  The polarimeter vector of the $\tau$ represents an optimal observable for the
measurement of the $\tau$ spin. In this paper we present an algorithm for the
computation of the $\tau$ polarimeter vector for the decay channels $\tau^{-}
\rightarrow \pi^{-}\pi^{+}\pi^{-}\nu_{\tau}$ and $\tau^{-} \rightarrow
\pi^{-}\pi^{0}\pi^{0}\nu_{\tau}$. The algorithm is based on a model for the
hadronic current in these decay channels, which was fitted to data recorded by
the CLEO experiment.
