Computing isophotos of surface of revolution and canal surface

Isophote of a surface consists of a loci of surface points whose normal vectors form a constant angle with a given fixed vector. It also serves as a silhouette curve when the constant angle is given as π/2. We present efficient and robust algorithms to compute isophotes of a surface of revolution and a canal surface. For the two kinds of surfaces, each point on the isophote is derived by a closed-form solution. To find each connected component in the isophote, we utilize the feature of surface normals. Both surfaces are decomposed into a set of circles, where the surface normal vectors at points on each circle construct a cone. The vectors which form a constant angle with given fixed vector construct another cone. We compute the parametric range of the connected component of the isophote by computing the parametric values of the surface which derive the tangential intersection of these two cones.