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**Offsetting operations in solid modelling.**
*(English)*
Zbl 0631.65144

Let X be a bounded set in \({\mathbb{R}}^ n\) \((n=2,3)\). The positive r-offset Y of X is defined as \(Y=\{p\in {\mathbb{R}}^ n:\exists q\in X\), \(\| p- q\| \leq r\}\). The authors study this and other related operations in a framework of computer graphics applications. Their “primary goal is to ensure that offset solids are treated like other solids in the modeller, i.e. that they can be displayed, combined by Boolean operations, further offset and so forth”. The main difficulty in achieving this goal is the boundary evaluation for resulting solids. To overcome this difficulty the authors introduce an extended version of CSG (constructive solid geometry) [cf. the second author, Representations of rigid solids: theory, methods and systems, ACM Comput. Surv. 12, 437-464 (1980)]. The paper contains a description of the implementation of the resulting experimental solid modelling system.

Reviewer: A.Kushkuley

### MSC:

65S05 | Graphical methods in numerical analysis |

65D15 | Algorithms for approximation of functions |

65Yxx | Computer aspects of numerical algorithms |

53A05 | Surfaces in Euclidean and related spaces |

### Keywords:

offsets; curves; surfaces; approximations; computational geometry; computer graphics; computer graphics applications; boundary evaluation; constructive solid geometry; experimental solid modelling system
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\textit{J. R. Rossignac} and \textit{A. A. G. Requicha}, Comput. Aided Geom. Des. 3, 129--148 (1986; Zbl 0631.65144)

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