Edge Length Interpolation

We propose a scheme to interpolate between a set of two or more 3-dimensional triangulated meshes with corresponding connectivity. The principle behind this is that meshes, when viewed as vectors of edge lengths, can be seen as points in a Euclidean shape space. Within this space, mesh interpolation corresponds to traversing straight lines between points, and due to the Euclidean structure of the underlying shape space, we can easily take averages and perform statistical shape analysis. We perform experiments in three important applications to illustrate these ideas. First, we demonstrate interpolation between various shapes and poses. Second, we illustrate statistical analysis on a large dataset of faces, calculating mean shapes and exploring new shapes by moving along the principal modes of variance of the dataset. Finally, we visualize morphs corresponding to conformal mappings, an important class of deformations, which form a subspace of the edge-length space.