Geometric Properties
As for parallel lines, a normal line to a curve is also normal to its parallels.
When parallel curves are constructed they will have cusps when the distance from the curve matches the radius of curvature. These are the points where the curve touches the evolute.
If the initial 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.
Read more about this topic: Parallel Curve
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