Exploring the Geometry of the Space of Shells

• Published in: Computer graphics forum Vol. 33; no. 5; pp. 247 - 256
• Main Authors: Heeren, B., Rumpf, M., Schröder, P., Wardetzky, M., Wirth, B.
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.08.2014
• Subjects: Analysis; Animation; Calculus; Categories and Subject Descriptors (according to ACM CCS); Computer animation; Computer graphics; Deformation; Elastic deformation; Extrapolation; Foundations; I.3.5 [Computer Graphics]: Computational geometry and object modeling-Physically based modeling; Mathematical analysis; Rigid-body dynamics; Shells; Studies; Transport

We prove both in the smooth and discrete setting that the Hessian of an elastic deformation energy results in a proper Riemannian metric on the space of shells (modulo rigid body motions). Based on this foundation we develop a time‐ and space‐discrete geodesic calculus. In particular we show how to...