Abstract: Named after the title, the PCCM transformation is a simple, explicit algorithm that creates large, smoothly joining bicubic Nurbs patches from a refined Catmull-Clark subdivision mesh. The resulting patches are maximally large in the sense that one patch corresponds to one quadrilateral facet of the initial, coarsest quadrilateral mesh before subdivision. The patches join parametrically $C^2$ and agree with the Catmull-Clark limit surface except in the immediate neighborhood of extraordinary mesh nodes; in such a neighborhood they join at least with tangent continuity and interpolate the limit of the extraordinary mesh node. The PCCM transformation integrates naturally with array-based implementations of subdivision surfaces.