Many model editing operations, such as morphing, blending, and shape deformation, require the ability to interactively transform the surface of a model in response to some control mechanism. For most computer graphics applications, it is important to preserve the local shape properties of input models during editing operations. Our work introduces the first, to our knowledge, mesh editing technique that explicitly preserves local shape properties. The method is based on a local shape representation, which we refer to as pyramid coordinates. The pyramid coordinates capture the local shape of the mesh around each vertex and help maintain this shape under various editing operations. They are based on a set of angles and lengths relating a vertex to its immediate neighbors. This representation is invariant under rigid transformations. Using pyramid coordinates, we introduce a new technique for mesh deformation and morphing based on a small number of user-specified control vertices. Our algorithm generate natural looking deformations and morphing sequences in seconds with minimal user interaction.