  We examine a class of techniques for 3D object manipulation on mobile
devices, in which the device's physical motion is applied to 3D objects
displayed on the device itself. This "local coupling" between input and display
creates specific challenges compared to manipulation techniques designed for
monitor-based or immersive virtual environments. Our work focuses specifically
on the mapping between device motion and object motion. We review existing
manipulation techniques and introduce a formal description of the main mappings
under a common notation. Based on this notation, we analyze these mappings and
their properties in order to answer crucial usability questions. We first
investigate how the 3D objects should move on the screen, since the screen also
moves with the mobile device during manipulation. We then investigate the
effects of a limited range of manipulation and present a number of solutions to
overcome this constraint. This work provides a theoretical framework to better
understand the properties of locally-coupled 3D manipulation mappings based on
mobile device motion.
