Let's say I have one spherical cap, resulting from cutting a sphere centered at origin and with radius R1
with a plane, whose normal goes into the direction of the x
axis. The spherical cap can be seen as a body with two surfaces, a planar surface and a spherical surface with total area equal to S1
. Now I have a second sphere, centered at another arbitrary point and with radius R2
. In the cases in which the spherical cap and the second sphere overlap, dividing the spherical face of the cap into two parts with resulting values for the partial spherical surfaces S1a
and S1b
, how can one calculate analytically S1a
and S1b
?
Analytical calculation of the resulting surface between a sphere and a spherical cap from another sphere
1
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geometry
spherical-geometry
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0clarified, thanks for the correction – 2011-10-06