On the geometry of parametrized bicubic surfaces

We provide a geometric study of the problem of finding and describing the double point locus of a bicubic surface. Our motivation is to determine whether a real bicubic patch over the unit square will have self intersections. And if so, to identify useful points and curves in order to determine basic features and to help graph the surface accurately. Here, we consider special interesting cases with additional structures, which are among the surfaces commonly used in CAGD (Computer Aided Geometric Design).