Orthotomic
Given a source S and a curve gamma, pick a point on gamma and find its tangent T. Then the locus of reflections of S about tangents T is the orthotomic curve (also known as the secondary caustic). The evolute of the orthotomic is the catacaustic. For a parametric curve (f(t),g(t)) with respect to the point (x_0,y_0), the orthotomic is
![画像:x_0-(2g^'[f^'(g-y_0)-g^'(f-x_0)])/(f^('2)+g^('2))](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/Orthotomic/Inline11.svg){kind=link}
![画像:y_0+(2f^'[f^'(g-y_0)-g^'(f-x_0)])/(f^('2)+g^('2)).](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/Orthotomic/Inline14.svg){kind=link}
See also
Catacaustic, Caustic, Circle Orthotomic, Diacaustic, InvoluteExplore with Wolfram|Alpha
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References
Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, p. 60, 1972.Referenced on Wolfram|Alpha
OrthotomicCite this as:
Weisstein, Eric W. "Orthotomic." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Orthotomic.html