Given a plane curve γ, its catacaustic (Greek ϰατα ϰαυστιϰóς ‘burning along’) is the envelope
of a family of Light rays reflected from γ 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 = ex reflecting the vertical rays
x = t is the catenary y = cosh(x+1).
