1. A method for animating computer-generated objects, the method comprising: receiving, at one or more computer systems, first position information generated by a first computer simulation of a first object at a first time of an animation sequence, the first object comprising a first mesh, wherein the first computer simulation is performed using one or more physics models, and wherein the first position information specifies a first position of a point of the first mesh; receiving, at one or more computer systems, second position information associated with a second object at a plurality of times that include the first time and a second time, the second object comprising a second mesh; projecting, with one or more processors associated with the one or more computer systems, the first position information of the first mesh to follow the second position information of the second mesh at the second time to generate projected position information of the first object at the second time of the animation sequence, wherein the projected position information specifies a second position of the point of the first mesh; after the following of the second position provides completed results to obtain the projected position information, performing a second computer simulation of the first object using the projected position information as input to direct the second computer simulation, the second computer simulation providing new position information of the first object at the second time, wherein the second computer simulation is performed using the one or more physics models that were used in the first computer simulation, and wherein the new position information specifies a third position of the point of the first mesh; and generating, with the one or more processors associated with the one or more computer systems, the animation sequence at the plurality of times using the first position information and the new position information of the first object.