2D computer graphics endowed with a self-rendering method—a procedure which assigns colors to the image pixels by an arbitrary algorithm. Complex models can be built by combining simpler objects, in the paradigms of object-oriented programming. In Euclidean geometry, a translation moves every point a constant distance in a specified direction. A translation can be described as a rigid motion: other rigid motions include rotations and reflections. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. A translation operator is an operator formula_1 such that formula_2 If v
Whitehead's point-free geometry chpt. 2 of "Process and Reality". For an advanced and detailed discussion of systems related to C, see Roeper (1997). Biacino and Gerla (1991) showed that every model of Clarke's theory is a Boolean algebra, and models of such algebras cannot distinguish connection from overlap. It is doubtful whether either fact is faithful to Whitehead's intent. Whitehead's point-free geometry In mathematics, point-free geometry is a geometry whose primitive ontological notion is "region" rather than point. Two axiomatic systems are set out below, one grounded in mereology, the other in mereotopology and known as "connection theory". A point can mark a