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Generating the final $ s$ from $ \hat{u}$ and $ \tilde{u} $.

The final $ s$ has the form $ \displaystyle s= \rho \Big( cos(\phi) \; \hat{u} + sin(\phi) \; \tilde{u} \Big)$ and $ \phi$ has one of the following values: $ \displaystyle \{ 0, \frac{\pi}{4}, \frac{\pi}{2}, \frac{3 \pi}{4}, \pi,$ $ \displaystyle \frac{-\pi}{4}, \frac{-\pi}{2}, \frac{-3 \pi}{4} \}$. We will choose the value of $ \phi$ which maximize 5.2.
Frank Vanden Berghen 2004-04-19