### 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 |
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Pages (from-to) | 15-22 |

Number of pages | 8 |

Journal | Computer Graphics Forum |

Volume | 22 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2003 Jan 1 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Computer Graphics Forum*,

*22*(1), 15-22. https://doi.org/10.1111/1467-8659.t01-1-00642

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*Computer Graphics Forum*, vol. 22, no. 1, pp. 15-22. https://doi.org/10.1111/1467-8659.t01-1-00642

**The perspective silhouette of a canal surface.** / Kim, Ku Jin; Lee, In Kwon.

Research output: Contribution to journal › Review article

TY - JOUR

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.

UR - http://www.scopus.com/inward/record.url?scp=0037354671&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037354671&partnerID=8YFLogxK

U2 - 10.1111/1467-8659.t01-1-00642

DO - 10.1111/1467-8659.t01-1-00642

M3 - Review article

VL - 22

SP - 15

EP - 22

JO - Computer Graphics Forum

JF - Computer Graphics Forum

SN - 0167-7055

IS - 1

ER -