### Abstract

We present an efficient and robust algorithm for computing the perspective silhouette of the boundary of a general swept volume. We also construct the topology of connected components of the silhouette. At each instant t, a three-dimensional object moving along a trajectory touches the envelope surface of its swept volume along a characteristic curve K ^{t}. The same instance of the moving object has a silhouette curve L ^{t} on its own boundary. The intersection K ^{t} ∩ L ^{t} contributes to the silhouette of the general swept volume. We reformulate this problem as a system of two polynomial equations in three variables. The connected components of the resulting silhouette curves are constructed by detecting the instances where the two curves K ^{t} and L ^{t} intersect each other tangentially on the surface of the moving object. We also consider a general case where the eye position changes while moving along a predefined path. The problem is reformulated as a system of two polynomial equations in four variables, where the zero-set is a two-manifold. By analyzing the topology of the zero-set, we achieve an efficient algorithm for generating a continuous animation of perspective silhouettes of a general swept volume.

Original language | English |
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Pages (from-to) | 109-116 |

Number of pages | 8 |

Journal | Visual Computer |

Volume | 22 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2006 Feb |

### Keywords

- Perspective silhouette
- Sweep surface
- Time varying silhouette
- Topology
- Zero-set computation

### ASJC Scopus subject areas

- Software
- Computer Vision and Pattern Recognition
- Computer Graphics and Computer-Aided Design

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## Cite this

*Visual Computer*,

*22*(2), 109-116. https://doi.org/10.1007/s00371-006-0371-1