Analytic properties of plane offset curves
Computer Aided Geometric Design
Algebraic properties of plane offset curves
Computer Aided Geometric Design
Rational curves and surfaces with rational offsets
Computer Aided Geometric Design
Offset-rational parametric plane curves
Computer Aided Geometric Design
An efficient method for analyzing the topology of plane real algebraic curves
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
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
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
Curvature formulas for implicit curves and surfaces
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Degree formulae for offset curves
Journal of Pure And Applied Algebra
Local shape of offsets to algebraic curves
Journal of Symbolic Computation
A delineability-based method for computing critical sets of algebraic surfaces
Journal of Symbolic Computation
Good local behavior of offsets to rational regular algebraic surfaces
Journal of Symbolic Computation
On convolutions of algebraic curves
Journal of Symbolic Computation
Local shape of generalized offsets to algebraic curves
Journal of Symbolic Computation
The shape of conchoids to plane algebraic curves
Proceedings of the 7th international conference on Curves and Surfaces
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In [Alcazar, J.G., Sendra, J.R. 2006. Local shape of offsets to rational algebraic curves. Tech. Report SFB 2006-22 (RICAM, Austria); Alcazar, J.G., Sendra, J.R. 2007. Local shape of offsets to algebraic curves. Journal of Symbolic Computation 42, 338-351], the notion of good local behavior of an offset to an algebraic curve was introduced to mean that the topological behavior of the offset curve was locally good, i.e. that the shape of the starting curve and of its offset were locally the same. Here, we introduce the notion of good global behavior to describe that the offset behaves globally well, from a topological point of view, so that it can be decomposed as the union of two curves (maybe not algebraic) each one with the topology of the starting curve. We relate this notion with that of good local behavior, and we give sufficient conditions for the existence of an interval of distances (0,@c) such that for all d@?(0,@c) the topological behavior of the offset O"d(C) is both locally and globally nice. A similar analysis for the trimmed offset is also done.