Parallel Curve

Parallel Curve

A parallel of a curve is the envelope of a family of congruent circles centered on the curve. It generalises the concept of parallel lines. It can also be defined as a curve whose points are at a fixed normal distance of a given curve.

It is sometimes called the offset curve but the term "offset" often refers also to translation. The term "offset curve" is used, e.g., in numerically controlled machining (and in other computer graphics applications), where it describes the shape of the cut made by a round cutting piece, which is "offset" from the trajectory of the cutter by a constant distance in the direction normal to the cutter trajectory at every point.

A curve that is a parallel of itself is autoparallel. The involute of a circle is an example.