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 $$y = \cosh(x\!+\!1)$$.