File:Latlon to tile.png

Summary

Formulas to convert latitude and longitude into tile x,y coordinates. Based upon File:Xy_tile.JPG.

\begin{align*}
    x &= \left\lfloor \frac{lon + 180}{360} \cdot 2^z \right\rfloor \\ \\
    y &=
        \left\lfloor
            \left(
                1 - \frac{
                    \ln \left(
                        \tan \left(
                            lat \cdot \frac{\pi}{180}
                        \right) + \frac{1}{\cos \left( lat \cdot \frac{\pi}{180} \right)}
                    \right)
                }{\pi}
            \right) \cdot 2^{z - 1}
        \right\rfloor
\end{align*}

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