Shape spaces for geometric modeling

Abstract

A novel framework to treat shapes in the setting of Riemannian geometry is presented. Shapes - triangular meshes - are treated as points in shape space. Useful Riemannian metrics in this space are introduced to aid the user in design and modeling tasks. In a second part a special class of developable surfaces is discussed. Fascinating and elegant shapes may be folded from a single planar sheet of material without stretching, tearing or cutting, if one incorporates curved folds into the design. An optimization-based computational framework for the design and digital reconstruction of surfaces which can be produced by curved folding is presented.