### Abstract

We consider the problem of converting boundary representations of polyhedral objects into constructive-solid-geometry (CSG) representations. The CSG representations for a polyhedron P are based on the half-spaces supporting the faces of P. For certain kinds of polyhedra this problem is equivalent to the corresponding problem for simple polygons in the plane. We give a new proof that the interior of each simple polygon can be represented by a monotone Boolean formula based on the half-planes supporting the sides of the polygon and using each such half-plane only once. Our contribution is an efficient and practical O(n log n) algorithm for doing this boundary-to-CSG conversion for a simple polygon of n sides. We also prove that such formulae do not always exist for general polyhedra in three dimensions.

Original language | English (US) |
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Pages | 31-40 |

Number of pages | 10 |

Volume | 22 |

No | 4 |

Specialist publication | Computer Graphics (ACM) |

DOIs | |

State | Published - Jan 1 1988 |

### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Computer Graphics and Computer-Aided Design

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## Cite this

*Computer Graphics (ACM)*,

*22*(4), 31-40. https://doi.org/10.1145/378456.378472