## Abstract

Given a solid S ⊂ R^{3} with a piecewise smooth boundary, we compute an approximation of the boundary surface of the volume which is swept by S under a smooth one-parameter motion. Using knowledge from kinematical and elementary differential geometry, the algorithm computes a set of points plus surface normals from the envelope surface. A study of the evolution speed of the so called characteristic set along the envelope is used to achieve a prescribed sampling density. With a marching algorithm in a grid, the part of the envelope which lies on the boundary of the swept volume is extracted. The final boundary representation of the swept volume is either a triangle mesh, a B-spline surface or a point-set surface.

Original language | English (US) |
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Pages (from-to) | 599-608 |

Number of pages | 10 |

Journal | Computer-Aided Design and Applications |

Volume | 2 |

Issue number | 5 |

DOIs | |

State | Published - 2005 |

Externally published | Yes |

## Keywords

- Envelope
- Marching algorithm
- Motion
- NC verification
- Point-set surface
- Swept volume

## ASJC Scopus subject areas

- Computational Mechanics
- Computer Graphics and Computer-Aided Design
- Computational Mathematics