### Abstract

An algorithm is presented to approximate planar offset curves within an arbitrary tolerance ∈ > 0. Given a planar parametric curve C(t) and an offset radius r, the circle of radius r is first approximated by piecewise quadratic Bézier curve segments within the tolerance c. The exact offset curve C_{r}(t) is then approximated by the convolution of C(t) with the quadratic Bézier curve segments. For a polynomial curve C(t) of degree d, the offset curve C_{r}(t) is approximated by planar rational curves, C^{a}_{r} (t)s, of degree 3d - 2. For a rational curve C(t) of degree d, the offset curve is approximated by rational curves of degree 5d - 4. When they have no self-intersections, the approximated offset curves, C^{a}_{r}(t)s, are guaranteed to be within edistance from the exact offset curve C_{r}(t). The effectiveness of this approximation technique is demonstrated in the offset computation of planar curved objects bounded by polynomial/ rational parametric curves.

Original language | English |
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Pages (from-to) | 617-630 |

Number of pages | 14 |

Journal | CAD Computer Aided Design |

Volume | 28 |

Issue number | 8 |

DOIs | |

Publication status | Published - 1996 Aug |

### All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Computer Graphics and Computer-Aided Design
- Industrial and Manufacturing Engineering

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## Cite this

*CAD Computer Aided Design*,

*28*(8), 617-630. https://doi.org/10.1016/0010-4485(95)00078-X