Given two curves, one is a parallel curve (also known as an offset curve) of the other if the points on the first curve are equidistant to the corresponding points in the direction of the second curve’s normal. Alternatively, a parallel of a curve can be defined as the envelope of congruent circles whose centers lie on the curve.
For a parametric curve in the plane defined by , its parallel curve with offset is defined by
From the definition, the family of parallel curves is then
where correspond to the catenary.
|Date of creation||2013-03-22 17:13:10|
|Last modified on||2013-03-22 17:13:10|
|Last modified by||stitch (17269)|