This paper describes an approach to the approximation of Loop subdivision surfaces for real-time rendering. The approach consists of two phases, which separately construct the approximation geometry and the normal field of a subdivision surface. It first exploits quartic triangular Bézier patches to approximate the geometry of the subdivision surface by interpolating a grid of sampled points. To remedy the artifact of discontinuity of normal fields between adjacent patches, a continuous normal field is then reconstructed by approximating the tangent vector fields of the subdivision surfaces with quartic triangular Bézier patches. For regular triangles, the approach reproduces the associated subdivision patches, quartic three-directional box splines.