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Geometric Aspects of Empirical Modelling: Issues in Design and Implementation


Empirical modelling is a new approach to the construction of physical (typically computer-based) artefacts.  Model construction proceeds in an open-ended and exploratory manner in association with the identification of observables, dependency and agency.  Knowledge of the referent is acquired through experiment, and --- through the use of metaphor --- interaction with the artefact is contrived so as to resemble interaction with the referent.  Previous research has demonstrated the potential for empirical modelling in many areas.  These include concurrent engineering, virtual reality and reactive systems development.

This thesis examines the relationship between empirical modelling and geometric modelling on computer systems.  Empirical modelling is suggested as complementary to variational and parametric modelling techniques commonly used in software packages for geometric modelling.  Effective techniques for exploiting richer geometric models in visual metaphors within empirical modelling are also developed.

Technical issues arising from geometric aspects of existing empirical modelling tools and case-studies are reviewed.  The aim is improve the efficiency of existing implementations, and to introduce data representations that better support geometric modelling.  To achieve this, a mathematical model (the DM Model) for representing the dependency between observables is introduced, and this is used as the basis for a new algorithm for propagating updates through observables.  A novel computing machine (the DAM Machine) that maintains dependencies representing indivisible relationships between words in computer store is derived from the DM Model.  Examples of the use of this machine for the representation of geometry are presented.  In implementation, a comparative efficiency gain is achieved by the DAM Machine over existing tools.  This allows for the real-time animation of models.

A novel and general approach to the representation of data, suitable for integrating empirical modelling and general Java applications, with additional support for collaborative working, is developed.  Object-oriented programming methods provide the foundation for new tools to support this representation.  The empirical world class library allows a programmer to implement new applications for shape modelling that support empirical modelling and integrate a wide range of shape representations.  A method of integrating these geometric techniques into spreadsheet-like environments that are well-adapted to support empirical modelling is proposed.