Object representation is the backbone of any solid modelling system. Hierarchical spatial decompositions of objects called octrees introduced very efficient algorithms for boolean set operations and some restricted classes of geometric transformations. Linear octrees, a compact encoding of the octrees, result in a significant reduction of storage requirements, and lead simpler algorithms for most modelling operations. This thesis investigates some properties of linear octrees with emphasis on object generation. By interpreting linear octree node digits as binary numbers, some simple conversion and node trimming algorithms are found, which when combined with a node enumeration algorithm, generate the linear octrees of cuboidal volumes efficiently. A simple and uniform approach is devised to perform arbitrary geometric transformations by means of cuboid generation. Experiments shows these algorithms maintain the efficiency of special cases while degrading linearly with the number of intermediate nodes generated. / Science, Faculty of / Computer Science, Department of / Graduate

The following is a study of the problem of computer generation of non-isomorphic regular graphs of degree d on n points. The uork consists of a study of various properties and representations of regular graphs and a discussion of hov these might be useful in solving the isomorphism problem in the computer generation of regular graphs. An algorithm for the generation of regular graphs of degree 3 on n points with a Hamiltonian cycle is presented. The algorithm is not ideal in that it does not generate distinct (ie. non-isomorphic) copies, and so a procedure for detecting graph isomorphism is used to process the list of graphs produced by the algorithm. / Science, Faculty of / Computer Science, Department of / Graduate

The performance of systems which employ a linear transformation and block quantization to encode visual information sources has been investigated. The effect of several relevant design parameters upon the behavior of these systems was examined theoretically. The performance criterion used was the rate measured in bits-per-picture sample required to transmit an image through a noiseless digital channel such that the average distortion in the received picture is less than a specified value. As a measure of image distortion, the mean-squared-error, well-known for its analytical tractability, was used. A second measure of image distortion which incorporates knowledge of the human visual system was examined. The new distortion index proposed by Stockham is expected to correlate well with subjective assessments of picture distortion although no experiments have been performed, as yet, to show this. In order to determine what, if anything, could be learned about this second distortion measure from theoretical considerations alone, a procedure was developed to estimate its value for given bit rates. These values were compared to the mean-squared-error distortion values obtained for the same bit rates in an attempt to gain some insight into the usefulness of the second distortion measure. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

This thesis describes the improvements in the mathematical aspects of the high-level programming language for interactive graphics (LIG). Improvement possibilities were investigated in three areas: dependence on the order of transformations, arithmetic expressions appearing in LIG statements, and the implementation to allow the programming of graphical functions. The method of implementation of the proposed improvements is also discussed. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Researchers developing high-level graphics languages have, according to the literature, focused their attention towards line-drawing graphics. Little effort has been devoted to systematic investigations of languages that handle graphical data representing line-drawings as well as solid areas. The latter type of graphical data is usually represented hy outlines, and solid area properties are visualized by hatching or filling techniques. A study of the literature on programming languages leads to the conclusion that graphical data should be treated as a data type. Based on the concept of treating graphical data as a data type in its own right, the mathematical and conceptual aspects of this type of data are investigated and established. Much scattered information, such as the representation of regions, has been unified using formal descriptions. Hatching, one of the many ways of achieving external representation of regions, is also investigated. A hatching algorithm is proposed and implemented that envelops the good features of others, and establishes a framework for hatching algorithms. Its implementation achieves the expected tasks. A proposal for a graphics language demonstrates the usefulness and feasibility of this type of graphics. Some of its features have been implemented. Finally, a fairly complete bibliography serves as a gateway for further research in this area. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Unknown

This thesis is concerned with the design and implementation of a surface fitting package in an interactive graphics environment. Surface fitting techniques are used to generate a smooth looking, easy to evaluate, bivariate function given a set of data points on some domain in the plane, and are thus useful for a variety of applications. We consider the implementation of a surface fitting technique using weighted least squares with tensor products of B-splines on regular data grids (i.e. the position of the data points can be represented as the cross product of two vectors). While somewhat more restrictive than other surface fitting methods, this technique, when applicable, is extremely efficient. Knot placement and weight placement are discussed as methods of adapting the spline surface to rapidly varying regions on the domain. A disadvantage of the original method used to solve for the coefficients of the spline surface is that the domain of the function to be approximated must be rectangular. An algorithm to extend the surface fitting method to non-rectangular domains, thus removing this restriction, is presented. An interactive surface fitting package is provided, which allows a user to fit a spline surface to a set of data points on a regular grid. This provides a powerful tool which may be used to effectively modify the spline surface and indicate the accuracy of the approximation. / Science, Faculty of / Computer Science, Department of / Graduate

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