Representing motion using chronogeneous transformation

Abstract

The author introduces a matrix representation of rigid and nonrigid 3D motion, which generalizes homogeneous transformation. He calls this transformation a chronogeneous transformation. Just as homogeneous transformations allow rigid transformations and projection to be represented in a linear manner, chronogeneous transformations allow an analogous representation for certain classes of continuous motion/structural deformation. The author categorizes these classes of motion. For example, uniform translation of a rigid object that rotates with uniform angular velocity about a fixed axis is one kind of motion that can be represented. It is straightforward to calculate the matrix representation given the underlying motion parameters and vice versa. It is also shown how the position of a point on an object changes as a result of simultaneous uniform chronogeneous camera and objection motion.<>