Equidistant Curve

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Equidistant Curve

 

The set of the ends of equal segments laid off in a fixed direction along the normals to a given plane curve L is known as an equidistant curve of L. For example, an equidistant curve of a circle is a circle. In Lobachevskian geometry an equidistant curve of a straight line—that is, the locus of points at a given distance from the line—is called an equidistant curve (with that line as base) or, less frequently, a hypercycle. In Euclidean geometry an equidistant curve of a straight line is a straight line.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
An analytical method is adopted to obtain the discrete points on the equidistant curve with downsampling subsequently.
However, the problem of equidistant curve has always been a difficult problem in Mathematics because a very small number of special functions of the equidistant curve can be obtained by mathematical methods.
Figure 5(a) shows the boundary tracking result that was completed in 6.87 s (tracking velocity: 2.55 [micro]m/s; step length: 10 nm), where blue star and pink squares represent the boundary point (BP) on the sample contour and discrete points on the equidistant curve, respectively.
Coxeter was able to demonstrate that each arc is of a type known to mathematicians as an equidistant curve. It bears the same relationship to a hyperbolic straight line as a line of latitude does to the equator on the surface of a sphere.