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 = e^x reflecting the vertical rays x = t is the catenary y = cosh(x+1).