Abstract: We present a shape description framework that generates a multitude of shape descriptors through a variety of design and continuum of parameter choices. Our parameter is a surface mesh, referred to as the template, which is supplied at run time, and allows generating different shape descriptors for the same model. Our framework extracts a numerical shape descriptor by computing a selected function on the model mesh, mapping (transferring) it to the template, expanding the mapped function in terms of a basis on the template, and collecting the expansion coefficients into a vector. We investigate possible design choices for the steps in the framework, and introduce novel approaches that provide further freedom in generating a multitude of previously unknown descriptors. We show that our approach is a generalization of the way some of the existing numerical descriptors are defined, and that for appropriate template choices one is able to reproduce some of the well-known descriptors. Finally, we show empirically that design and parameter choices have non-trivial effects on the descriptor's performance, and that better retrieval results can be obtained by combining descriptors obtained via different templates.