[FEATURE REQUEST / question] ellipsoidal model for distance

[kkdd]

Hello, For mitigating the distortion error in distance, $r$, arisen from spherical model (= S2 geometry), I think that ellipsoidal model would be better, and it would traditionally consist of the following:

• ellipsoidal model + cylindrical projection (e.g., Braun projection) + R-tree (e.g., Priority R-Tree)

Do you have any ideas about it?

• Ellipsoidal model is differentially (i.e., in short range) represented as follows:

$$ \begin{align} dr &= \sqrt{dE^2+dN^2} \ dE &= \left(\frac{R}{\sqrt{1-e^2\sin^2 \phi }}\right) \cos \phi d \lambda \ dN &= \left(\frac{R\ (1- e^2)}{\left(1-e^2 \sin^2 \phi\right)^{3/2}}\right) d \phi \ \end{align} $$

• The Braun projection is represented as follows:

$$ \begin{align} x &= R\lambda \ y &= 2 R \tan \frac{\phi}{2} \ \chi &= \tan \frac{\phi}{2} \ d \phi &= \frac{2}{1 + \chi^2} d \chi \ \cos \phi &= \frac{1 - \chi^2 }{1 + \chi^2}\ \sin \phi &= \frac{2 \chi}{1 + \chi^2} \end{align} $$