The Perspective Silhouette of a Canal Surface

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.

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