A scanline algorithm is described which renders bicubic patches directly from the parametric description without producing a polygonal approximation. The algorithm is partially based on earlier work by Whitted. A primitive object, called a “curved-edge polygon”, is defined, and an algorithm for breaking down a bicubic patch into the primitive objects is described. A general surface intersection method is employed to provide a robust silhouette edge detector. Shades are computed by calculating a cubic approximation to the normal surface and performing either a cubic or a linear interpolation of the bounding edge normals across the scanline. Subdivision of parametric surfaces is used to reduce the complexity of the surfaces being rendered, providing dramatic improvement in the results of both the silhouette detector and the shading methods.