When we use the Sphere interaction mechanism, we map the
menu onto the surface of a sphere. Think of it as printing out a picture of a
normal Circle Menu and taping to a beach ball. Look at the menu from above and
turn the ball away from where the mouse moves. So if you're standing with the
ball in front of you, looking down at the menu, and the mouse moves towards you,
roll the ball towards away from yourself. The result is that the menu options
that are in the direction of the mouse's motion are brought closer to the menu's
center while the options away from where the mouse has moved are taken away. The
advantage of doing this with a sphere is that the further a menu option is taken
away from the center of the menu, the more mouse motion it will take to push it
even further and the radius of the sphere is the absolute furthest a menu option
can go from the menu center. This keeps options from running too far away and
from going off the screen as some interaction methods may do.
Also, just like in the Pie Menu interaction mechanism, the menu option closest to
the mouse actually follows the mouse around, anticipating that it is the option
that the user wants.