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Let the sets of points $(p_1, p_2)$ and $(q_1,q_2)$ define the endpoints of the long axes of for two finite cylinders, $C_1$ and $C_2$, of radii $r_1$ and $r_2$, in three-dimensional space. What is a general method of calculating the exact intersection volume of the two cylinders? Does the problem become easier if one only wants to know the volume within some small error?

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Let the sets of points $(p_1, p_2)$ and $(q_1,q_2)$ define the long axes of two finite cylinders, $C_1$ and $C_2$, of radii $r_1$ and $r_2$, in three-dimensional space. What is a general method of calculating the exact intersection volume of the two cylinders? Does this the problem become easier if I one only want wants to know the volume within some small error?

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# Calculating the exact intersection volume of two finite cylinders in three-dimensional space

Let the sets of points $(p_1, p_2)$ and $(q_1,q_2)$ define the long axes of two finite cylinders, $C_1$ and $C_2$, of radii $r_1$ and $r_2$, in three-dimensional space. What is a general method of calculating the exact intersection volume of the two cylinders? Does this problem become easier if I only want to know the volume within some small error?