Equations for Geometric Operations

(1) X = x.cos(q) + y.sin(q) + x_displace + x.x_stretch + x.y.x_cross

(2) Y = y.cos(q) - x.sin(q) + ydisplace + y.ystretch + x.y.ycross

(3) X = x.cos(q) - y.sin(q) - m.cos(q) + n.sin(q) + m

(4) Y = y.cos(q) + x.sin(q) - m.sin(q) - n.cos(q) + n

(5) gray(P1) = (1 - x).gray(floor x, floor y) + x.gray(ceilingx, floor y)

(6) gray (P2) = (1 - x).gray(floorx, ceiling y) + x.gray(ceiling x, ceiling y)

(7) gray(p3) = (1 - y).gray(P1) + y.gray(P2)