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?
In any control system that is functioning properly, the methods used to control a signal won’t be correlated with the signal they’re controlling.
Worse, there will be several variables that DO show relationships, and may give the wrong impression. You’re looking at variables A, B, C, and D. You see that when A goes up, so does B. When A goes down, C goes up. D never changes and isn’t related to anything else — must not be important, certainly not related to the rest of the system. But of course, A is the angle of the road, B is the gas pedal, C is the brake pedal, and D is the speed of the car.