Using computer to model reactions of objects to simulated physical interactions

The present invention discloses using computer to model reactions of objects to simulated physical interactions. Especially, in modeling contact between two or more objects (such as a robotic arm placing a block on a stack of blocks) or articulations of a series of linked joints (such as modeling a backhoe), current techniques can introduce additional energy into the system or fail to resolve a constraint imposed on the system. The current techniques attempt to resolve these issues, for example, by using very small time steps. Very small time steps, however, can significantly increase computational costs of the modeling simulation. The disclosed simulation system for rigid bodies uses a time interval to reduce linearization artifacts due to the small time steps and reduce computational costs with faster solver convergence by permitting more efficient bias calculations. High mass handling can also be improved through the more efficient bias calculations. 本发明公开了使用计算机对对象的反应进行建模以模拟物理交互。具体地，在对两个或更多个对象之间的接触进行建模(例如，