I am a member of the Geometric Computing and Computer Vision research group at the School of Computer Science, Cardiff University. My research interests lie in the areas of geometric and solid modelling, computational geometry, differential geometry and related topics in computer graphics. I am also interested in physical modelling, in particular for quantum and nano technology, and some aspects of parallel computing. I have been working on reverse engineering geometric models with a focus on beautification and design intent detection, detecting approximate symmetries and regular patterns, geometric constraints, reliefs, mesh processing and filtering, curve smoothing, free-form surfaces and point-based modelling.
Current Focus
Currently I am mainly working on low-level representations of shape for modelling and simulation operations, but also describing shape in terms of high level properties for creating, editing and analysing geometric models. This is aimed at computer-aided design applications for modelling conventional devices, but also for modelling and controlling quantum systems to build novel quantum devices.
Current projects include:
- Point sampling
- Physical simulations using points
- Smoothing boundary curves
- Filtering and processing of irregular meshes with uncertainties
- Visualisation and simulation of quantum systems
For more details see the sections to the left, sorted roughly by the type of objects considered.
Some Details
Understanding, describing and handling geometric properties and the shape of solid physical objects and building suitable computational models of them has a variety of applications related to computer-aided design and also involves interesting geometrical questions. I have been working on reverse engineering geometric models with the particular aim of automatically generating a high level description of a model, which has either been reconstructed from measurements of a real object or is simply a basic CAD model without any information about intended properties and its design. This work resulted in a system for detecting a likely design intent description in approximate models and beautification of such models based on various algorithms for detecting approximate symmetries and other regularities, selecting suitable intended regularities, and enforcing such regularities on a model using geometric constraints to improve an approximate model or edit a model. The ultimate goal of this work is to devise a system which can automatically produce different interpretations of a model (in terms of some suitable notion of regularity) in real-time to enable an engineer to easily create, modify and analyse such models without restrictions based on how it has been created initially or is currently interpreted due to a specific set of regularities used to describe the model. This should be done not only for solid physical objects, but for any geometric models of physical systems, such as quantum systems, to help understand their operation and create and modify them for a particular purpose.
An interesting approach to computing with geometric objects is to represent them as a discrete point sets where each point is a sample of the underlying geometry. This computationally very simple representation has been used for rendering, but is also be suitable for other modelling operations and simulations. In general low-level representations may allow efficient processing. However, additional high-level descriptions of the properties of the point set it may make it simple to edit the point set and at the same time allow us to use the point representation for analysing the object and in simulations. Such descriptions may at least be partly computed automatically from the low-level representation. Work on this resulted in an approach to sampling and ongoing work into using point sets for simulations. This is aimed particularly at modelling quantum systems for applications in nano technology.
As time wore along, his absorption in the irregular wall and ceiling of his room increased; for he began to read into the odd angles a mathematical significance which seemed to offer vague clues regarding their purpose.
Research,http://www.langbein.org/research [29/October/2008, 15:36].
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