FIG. 7C illustrates aspects of motion patterns 780 that can be used as part of an animation state-space in accordance with some embodiments, and FIG. 7D illustrates aspects of a computer model that can be used as part of a system for generating and displaying animations in accordance with some embodiments. FIG. 7D illustrates a bone 760 having joints 750 and 770. In FIG. 7D, joint 750 is a reference point for bone 760, and joint 770 is a control point, with motion patterns for control point 770 defined in a spherical surface 774 around joint 770 having a maximum range of motion 772 illustrated as range 772A and 772B.