Question: Geometry L&R algorithm

[YGuangye]

Hi mittinatten,

According to https://freesasa.github.io/doxygen/Geometry.html , the angle $2\pi - \gamma_s$ is always multiplied by $R_i$ to get the SASA of a atom.

I read the explanation there and thought that the SASA of atom $i$, $A_i$ was

$$ A_i = \delta \sums{R{i,s}^{'}(2\pi - \gamma_s)} $$

but this is not what FreeSASA do. You stated that

The angle is multiplied by $R_i$ (not $R_{i}^{'}$) to give the area of a conical frustum circumscribing the sphere at the slice.

and, unfortunately, I am struggling to undestand this. Could you give me some hints?

Thank you.

[mittinatten]

I have lost my notes from the derivation, but the clue is that we are calculating the area of a conical frustrum, not a cylinder.