If the progenitor curve is a boundary of a planar set and its parallel curve is without self-intersections, then the latter is the boundary of the Minkowski sum of the planar set and the disk of the given radius.
12.
In the area of 2D computer graphics known as vector graphics, the ( approximate ) computation of parallel curves is involved in one of the fundamental drawing operations, called stroking, which is typically applied to polylines or polybeziers ( themselves called paths ) in that field.
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In Computer-aided design the preferred term for a parallel curve is "'offset curve "'( In other geometric contexts, translation . ) Offset curves are important for example in numerically controlled machining, where they describe for example the shape of the cut made by a round cutting tool of a two-axis machine.
14.
Parametric coords in 2D use parallel curves on a surface, however, which doesn't sound like what you have here . ( I think the article here might be called curvilinear coordinates instead of parametric coordinates, but it's written in such an inaccessible way ( no pics ! ), that I find it hard to understand . ) StuRat 00 : 19, 26 March 2006 ( UTC)
