Ellipse Parallel Curves
EllipseParallelCurves
The parallel curves for (outward) offset k of an ellipse with semi-axis lengths a and b are given by
x_p = [画像:(a+(bk)/(sqrt(a^2sin^2t+b^2cos^2t)))cost]
(1)
y_p = [画像:(b+(ak)/(sqrt(a^2sin^2t+b^2cos^2t)))sint.]
(2)
The plots above show ellipse parallel curves for ellipses with a/b=0.5 and 0.9.
Each parallel curve can be written as an octic algebraic curve in x_p and y_p.
EllipseInwardParallelCurves
The plot above shows a close-up for "inward" ellipse parallel curves. Talbot's curve resembles these curves.
See also
Ellipse, Parallel Curves, Talbot's CurveExplore with Wolfram|Alpha
WolframAlpha
More things to try:
Cite this as:
Weisstein, Eric W. "Ellipse Parallel Curves." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EllipseParallelCurves.html