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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
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