The Perspective Silhouette of a Canal Surface

Abstract

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 trajectoryC(t)of its center and a radius functionr(t). This moving sphere,S(t), touches the canal surface at a characteristic circleK(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 sphereS(t)from a given viewpoint consists of a circleQ(t); by identifying the values oftat whichK(t)andQ(t)touch, we can find all the connected components of the silhouette curve of the canal surface.ACM CSS: I.3.7 Computer Graphics-Three Dimensional Graphics and Realism