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- A parallel of a curve is the envelope of a family of congruent circles centered on the curve. It generalises the concept of parallel (straight) lines. It can also be defined as a curve whose points are at a constant normal distance from a given curve.
en.wikipedia.org/wiki/Parallel_curve
Two definitions of a parallel curve: 1) envelope of a family of congruent circles, 2) by a fixed normal distance. The parallel curves of a circle (red) are circles, too. A parallel of a curve is the envelope of a family of congruent circles centered on the curve. It generalises the concept of parallel (straight) lines.
In geometry, parallel lines are coplanar infinite straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance.
In Euclidean geometry, parallel lines are always parallel in both directions, but hyperbolic lines are only parallel in one direction, and they diverge in the other direction. So given a line, and a point not on that line, there are two parallel lines, one in each direction.
The parallel curves of a curve are the curves , parallel of index a of , obtained by algebraically copying a "length" a from the points on on the oriented normal; in other words, they are the loci of the points M = where is the normal vector at M0.
The curves (G 1) and (G 2) are parallel if we can determine current points M 1 and M 2, respectively, such that and . For an initial curve with current point , a parallel is a set (G a) of points where , the angle being the torsion angle (see the notations).
Parallel lines are the lines that never intersect each other and are equidistant. Learn about parallel lines, transversal, properties, equations, examples & more.
Feb 9, 2018 · 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.
