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
Distance from a point to a plane We define formula_8, formula_9, formula_10, and formula_11, to obtain formula_1 as the plane expressed in terms of the transformed variables. Now the problem has become one of finding the nearest point on this plane to the origin, and its distance from the origin. The point on the plane in terms of the original coordinates can be found from this point using the above relationships between formula_13 and formula_14, between formula_15 and formula_16, and between formula_17 and formula_18; the distance in terms of the original coordinates is the same as the distance in terms of the revised coordinates. The formula for