A fast implicit integration method for solving dynamic equations of movement

摘要

The use of physics is a way to improve realism in Virtual Reality. In order to calculate virtual objects movement in a real-time physically based simulation, you have to solve ODE (Ordinary Differential Equations) relative to time. This solution has to be fast enough to display the scene at an interactive rate or to control an haptic device and to be as reliable as possible.We show that the use of the Euler implicit method is possible in a real-time environment. This one offers control about stability and thus has a good behaviour with stiff ODE, which are hard to solve. For this purpose, we propose to solve the non-linear system from Euler's integration in a way less costly than usual Newton like techniques by applying Broyden's method.