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minor fix

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Martin Thoma 2013-12-12 00:10:19 +01:00
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@ -402,7 +402,8 @@ $t$:
So the solution is given by
\begin{align*}
x_S &:= - \frac{b}{2a} \;\;\;\;\; \text{(the symmetry axis)}\\
w &:= y_P+\frac{b^2}{4a}-c \;\;\; \text{ and } \;\;\; \alpha := \frac{(1- 2 aw)}{2 a^2} \;\;\;\text{ and }\;\;\; \beta := \frac{-z}{2 a^2}\\
w &:= y_P+\frac{b^2}{4a}-c \;\;\; \text{ and } \;\;\; z := x_P+\frac{b}{2a}\\
\alpha &:= \frac{(1- 2 aw)}{2 a^2} \;\;\;\text{ and }\;\;\; \beta := \frac{-z}{2 a^2}\\
t &:= \sqrt[3]{\sqrt{3 \cdot (4 \alpha^3 + 27 \beta^2)} -9\beta}\\
\underset{x\in\mdr}{\arg \min d_{P,f}(x)} &= \begin{cases}
x_1 = +\sqrt{a (y_p + \frac{b^2}{4a} - c) - \frac{1}{2}} + x_S \text{ and } &\text{if } x_P = x_S \text{ and } y_p + \frac{b^2}{4a} - c > \frac{1}{2a} \\