Abstract-- We present a novel GPU-based algorithm for highquality rendering of bivariate spline surfaces. An essential difference to the known methods for rendering graph surfaces is that we use quartic smooth splines on triangulations rather than triangular meshes. Our rendering approach is direct since we do not use an intermediate tessellation but rather compute raysurface intersections (by solving quartic equations numerically) as well as surface normals (by using Bernstein-B