The rolling ball

Publisher Summary Interactive graphics systems often need techniques that allow the user to rotate graphical objects freely in three-dimensional space, using commonly available two-dimensional input devices such as a mouse. This chapter presents the rolling-ball method for mouse-driven three-dimensional orientation control along with some of its interesting extensions to other scientific visualization problems. The rolling-ball technique exploits a continuous two-dimensional motion to reach any arbitrary three-dimensional orientation. The rolling-ball technique provides an approach to controlling three degrees of rotational freedom in interactive graphics systems with two-dimensional input devices that do not depend on the state, position, or history of the input device. Because of the algorithm's rich group-theoretical origins, a number of related scientific visualization applications naturally present themselves. Becoming fluent with the technique requires some effort on the part of the user. But once mastered, the rolling-ball method provides context-free, exploratory orientation adjustment that strongly supports the feeling of direct manipulation. Moving the input device in small clockwise circles produces a rotation of the spatial part of the coordinate frame in the clockwise direction, which is the opposite of the result for standard O(3) rotations. This effect, known as the Thomas Precession, makes the rolling-ball technique a very natural one for Lorentz transformations.