Good vibrations: modal dynamics for graphics and animation

Many of the problems of simulating and rendering complex systems of non-rigid objects can be minimized by describing the geometry and dynamics separately, using representations optimized for either one or the other, and then coupling these representations together. We describe a system which uses polynomial deformation mappings to couple a vibration-mode ("modal") representation of object dynamics together with volumetric models of object geometry. By use of such a hybrid representation we have been able to gain up to two orders of magnitude in efficiency, control temporal aliasing, and obtain simple, closed-form solutions to common (non-rigid) inverse dynamics problems. Further, this approach to dynamic simulation naturally lends itself to the emphasis and exaggeration techniques used in traditional animation.