Method and apparatus for generating a primitive extension defining a generalized primitive is described. The primitive extension defines the connectivity and vertices used to specify a collection of connected primitives, such as a strip-type or fan-type generalized primitive. A generalized primitive includes a number of vertices where some of the vertices are shared with neighboring primitives. The primitive extension includes an originating primitive, vertex data, and connectivity information. The primitive extension provides a general interface for describing a variety of connected primitives.