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 far more pernicious issue with pangrams, as a means for evaluating typefaces, is how poorly they portray what text actually looks like. Every language has a natural distribution of letters, from most to least common, English famously beginning with the E that accounts for one eighth of what we read, and ending with the Z that appears just once every 1,111 letters. Letter frequencies differ by language and by era — the J is ten times more popular in Dutch than English; biblical English unduly favors the H thanks to archaisms like thou and sayeth — but no language behaves the way pangrams do, with their forced distribution of exotics. Seven of the most visually awkward letters, the W, Y, V, K, X, J, and Z, are among the nine rarest in English, but pangrams force them into every sentence, guaranteeing that every paragraph will be riddled with holes. A typeface designer certainly can’t avoid accounting for these unruly characters, but there’s no reason that they should be disproportionately represented when evaluating how a typeface will perform.