In optics, a caustic is the envelope of light rays reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface. The caustic is a curve or surface to which each of the light rays is tangent, defining a boundary of an envelope of rays as a curve of concentrated light.
A piece of milled plexiglass acting as a projecting lens; via the Computer Graphics and Geometry Lab at the École Polytechnique Fédérale de Lausanne
New milling techniques applied to glass and plexiglass panels could be used to “create windows that are also cryptic projectors, summoning ghostly images from sunlight.”
[Pauly and Bompas] hope that the technique will be used in architectural design, to create windows that mould sunlight and throw images or patterns onto walls or floors,” which, if timed, milled, and manipulated just right, could produce a slowly animated sequence of images being projected by an otherwise empty window during different times of day.
To control the shape of a caustic pattern generated by a specular or refractive surface, we need to solve the inverse problem: how can we change the surface geometry, such that incident light is redirected to produce a desired caustic image?
The goal of these pages is not to be a model of concision, maximizing entertainment value per word, or to preach to a choir by elegantly repeating a conclusion. Rather, I am attempting to explain things to my future self, who is intelligent and interested, but has forgotten. What I am doing is explaining why I decided what I did to myself and noting down everything I found interesting about it for future reference. I hope my other readers, whomever they may be, might find the topic as interesting as I found it, and the essay useful or at least entertaining–but the intended audience is my future self.