As solid-model-based computer-aided design (CAD) systems become more pervasive, more and more organizations are trying to use them directly as the geometry base from which grids for computational fluid dynamics (CFD) are generated. The boundary representations produced by these CAD systems provide an accurate definition of the surface geometry, albeit in a form that in not necessarily consistent with the engineering intent. This is due to the fact that the topology of the boundary representations are as much a function of the CAD operations used to produce them as they are of the shape of the configuration that is being modeled. A few years ago, an extension of traditional edge-face boundary representations, called chains and quilts, was developed that allows the analyst to group faces into quilts and edges into chains so as to be consistent with the aerodynamic intent. But since chains and quilts were viewed simply as a collection, there was not a single global parameterization within that collection, which sometimes limited their utility. Described herein is a new method for globally parameterizing quilts in a two-step process: first, the quilt is either projected or unrolled to an intermediate representation; and second, a block-structured-grid-like process is used in the intermediate representation to create the final parameterizations. Computed results for two configurations to which the new technique has been applied are shown as well as summary statistics for the entire test suite.