Prof. Dr. Konrad Polthier
M.Sc. Martin Skrodzki
Duration: 01.07.2016 - 30.06.2020
Freie Universität Berlin
In the project “Computational and structural aspects of point set surfaces”, we will develop discrete differential geometric representations for point set surfaces and effective computational algorithms. Instead of first reconstructing a triangle based mesh, our operators act directly on the point set data. The concepts will have contact to meshless methods and ansatz spaces of radial basis functions. As proof of concept of our theoretical investigations we will transfer and implement key algorithms from
surface processing, for example, for surface parametrization and for feature aware mesh filtering on point set surfaces.
Point set surfaces have a more than 15 year long history in geometry processing and computer graphics as they naturally arise in 3D-data acquisition processes. A guiding principle of these algorithms is the direct processing of raw scanning data without prior
meshing – a principle that has a long-established history in classical numerical computations. However, their usage mostly restricts to full dimensional domains embedded in R2 or R3 and a thorough investigation of a differential geometric representation of point set surfaces and their properties is not available.
Inspired by the notion of manifolds, we will develop new concepts for meshless charts and atlases. These will be used to implement higher order differential operators including curvature descriptors. On this solid basis of meshless differential operators, we will develop novel algorithms for important geometry processing tasks, such as feature recognition, filtering operations, and surface parameterization.