For a curve with corners, we must define the parallel curve in a special way, since there is no well-defined normal vector to a curve at a corner. The key is realizing that there is not one but a collection of points a distance d away from each corner point. This collection of points forms a circular arc of radius d centered at the corner. The edges of this arc touch the parallel curves emanating from the two portions of the curve on either side of the corner.

This demo shows the parallel curves of regular polygons with number of sides between one and ten. You can choose the polygon with a slider in the control panel. The Parallels window shows a set of parallel curves. That set is modified by the parallels type-in on the control panel: the first two numbers are the bounds of d , the third is the number of parallels to be drawn. Thus, if you enter (0,0,1) , you will see the polygon itself. In the 1 Parallel window, a single parallel curve is drawn at a distance d controlled by the tapedeck.