3-DIMENSIONAL ROTATIONS BY 3 SHEARS

We show that a rotation in three dimensions can be achieved by a compo sition of three shears, the first and third along a specified axis and the second along another given axis orthogonal to the first; this pro cess is invertible. The resulting rotation algorithm is practical for the processing of fine-grained digital images, and is well adapted to the access constraints of common storage media such as dynamic RAM or magnetic disk. For a 2-D image, rotation by composition of three shear s is well known. For 3-D, an obvious nine-shear decomposition has been mentioned in the literature. Our three-shear decomposition is a sizab le improvement over that, and is the best that can be attained-just tw o shears won't do. Also, we give a brief summary of how the present th ree-shear decomposition approach generalizes to any linear transformat ions of unit determinant in any number of dimensions. (C) 1997 Academi c Press.