Thesis (MSc (Mathematical Sciences))--Stellenbosch University, 2008. / In this thesis we consider the modelling of a particular layout optimisation problem, namely, the LEGO construction problem. The LEGO construction problem, in short, concerns the optimal layout of a set of LEGO bricks to represent a given object. Our goal is to develop a software package which LEGO enthusiasts can use to construct LEGO sculptures for any real-world object. We therefore not only consider the layout optimisation problem, but also the generation of the input data required by the LEGO construction problem. We show that by using 3D geometric models to represent the real-world object, our implemented voxelisation technique delivers accurate input data for the LEGO construction problem. The LEGO construction problem has previously been solved with optimisation techniques based on simulated annealing, evolutionary algorithms, and a beam search approach. These techniques all indicate that it is possible to generate LEGO building instructions for real-world objects, albeit not necessarily in reasonable time. We show that the LEGO construction problem can be modelled easily with cellular automata, provided that cells are considered as clusters which can merge or split during each time step of the evolution of the cellular automaton. We show that the use of cellular automata gives comparable layout results in general, and improves the results in many respects. The cellular automata method requires substantially less memory and generally uses fewer LEGO bricks to construct the LEGO sculpture when using comparable execution times.

Thesis (MSc (Computer Science))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: The aim of this thesis is to develop a generic 3D virtual environment development platform for autism spectrum disorder (ASD) therapy tools. The potential of using computerised therapy tools for ASD therapy is well known. However, the development of such tools is expensive and time-consuming, and is language and culture speci c. This work intends to alleviate these problems. The design of the platform is based on known game engine designs, but adapted for the requirements of ASD therapy tools. It supports standard features such as 3D rendering, animation and audio output. Speci c features, aimed at ASD therapy tools and educational games, included in our engine are: replays, data capturing, remote monitoring over a network and language localisation. We also implemented an input hardware abstraction layer to allow support for non-standard input peripherals in the future, without modifying existing game implementations. Furthermore, to separate the development of games and tools from the engine, we include wrapper libraries in our engine for Lua and Java. We successfully developed our engine and implemented a number of prototype therapy tools and educational games. These implementations confirmed that the engine works as expected. Some of these programs are currently in use at a local primary school. / AFRIKAANSE OPSOMMING: Die doel van hierdie tesis is om 'n 3D virtuele omgewing en ontwikkelingsplatform vir outistiese spektrum versteuring (OSV) terapiemiddels te ontwikkel. Die gebruik van rekenaargebaseerde terapiemiddels vir OSV terapie is bekend. Om sulke terapiemiddels te ontwikkel is egter duur, tydrowend en is dikwels gerig op spesi eke taal- en kultuurgroepe. Hierdie werk het dit ten doel om hierdie probleme te bowe te kom. Die ontwerp van die platform is gebaseer op die ontwerp van bekende videospeletjie-enjins, maar is aangepas vir die benodigdhede van OSV terapiemiddels. Dit ondersteun standaard funksionaliteit soos 3D uitbeelding, animasie en klank. Ons platform sluit in spesi eke funksionaliteit, wat gerig is op OSV terapiemiddels en opvoedkundige speletjies, naamlik: kykweer, datavaslegging, afstandswaarneming oor 'n netwerk en taal-lokalisering. Verder is 'n abstrakte koppelvlak vir toevoerapparatuur ontwikkel, wat dit moontlik maak om in die toekoms nie-standaard toevoerapparatuur te ondersteun, sonder om bestaande speletjies se implementasies aan te pas. Verder, om die ontwikkeling van speletjies en terapiemiddels te skei van die enjin, is koppelvlakke ontwikkel wat dit moontlik maak om die enjin in Lua en Java te gebruik.