Computing and visualizing pose-interpolating 3D motions

CAD and animation systems offer a variety of techniques for designing and animating arbitrary movements of rigid bodies. Such tools are essential for planning, analyzing, and demonstrating assembly and disassembly procedures of manufactured products. In this paper, we advocate the use of screw motions for such applications, because of their simplicity, flexibility, uniqueness, and computational advantages. Two arbitrary control-poses of an object are interpolated by a screw motion, which, in general, is unique and combines a minimum-angle rotation around an axis A with a translation by a vector parallel to A. We explain the advantages of screw motions for the intuitive design and local refinement of complex motions. We present a new, simple and efficient algorithm for computing the parameters of a screw motion that interpolates any two control-poses and explain how to use it to produce animations of the moving objects. Finally, we discuss a new and efficient variant of a known procedure for computing a set of faces which may be used to display the 3D region swept by a polyhedron that moves along a screw motion.