• Journal of Korea Game Society
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• v.18 no.1
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• pp.125-134
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• 2018

This paper presents a practical method to efficiently extract the rotational part of a $3{\times}3$ matrix that changes continuously in time. This is the key technique in the corotational FEM and the shape matching deformation popular in physics-based dynamic deformation. Recently, in contrast to the traditional polar decomposition methods independent of time, an iterative method was proposed that formulates the rotation extraction in a physics-based way and exploits an incremental representation of rotation. We develop an optimization method that reduces the number of iterations under the assumption that the maximum magnitude of the incremental rotation vector is limited within ${\pi}/2$. Realistic simulation of dynamic deformation employs a sufficiently small time step, and thus this assumption is not problematic in practice. We demonstrate the efficiency and practicality of our method in various experiments.