Let O be a fixed point in the plane, k a given nonzero real number, theta and dir denote a given sensed angle. By the homology ( or stretch-rotation, or spiral-rotation)  we mean the product  where  is the rotation with respect to O an angle theta in direction dir and  is the dilatation with respect to the center O and ratio k.

Point O is called the center of the homology, k the ratio of the homology, theta and dir the angle of the homology.

For a detailed description of Q (the object created), use the routine detail (i.e., detail(Q))

The command with(geometry,StretchRotation) allows the use of the abbreviated form of this command.