Semi-Implicit integration methods

The method described here was proposed in Interactive Animation of Cloth-like Objects for Virtual Reality(Mathieu Desbrun, Mark Meyer, Alan H. Barr). We will only present the main ideas of this method. In the integration process, instabilities are due to high frequencies. The idea is to filter the force field to attenuate high frequencies. Here is a general description of the method :

  • Compute the inverse matrix of linear forces

    This step is only made at the begining of the simulation. This inverse matrix remains unchanged during all the simulation.

  • Filter the force field by the previously obtained matrix

    It is a standard matrix-vector product.

  • Make an Euler integration step to retrieve velocities and positions

    As we filtered the force field, instability is no more an issue.

  • Post-correction step

    This step is used to preserve the angular momentum.

This method gives good results, but it is usable for small system only because of the matrix inversion step at the beginning of the simulation, which is very expensive.


All rights reseverd to Roque Marie, Parle Thomas, Reboul Alexandre, Tornieri Christophe