PlanetPhysics/Catacaustic

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Given a plane curve , its catacaustic (Greek `burning along') is the envelope of a family of light rays reflected from after having emanated from a fixed point (which may be infinitely far, in which case the rays are initially parallel).

For example, the catacaustic of a logarithmic spiral reflecting the rays emanating from the origin is a congruent spiral. The catacaustic of the exponential curve, , reflecting the vertical rays, , is the catenary .