Consider shifting part of one plane according to specifications contained in another; to shear a plane, lines should be shifted sideways, some more than others. Thus cells in the sheared plane should first shift along a line while the control line is being copied alongside itself.
On the next pass, two lines will shift while a third line is being added to the control region. The total shift will be equal to the depth of each line in the control region, the base line having shifted a distance equal to its full depth, the line at the top will have shifted just one cell, while the remainder have yet to move.
Planes are not commonly sheared as a visual exercise, but it turns out that the composite of three shears produces a rotation; consequently images can be rotated within the CAM memory without outside intervention, via the evolution of appropriate automata. To see how this can happen, consider the matrix representation of a shear parallel to the x-axis:
Equivalently, a y-shear has the form
Compounding the shears requires multiplying the coefficient matrices; a product of three shears gives
If a=1, implying a unit shear to the left, and b=-1, implying a unit shear downwards, the final coefficient matrix is
which is readily recognized as a clockwise rotation by 
; this
relation persists even with the CAM
board's cyclic boundaries.
Reversing the signs of a and b reverses the sense of the rotation;
the center of the rotation is the point of intersection of the original
guide lines.
Rotation is not an instantaneous process; the procedure just described requires three sweeps through the whole screen. The process ought to be compared to reading the contents of one or more bitplanes into an external memory, then restoring them, having modified their contents separately or else in conjunction with the restoration. The accessibility of the external memory has to balanced against the restricted range of any internal modification.