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Parallel Curve

\begin{figure}\begin{center}\BoxedEPSF{ParallelCurves.epsf scaled 700}\end{center}\end{figure}

The two branches of the parallel curve a distance $k$ away from a parametrically represented curve $(f(t),g(t))$ are

$\displaystyle x$ $\textstyle =$ $\displaystyle f\pm {kg'\over\sqrt{f'^2+g'^2}}$  
$\displaystyle y$ $\textstyle =$ $\displaystyle g\mp {kf'\over\sqrt{f'^2+g'^2}}.$  

The above figure shows the curves parallel to the Ellipse.


Gray, A. ``Parallel Curves.'' §5.7 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 95-97, 1993.

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 42-43, 1972.

Lee, X. ``Parallel.''

Yates, R. C. ``Parallel Curves.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 155-159, 1952.

© 1996-9 Eric W. Weisstein