| EPSRC Reference: |
GR/R52329/01 |
| Title: |
Symmetry Sets and medical axes, including affinely invariant versions, in two and three dimensions |
| Principal Investigator: |
Giblin, Professor P |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematical Sciences |
| Organisation: |
University of Liverpool |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 October 2001 |
Ends: |
30 September 2004 |
Value (£): |
67,862
|
| EPSRC Research Topic Classifications: |
|
| EPSRC Industrial Sector Classifications: |
| Communications |
No relevance to Underpinning Sectors |
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
I propose to build on existing research by myself and others concerning symmetry sets (SS) and medial axes (MA) in two and three dimensions. There are two main themes to the proposed research, though these are related. Each will be pursued both experimentally and theoretically, and each will take into account related research by colleagues in Engineering departments. (i) Investigation and comparison of various definitions of affinely invariant symmetry sets, for plane curves which may have inflexions. Specialization to medial axes and their properties. Possibly extensions of at least one of these to three dimensions. (ii) Investigation of classical (euclidean) symmetry sets and medial axes in two and three dimensions. Precise conditions for a plane set to be the medial axis of some smooth curve, especially at singularities of the MA. The SS/MA in three dimensions, including the detailed geometry, the properties of the radius function and the vector field which this defines on the SS/MA, and curvature properties of the generating surface and its SS/MA.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
http://www.liv.ac.uk |