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.
Read more about Parallel Curve: Alternative Definitions, Parametric Curve, Geometric Properties, Self-parallel Spirals
Famous quotes containing the words parallel and/or curve:
“If from the earth we came, it was an earth
That bore us as a part of all the things
It breeds and that was lewder than it is.
Our nature is her nature. Hence it comes,
Since by our nature we grow old, earth grows
The same. We parallel the mother’s death.”
—Wallace Stevens (1879–1955)
“I have been photographing our toilet, that glossy enameled receptacle of extraordinary beauty.... Here was every sensuous curve of the “human figure divine” but minus the imperfections. Never did the Greeks reach a more significant consummation to their culture, and it somehow reminded me, in the glory of its chaste convulsions and in its swelling, sweeping, forward movement of finely progressing contours, of the Victory of Samothrace.”
—Edward Weston (1886–1958)