Analytic properties of plane offset curves
Computer Aided Geometric Design
Algebraic properties of plane offset curves
Computer Aided Geometric Design
Parametric generalized offsets to hypersurfaces
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
A Laguerre geometric approach to rational offsets
Computer Aided Geometric Design
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Local shape of offsets to algebraic curves
Journal of Symbolic Computation
Good global behavior of offsets to plane algebraic curves
Journal of Symbolic Computation
Good local behavior of offsets to rational regular algebraic surfaces
Journal of Symbolic Computation
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Offsetting is an important operation in computer aided design, with applications also in other contexts like robot path planning or tolerance analysis. In this paper we study the local behavior of an algebraic curve under a variation of the usual offsetting construction, namely the generalized offsetting process (Sendra and Sendra, 2000a). More precisely, here we discuss when and how this geometric construction may cause local changes in the shape of an algebraic curve, and we compare our results with those obtained for the case of classical offsets (Alcazar and Sendra, 2007). For these purposes, we use well-known notions of Differential Geometry, and also the notion of local shape introduced in Alcazar and Sendra (2007). Our analysis shows important differences between the topological properties of classical and generalized offsets, both at regular and singular points.