Patent ID: 7898541

Claim:
A method for animating a turning of a turning portion of an electronically represented three-dimensional object by a computer, the method including: dividing an animation of a turning portion of a an electronically represented three-dimensional object into at least a first plurality of animation frames and a second plurality of animation frames; and deforming the turning portion of the three-dimensional object by curling at least a part of the turning portion about an imaginary cone, the imaginary cone having a cone apex, a cone side, a cone axis, and a cone angle defined as an angle between the cone axis and the cone side, the curling including mapping a point on the turning portion to a point on the imaginary cone for each of the first plurality of animation frames and the second plurality of animation frames, the mapping the point on the turning portion to the point on the imaginary cone further comprising: defining a first circle with a center at the cone apex and intersecting the point on the turning portion; defining a second circle around the imaginary cone and intersecting an intersecting point corresponding to the intersection of the cone side and the first circle; and mapping the point on the turning portion to the point on the cone on the second circle a distance along the circle from the intersecting point equal to an arc length from the point on the turning portion to the intersecting point along the first circle, wherein between subsequent frames in the first plurality of animation frames, the cone angle gradually decreases from around 90° to a first predetermined minimum cone angle, and the cone apex moves substantially along the cone axis from a first apex position closer to the turning portion of the three-dimensional object to a second apex position farther from the turning portion of the three-dimensional object, and between subsequent frames in the second plurality of animation frames, the cone angle gradually increases from a second predetermined minimum cone angle to around 90°, and the cone apex moves substantially along the cone axis from a third apex position farther from the turning portion of the three-dimensional object toward a fourth apex position closer to the turning portion of the three-dimensional object.