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- 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.
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.
Parallel curves. The curves (G 1) and (G 2) are parallel if we can determine current points M1 and M2, 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).
Two curves are said to be parallel of one another if any curve normal to one is normal to the other; it can be proved that, then, the distance between two points with common normal is a constant, called parallelism distance.
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.
- ParallelCurve
- 2013-03-22 17:13:10
- 2013-03-22 17:13:10
- parallel curve
Nov 7, 2024 · Parallel curves, frequently called "offset curves" in computer graphics applications, are curves which are displaced from a base curve by a constant offset, either positive or negative, in the direction of the curve's normal.
Parallel Curves. Curves can also be parallel when they keep the same distance apart (called "equidistant"), like railroad tracks. The red curve is parallel to the blue curve in both these cases: Parallel Surfaces. Surfaces can also be parallel, like this: Lines and Planes.
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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.
