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Mirrors that are convex in some places and concave in others can generate images of extended objects (such as the viewer’s face) that are curiously distorted and often topologically disrupted. Understanding these images involves the caustics of the family of rays emitted by each point of the object, and the totality of all such families constituting the rays from all points of the object. The general theory is illustrated by the simplest mirror with an inflection, whose profile is a cubic function. Simulations, and observations with a flexible plastic mirror, show how the image changes as the viewer moves relative to the mirror.

Inflection reflection: images in mirrors whose curvature changes sign