Light from a point P(x,y,z) in 3D space is projected in a straight line POQ through a pinhole O(0,0,0) on to a flat screen, photographic plate or plane, a fixed distance d behind the pinhole, to a point Q(X,Y) in 2D space, where (0,0) in this XY plane, representing the screen, is defined by the projection of a beam of light along the z axis perpendicular to the screen passing through the hole (i.e., all points (0,0,z) a distance z from O are projected on to one point (0,0) in the XY plane); the X axis is parallel to but is in the opposite direction to the x axis; and the Y axis is parallel to but is in the opposite direction to the y axis. (The mapping of points in 3D space through an aperture on to a flat screen is the basic principle on which optics, perspective and photography rest.) Find the values of X and Y in terms of x, y, z and d.