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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).
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.
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.
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
Finding parallel curves to some algebraic objects are simple, especially lines and circles (P(y, d) means the parallel curve to curve y at uniform distance d). Lines: y = mx + b. P(y, d) = (mx + b) ± (d ∗ 1 +m2− −−−−−√) Circles: y = ± r2 −x2− −−−−−√. P(y, d) = ± (r ± d)2 −x2− −−−−−−−−−√.
Nov 10, 2020 · The graph of parametric equations is called a parametric curve or plane curve, and is denoted by \(C\). Notice in this definition that \(x\) and \(y\) are used in two ways. The first is as functions of the independent variable \(t\).
