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 line the same point and the line is |"ax" + "c"| / |"a"|, as measured along a horizontal line segment. If the line passes through two points "P"=("x","y") and "P"=("x","y") then the distance of (x,y) from the line is: The denominator of this expression is the distance between "P" and "P". The numerator is twice the area of the triangle with its vertices at the three points, (x,y), "P" and "P". See: . The expression is equivalent to formula_4, which can be obtained by rearranging the standard formula for the area of a triangle: formula_5, where "b" is the length of