Abstract: A basic element of Digital Geometry Processing algorithms is the establishment of a smooth parameterization for a given model. In this paper we propose an algorithm which establishes parameterizations for a set of models. The parameterizations are called consis-tent because they share the same base domain and respect features. They give immediate correspondences between models and allow remeshes with the same connectivity. Such remeshes form the basis for a large class of algorithms, including principal component analysis, wavelet transforms, detail and texture transfer between models, and $<$i$>$n$<$/i$>$-way shape blending. We demonstrate the versatility of our algorithm with a number of examples.