properties of parallel curves
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Two plane curves are parallel curves of each other, if every normal of one curve is also a normal of the other curve (then one may show that the distance of the corresponding points of the curves is a ).
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Two curves are parallel curves of each other, if they are the loci of the end points of a line segment which moves perpendicularly to its own direction.
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Every regular curve having a continuous curvature has an infinite family of parallel curves.
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The parallelism of curves is an equivalence relation.
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The two parallel curves on both sides of a curve at the distance form the envelope of the family of circles with center on and radius .
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Title | properties of parallel curves |
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Canonical name | PropertiesOfParallelCurves |
Date of creation | 2013-03-22 17:14:30 |
Last modified on | 2013-03-22 17:14:30 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 6 |
Author | pahio (2872) |
Entry type | Topic |
Classification | msc 51N05 |