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
Inversion in a sphere the radius of the sphere is 1. Then every point can be written in the form "r"v, where "r" is the distance from the point to the origin and v is a unit vector; moreover, for every point apart from the origin this representation is unique. Given such a representation of a point, its image under spherical inversion is defined to be the point "r"v. This defines a homeomorphism from formula_1 to itself. As a map from Euclidean space to itself, the spherical inversion map is not defined at the origin, but we can extend it to formula_2, the one-point