Abstract: We present a novel method for high-performance GPU-based rendering of Catmull-Clark subdivision surfaces. Unlike previous methods, our algorithm computes the true limit surface up to machine precision, and is capable of rendering surfaces that conform to the full RenderMan specification for Catmull-Clark surfaces. Specifically, our algorithm can accommodate base meshes consisting of arbitrary valence vertices and faces, and the surface can contain any number and arrangement of semisharp creases and hierarchically defined detail. We also present a variant of the algorithm which guarantees watertight positions and normals, meaning that even displaced surfaces can be rendered in a crack-free manner. Finally, we describe a view-dependent level-of-detail scheme which adapts to both the depth of subdivision and the patch tessellation density. Though considerably more general, the performance of our algorithm is comparable to the best approximating method, and is considerably faster than Stam's exact method.