Lines Matching refs:hat

102 For example, let $\hat x, \hat y = |1-f|x, |1-f|y$. Computing $\hat x_t$ with respect to $\hat x,
103 \hat y$ allow us to have $t = f + (1 - f)x_t = f + \text{sign}(1-f) \cdot \hat x_t$. That saves us
122 4. Let $\hat x = |1 - f|x', \hat y = |1 - f|y'$
123 5. If $r_1 = 1$, let $\hat x_t = (\hat x^2 + \hat y^2) / \hat x$
125     let $\hat x_t = \sqrt{\hat x^2 + \hat y^2} - \hat x / r_1$
127   1. return invalid if $\hat x^2 - \hat y^2 < 0$
128   2. let $\hat x_t =  -\sqrt{\hat x^2 - \hat y^2} - \hat x / r_1$ if we've swapped $r_0, r_1$,
131   3. let $\hat x_t =  \sqrt{\hat x^2 - \hat y^2} - \hat x / r_1$ otherwise
133 8. $t$ is invalid if $\hat x_t < 0$ (this check is unnecessary if $r_1 > 1$)
134 9. Let $t = f + \text{sign}(1 - f) \hat x_t$
137 In step 7, we try to select either the smaller or bigger $\hat x_t$ based on whether the final $t$
138 has a negative or positive relationship with $\hat x_t$. It's negative if we've swapped, or if
141 Note that all the computations and if decisions not involving $\hat x, \hat y$  can be precomputed
142 before the shading stage. The two if decisions  $\hat x^2 - \hat y^2 < 0$ and $\hat x^t < 0$  can