| EPSRC Reference: |
EP/E025889/1 |
| Title: |
Non-uniform subdivision surfaces |
| Principal Investigator: |
Dodgson, Professor NA |
| Other Investigators: |
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| Department: |
Computer Science and Technology |
| Organisation: |
University of Cambridge |
| Scheme: |
Standard Research |
| Starts: |
01 March 2007 |
Ends: |
28 February 2011 |
Value (£): |
356,618
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| EPSRC Research Topic Classifications: |
| Design & Testing Technology |
Image & Vision Computing |
| Numerical Analysis |
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The current standard representation for free-form surfaces, as used in aerospace, shipbuilding, automotive design and increasingly in consumer items, is the non-uniform rational B-spline (NURBS), which specifies a shape in terms of a regular grid of control points. A newer representation, subdivision surfaces, promises to provide significant advantages: in particular, they do not insist on total regularity of grid, thus allowing a shape to be defined more naturally by grids which locally follow the features of the shape. A simple example is the bottom of the windscreen pillar of a car, where the flow of the shape down the pillar needs to be blended with the fore-and-aft flow of the shape of the side of the car. A NURBS-based modelling system requires that the geometry be specified as a set of separate NURBS pieces. These must be laboriously joined together to ensure appropriate mathematical properties (e.g. continuity of curvature) across the joins and such properties can, in general, only be achieved approximately. A subdivision-based system, by contrast, handles such situations as part of the basic mechanism. The problem that prevents their wide use in the computer-aided design industry is that they are not a true superset of NURBS, being based on uniform grid theory. We intend to address the generalisation of subdivision to the non-uniform case, thus opening the way for the acceptance of this generalisation as the next standard. There are three strands to the proposed research: (a) extending subdivision to the non-uniform, rational case, which will make subdivision a true superset of NURBS for low orders (in particular the widely used cubics) for closed surfaces and the interiors of open surfaces; (b) extending subdivision to handle edge conditions at the edges of mesh pieces in analagous ways to NURBS so that open surfaces can be handled in their entiriety; (c) extending subdivision to handle the higher orders which are used in some computer-aided design systems, in particular to quintics.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
http://www.cl.cam.ac.uk/research/rainbow/projects/subdnurbs/ |
| Further Information: |
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| Organisation Website: |
http://www.cam.ac.uk |