### Abstract

Our CSG modeller, sVLIs, uses interval arithmetic to categorize implicit functions representing primitive shapes against boxes; this allows an efficient implementation of recursive spatial division to localize the primitives for a variety of purposes, such as rendering or the computation of integral properties. Affine arithmetic allows a track to be kept on the contributing terms to an interval, which often reduces the conservativeness of interval arithmetic. In particular, by tracking the asymmetric contributions of even and odd powers of intervals that contain zero, tighter bounds can be kept on resulting interval values. This paper shows how such techniques can be implemented in the svLIs modeller, and offers a comparison of doing so with using conventional interval arithmetic.

Original language | English |
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Pages (from-to) | 1-14 |

Number of pages | 14 |

Journal | Uncertainty in Geometric Computations |

Volume | 704 |

Publication status | Published - 2002 |

## Cite this

Bowyer, A., Martin, R., & Shou, H. H. (2002). Affine intervals in a CSG geometric modeller.

*Uncertainty in Geometric Computations*,*704*, 1-14.