithm for using these extensions and discuss a number of optional enhancements and optimizations. The final output of the algorithm is a detailed mesh model, suitable for use in real-time or offline graphics applications. We also test our extension’s performance and range of output with three categories of testing: performance testing, output range testing, and variation testing. The results of the testing with our proof-of-concept implementation show that our unoptimized algorithm is slower than conventional shape grammar implementations, with a running time that is O(N^3) for an N^3 voxel grid. However, there is scope for further optimization to our algorithm, which would significantly reduce running times and memory consumption. We outline and discuss several such avenues for performance enhancement. Additionally, testing reveals that our algorithm is able to successfully produce a broad range of detailed outputs, exhibiting many features that would be very difficult to accomplish using mesh-based shape grammar implementations. This range of 3D models includes fractals, skyscraper buildings, space ships, castles, and more. Further, stochastic rules can be used to produce a variety of models that share a basic archetype, but differ noticeably in their details.