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 contents of the city's images which are referable to physical forms can conveniently be classified into five types of elements: paths, edges, districts, nodes, and landmarks.
Paths are the channels along which the observer customarily, occasionally, or potentially moved.
Edges are the linear elements not used or considered as paths by the observer. They are the boundaries.
Districts are the medium-to-large sections of the city, conceived of as having two-dimensional extent.
Nodes are points, the strategic spots in a city into which an observer can enter, and which are the intensive foci to and from which they are traveling.
Landmarks are another type of point-reference, but in this case the observer does not enter within them, they are external. They are usually a rather simply defined physical object: building, sign, store, or mountain.