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Parametric generalized offsets to hypersurfaces. (English) Zbl 0878.68134

Summary: We extend the classical notion of offset to the concept of generalized offset to hypersurfaces. In addition, we present a complete theoretical analysis of the rationality and unirationality of generalized offsets. Characterizations for deciding whether the generalized offset to a hypersurface is parametric or it has two parametric components are given. As an application, an algorithm to analyse the rationality of the components of the generalized offset to a plane curve or to a surface, and to compute rational parametrizations of its rational components, is outlined.

MSC:

68U07 Computer science aspects of computer-aided design
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
14Q10 Computational aspects of algebraic surfaces
51N35 Questions of classical algebraic geometry

Keywords:

hypersurfaces
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