We present an ontology of objects, functions, and generic shape representation that supports form-function reasoning. By reasoning from the mechanical and other functions of objects to their geometric shape requirements, we deduce the generic shape representation of objects, which we represent as a partial boundary representation composed of primitive geometric shape elements and their spatial and other relations. We use this ontology to model a knowledge base of everyday objects, including their generic shapes. This ontology can support applications such as product design and object recognition.