On the modified conjugate gradient method in cloth simulation

The seminal paper on cloth simulation by Baraff and Witkin [4] presents a modified preconditioned conjugate gradient (MPCG) algorithm for solving certain large, sparse systems of linear equations. These arise when employing implicit time integration methods aimed at achieving large step cloth simulation in the presence of constraints. This paper improves the robustness and efficiency of this MPCG algorithm. We prove convergence. For this, we recast the algorithm into a linear algebra setting, identifying its filtering procedure as an orthogonal projection. This leads not only to a convergence proof but also to a correction in the initiation stage of the original algorithm that improves its efficiency. We give an example to illustrate the performance improvement offered by this correction.