Three areas of geometric modelling have been studied in this thesis: the computation of the convex hull of a model, the labelling of the connected components of a model, and the calculation of the minimum distance between two objects in a model. The models considered for each area of research are solid models which have been defined set-theoretically, i.e. using computational solid geometry (CSG). Although the areas of research have been considered independently of the dimensionality of the models, methods developed in this work have been implemented for three-dimensional models.
The following new results are presented in this thesis:
1. Computing the convex hull of set-theoretically defined model. A point-set that represents the model is generated by one of three methods (one for polyhedral models, two for non-polyhedral models). The convex hull of this point-set is then found by using an existing convex hull algorithm.
2. A heuristic method of computing the connectivity between two points within a given model. This works using a divide-and-conquer method to attempt to find a series of points which are connected.
3. A connected-component labelling algorithm utilising a binary tree storage structure for a model by dividing a model and storing the divided model in a binary tree. Neighbouring nodes in the binary tree are examined to compute connected components. \item An algorithm for the computation of the minimum distance between two models by dividing the models recursively and concentrating the division on areas in which the minimum distance is more likely to be found.