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In my current research, I am looking at calculating the local porosity of a porous media in cylindrical coordinate (notably, two co-centric cylinders).

To obtain an accurate approximation, I need to calculate the area of intersection between the surface of a cylinder with a radius $R$ for which the axis is in $(0,0,0)$ and a sphere of radius $r<R$ for which the center can vary (i.e it can be anywhere between the two co-centric cylinders).

Could somebody point me in the direction of an analytical solution to calculate the area of intersection between these two surfaces or at least a fast algorithm?

Best regards, BB

BlaB
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These two references might help:

(1) Murilo G. Coutinho. Dynamic Simulations of Multibody Systems. Springer, 2001. (Springer link)
Contents

(2) James Miller. "Geometric approaches to nonplanar quadric surface intersection curves." ACM Transactions on Graphics (TOG) 6.4 (1987): 274-307. (ACM link)
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Joseph O'Rourke
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