Search results
Parallel curve. Parallel curves of the graph of for distances. 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.
The curves and are parallel if respective current points M 1 and M 2 can be determined so that . For an initial curve with current point , a parallel curve is a set of points . Cartesian parametrization: . The parallel curves of an algebraic curve are algebraic. Curvilinear abscissa at the current point on (oriented by the same tangent vector ...
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). The surface area of the strip between two corresponding arcs of (G 0) and (G a) is equal ...
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 two branches of the parallel curve a distance away from a parametrically represented base curve are. where and .
Feb 9, 2018 · parallel curve. 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
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.
People also ask
How do you know if a curve is a parallel curve?
What is an example of a parallel curve?
Is a red curve parallel to a blue curve?
What is the involute of a parallel curve?
Why do parallel lines have cusps?
Is a parallel curve of a line a concentric circle?
May 19, 2021 · The curvature of parallel curves differs, while the slopes of the curves are identical at corresponding points on the curves where perpendicular segments cross. Examples of parallel curves in nature are presented, and curve fitting is used to estimate the formula for a curve that is parallel to a parabola in the same plane.
