The perspective silhouette of a canal surface

Ku Jin Kim, In Kwon Lee

Research output: Contribution to journalReview article

19 Citations (Scopus)

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 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.

Original language English 15-22 8 Computer Graphics Forum 22 1 https://doi.org/10.1111/1467-8659.t01-1-00642 Published - 2003 Jan 1

Canals
Trajectories

All Science Journal Classification (ASJC) codes

• Computer Networks and Communications
• Computer Graphics and Computer-Aided Design

Cite this

Kim, Ku Jin ; Lee, In Kwon. / The perspective silhouette of a canal surface. In: Computer Graphics Forum. 2003 ; Vol. 22, No. 1. pp. 15-22.
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In: Computer Graphics Forum, Vol. 22, No. 1, 01.01.2003, p. 15-22.

Research output: Contribution to journalReview article

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T1 - The perspective silhouette of a canal surface

AU - Kim, Ku Jin

AU - Lee, In Kwon

PY - 2003/1/1

Y1 - 2003/1/1

N2 - 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.

AB - 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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