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