PlanetPhysics/Catacaustic

Given a plane curve $\gamma$, its catacaustic (Greek $\varkappa \alpha \tau \acute{\alpha }\varkappa \alpha \upsilon \sigma \tau \iota \varkappa \acute{o}\varsigma$ `burning along') is the envelope of a family of light rays reflected from $\gamma$ 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, $y=e^x$, reflecting the vertical rays, $x=t$, is the [[../Catenary/|catenary]] $y=\cosh (x+1)$.