GAMM - Mitteilungen. Nov 2014, Vol. 37 Issue 2, p184, 32 p.
Byline: Martin Rumpf(1), Max Wardetzky(2) Keywords: geometric partial differential equations; geometric functionals; thin shells; shape spaces Abstract Triggered by the development of new hardware, such as laser range scanners for high resolution acquisition of complex geometric objects, new graphics processors for realtime rendering and animation of extremely detailed geometric structures, and novel rapid prototyping equip-ment, such as 3D printers, the processing of highly resolved complex geometries has established itself as an important area of both fundamental research and impressive applications. Concepts from image processing have been picked up and carried over to curved surfaces, physically based modeling plays a central role, and aspects of computer aided geometry design have been incorporated. This paper aims at highlighting some of these developments, with a particular focus on methods related to the mechanics of thin elastic surfaces. We provide an overview of different geometric representations ranging from polyhedral surfaces over level sets to subdivision surfaces. Furthermore, with an eye on differential-geometric concepts underlying continuum mechanics, we discuss fundamental computational tasks, such as surface flows and fairing, surface deformation and matching, physical simulations, as well as spectral and modal methods in geometry processing. Finally, beyond focusing on single shapes, we describe how spaces of shapes can be investigated using concepts from Riemannian geometry. ([c] 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) Author Affiliation: (1)Institut for Numerical Simulation, University of Bonn, Endenicher Allee 60, 53115 Bonn, Germany (2)Institute of Numerical and Applied Mathematics, University of Gottingen, Lotzestr. 16-18, 37083 Gottingen, Germany