Implementing and interpolating rotations from a computing input device

摘要

Novel and simple methods, systems, and computer program products for implementing a 3D rotation using input from a mouse, trackball, or other input device are described. Methods of implementing rotations are presented which lead to new realizations of the 3D rotation group and its double-cover, the unit quaternions. New methods, systems, and computer program products are also presented for interpolating rotations of a 3D scene that is more efficient than previously-known quaternion-based methods. The new methods are also used to derive the quaternion composition formula from the geometry of 3D rotations.

主权项

1. A computer program product for implementing a method for calculating rotations of a graphical object for display upon a computer system display using input from a computing input device, the computer program product comprising one or more computer hardware storage devices having computer executable instructions encoded thereon which, when executed upon one or more computer processors, perform the method comprising:
accessing a stored graphical data structure comprising data defining a graphical object which is to be displayed on a computer system display device; receiving input from a computing input device, the input comprising data associated with an intended rotation of the graphical object; receiving one or more data structures comprising two rotations, A1 and A2, the two rotations associated with the intended rotation of the graphical object; expressing each rotation as a composition of two reflections, each reflection having a common initial reflection for each of the rotations, such that A1=R1R and A2=R2R1 and each reflection Rj being of the form Rj=2ujujT−I; interpolating two unit vectors, u0 and u1, by us, 0