Applications of Higher Geometries

01.04.2005 - 31.03.2011
Research funding project
Various problems of Computer Aided Design, Geometric Modeling and Robotics have successfully been solved by applying techniques of classical geometry in combination with methods from approximation theory, numerical analysis and geometric data processing. Those geometric concepts, which are known under the term higher geometries, include the various differential geometries (elementary Euclidean, affine and projective), and the representation of groups by their action on varieties of geometric objects, like Laguerre sphere geometry, line geometry, or kinematic spaces. Geometric methods will also be applied in Computer Vision, Image Processing and Pattern Recognition, in both two and three dimensions. The main topics here are the geometry of shape manifolds, approximation in kinematic spaces and shape spaces, computational line and sphere geometry, and the connection between differential morphology and kinematic geometry.

People

Project leader

Project personnel

Institute

Grant funds

  • FWF - Österr. Wissenschaftsfonds (National) Austrian Science Fund (FWF)

Research focus

  • Mathematical and Algorithmic Foundations: 100%

Publications