The Perspective Silhouette

We present an efficient and robust algorithm for parameterizing the perspective silhouette of a canal surface and detecting each connected component of the silhouette. A canal surface is the envelope of a moving sphere with varying radius, defined by the trajectory C t of its center and a radius function r t . This moving sphere, S t , touches the canal surface at a characteristic circle K t . We decompose the canal surface into a set of characteristic circles, compute the silhouette points on each characteristic circle, and then parameterize the silhouette curve. The perspective silhouette of the sphere S t from a given viewpoint consists of a circle Q t ; by identifying the values of t at which K t and Q t touch, we can find all the connected components of the silhouette curve of the canal surface.