Thesis (M. Sc. (Computer Science))--Rhodes University, 2006. / Submitted in partial fulfilment of the requirements of the degree of Master of Science.

Thesis (MScIng)--University of Stellenbosch, 2005. / Appendix B on CD-ROM in pocket in book. Bibliography. Also available via the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: Chandrajit L. Bajaj. Vita. Includes bibliographical references.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 71-79). Also available in electronic version.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 82-87). Also available in electronic version.

Thesis (Ph.D.)--York University, 2005. Graduate Programme in Computer Science. / Typescript. Includes bibliographical references (leaves 210-216). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNR11609

This research examines procedural modeling in the eld of computer graphics. Procedural modeling automates the generation of objects by representing models as procedures that provide a description of the process required to create the model. The problem we solve with this research is the creation of a procedural modeling environment that consists of a procedural modeling language and a set of non-interactive modeling tools. A goal of this research is to provide comparisons between 3D manual modeling and procedural modeling, which focus on the modeling strategies, tools and model representations used by each modeling paradigm. A procedural modeling language is presented that has the same facilities and features of existing procedural modeling languages. In addition, features such as caching and a pseudorandom number generator is included, demonstrating the advantages of a procedural modeling paradigm. The non-interactive tools created within the procedural modeling framework are selection, extrusion, subdivision, curve shaping and stitching. In order to demonstrate the usefulness of the procedural modeling framework, human and furniture models are created using this procedural modeling environment. Various techniques are presented to generate these objects, and may be used to create a variety of other models. A detailed discussion of each technique is provided. Six experiments are conducted to test the support of the procedural modeling benets provided by this non- interactive modeling environment. The experiments test, namely parameterisation, re-usability, base-shape independence, model complexity, the generation of reproducible random numbers and caching. We prove that a number of distinct models can be generated from a single procedure through the use parameterisation. Modeling procedures and sub-procedures are re-usable and can be applied to different models. Procedures can be base-shape independent. The level of complexity of a model can be increased by repeatedly applying geometry to the model. The pseudo-random number generator is capable of generating reproducible random numbers. The caching facility reduces the time required to generate a model that uses repetitive geometry.

Ph.D. / In this thesis we undertake a study of formal three-dimensional representational and acceptor methods. In lieu hereof then, we give a short overview of such strategies existing in the literature. Graph and graph grammar theory present us with a powerful two dimensional representational method, and we propose to extend these concepts to the three-dimensional case. We therefore give a short discussion on the theory of graphs and graph grammars. As point of departure, we review the concepts of a structure parameter and structure graph (SG) introduced by us in [BEH,93] and show that these concepts enable us to describe objects in three-dimensional space. We propose various modified graph grammar extensions that generates structure graphs, referred to as Structure Graph Grammar extensions (SGG's) by combining context provisions with the rewriting rules of the various grammar systems. This proposed methodology of ours culminates in the combination of production rule bounded contexts and globally specified contexts, thus defining Structure Graph Grammar extension 7 (SGG-7). We show the applicative value of the three dimensional generative abilities of SGG's by considering the generation of various chemical structural formulae. Brandenburg and Skodinis mentions in [BS,95] that there is a shortcoming in the theory of graph grammars in the sense that in general, there exists no accepting device for graph grammar systems. The following quote from [BS,95,p.336] illustrates this point: "There are no graph automata, which fit to the major classes of graph languages. This is a gap in the theory of graph languages." Regarding the class of languages generated by SGG-7, we propose to fill this gap by introducing an Structure Graph Automaton (SGA) to accept this class of languages.

A new stereo matching paradigm is introduced as an integrated process of highly discriminating steps, adopting congruously all the fundamental steps of the stereo vision problem. The central objective is the extraction of a disparity map from which the depth map will be derived. A unique representation of the two dimensional (2-D) stereo images into linear, orthogonal, and spatially-varying attributes serve as the mathematical foundation from which the proposed stereo matching method has evolved. The devised attributes contribute equally to the decision making process and provide information on the characterization of a potential match and its validation through a consistency check. A fundamental contribution of this thesis is in creating the possibility for the design of a dimensionally-augmented vision system (2½ -D representation) based on an effective stereo paradigm with realistic computational requirements. In this design configuration, the geometrical mappings between the 3-D real-world measurements with the measurements obtained using the proposed 2½ -D-D representation are established. Computer results for the intended objective of creating highly accurate disparity maps for various scenes with varying complexities clearly demonstrate the soundness of the proposed method both in terms of its matching effectiveness and its realistic computational power requirements. Future objectives point to the development of enhanced algorithms for scene interpretation and understanding based on this augmented representation.

A Thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Doctor of Philosophy Johannesburg, 2018 / Two dimensional gravity models and a few magnetic models limited to short profiles in the eastern sections of the BC have been used to propose conflicting geometries for the Rustenburg Layered Suite (RLS), especially between the western and eastern lobes; one school argued for completely separate intrusions, while the other proposed that the outcropping lobes are connected at depth. These competing models suggest different emplacement models. They provide a valuable starting point, but, 2.5D potential field modelling is not well suited to modelling complex three dimensional geology. Also, in previous work the magnetics or only the gravity data were modelled independently. Here I present the first full three dimensional potential field forward modelling of the central and southern Bushveld Complex (BC) which has been used to test the geometry of the Bushveld Complex in areas obscured by younger geological cover. Both gravity and magnetic data have been used to develop a geological model that is consistent with both data sets. Joint 3D modelling of regional gravity and magnetic data combined with published crustal thickness models derived from broadband seismic tomography studies were used to create a 3D model of the central and southeastern sections of the BC, as well as the southern part of the northern lobe. Eight downhole logs with more than 730 000 new density and magnetic susceptibility measurements from the RLS were combined with existing data to determine values for Bushveld Complex lithologies that were used in the model. The 3D model has a complex geometry with thick continuous RLS in most of the western lobe, thinner RLS in the south-eastern lobe, but a disrupted RLS in the eastern lobe. Large domes of Transvaal dolomite or thicker granites and granophyre in the eastern lobe interrupt the continuity of the RLS. The western and eastern lobes are therefore broadly connected, with major disruptions largely in the eastern lobe. However, they are not separate intrusions, but represent a single magma chamber affected by pre-existing and syn-magmatic updoming. The model includes the whole thickness of the crust and requires dense material at the crust mantle boundary. Thus, for the first time, I have imaged the remnants of magma staging chambers. The chambers, constrained by the extent of the diffuse crust-mantle transition as determined from teleseismic data, underlie the whole Bushveld Complex, but is thickest under the northern, south-eastern and western parts of the complex. I propose feeders that correlate with the chambers in the northern lobe near the large gravity high near Polokwane and in the south-eastern lobe. / MT 2019