Kontinuation commented on PR #845:
URL: https://github.com/apache/sedona/pull/845#issuecomment-1569368208
We can derive a more accurate formula of lat-lon envelope for haversine
distance $D$:
$$
\begin{align*}
\Delta \textrm{lat} &= \frac{D}{R} \\
\Delta \textrm{lon} &= \max (\frac{D}{R \cos(\textrm{lat} + \Delta
\textrm{lat})}, \frac{D}{R \cos(\textrm{lat} - \Delta \textrm{lat})})
\end{align*}
$$
where $\textrm{lat}$, $\textrm{lon}$ is the center of the envelope; $R$ is
the radius of the earth. The center point is expanded by $\Delta \textrm{lat}$,
$\Delta \textrm{lon}$ to obtain the envelope for coarse-grained filtering. The
envelope can also be expanded by a constant factor slightly greater than 1 to
get rid of false negatives.
For spheroid distance, we can use the same formula for sphere distance, but
with a different $R$ value. We can take the equatorial radius of the spheroid
as $R$ (approximately 6378 km) and the resulting envelope should be inclusive.
I'm not sure if I'm doing the math correctly, I can find some other
references on this topic.
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