An analytical visibility method for displaying parametrically defined surfaces

This paper describes an analytical method to determine the visible parts of a Cartesian product surface. The bounds of these visible areas are determined in terms of the (u,v)-parameter-plane. This leads to many advantages over approximating algorithms. The new method allows the calculation and display of only the boundaries and contour curves with high precision. It calculates the critical points of a surface (contours, overlapping contours, penetrations) with machine precision, independent of the resolution of the output device and makes the parallel output on vectorand raster-devices possible. The results of this method are invarying under image-transformations.