Volume xx (200y), Number z, pp. 1–8 The Perspective Silhouette of a Canal Surface.pdf

Volume xx (200y), Number z, pp. 1–8 The Perspective Silhouette of a Canal Surface Ku-Jin Kim The Graduate School of Information and Communication Ajou University, Suwon 442-749, South Korea Email: kujinkim@ #Phone: +82-31-219-1834 In-Kwon Lee Division of Media, Ajou University, Suwon 442-749, South Korea Email: iklee@ajou.ac.kr #Phone: +82-31-219-1855 Abstract We pr esent an efficient and robust algorithmfor par ameterizing 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 charac- teristic circles, compute the silhouette points on each characteristic circle, and then par ameterize the silhouette curve. Theperspective silhouette of the sphere S
t fr om a given viewpoint consists of a circle Q t ; by identifying
 the values of t at which K
t and Q t
 touch, we canfind all the connected components of the silhouette curve of the canal surface. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: Three Dimensional Graph- ics and Realism 1. Introduction silhouettes of polyhedral models. They fou