Cylinder-Cylinder Intersection
Consider two cylinders as illustrated above (Hubbell 1965) where the cylinders have radii r_1 and r_2 with r_1<=r_2, the larger cylinder is oriented along the z-axis, and where the axes of the two cylinders intersecting at an angle beta. Then the volume of the region of intersection is given by
![画像:(8r_2^3)/(sinbeta)[(1+k^2)E(k)-(1-k^2)K(k)]](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/Cylinder-CylinderIntersection/Inline14.svg){kind=link}
where
| [画像: k=(r_1)/(r_2). ] |
(6)
|
Here, K(k) and E(k) are complete elliptic integrals of the first and second kinds, respectively, _2F_1(a,b;c;z) is a hypergeometric function, and (n; k) is a binomial coefficient.
The intersection of two (or three) right cylinders of equal radii intersecting at right angles is known as the Steinmetz solid.
See also
Cylinder, Steinmetz SolidExplore with Wolfram|Alpha
References
Hubbell, J. H. "Common Volume of Two Intersecting Cylinders." J. Research National Bureau of Standards--C. Engineering and Instrumentation 69C, 139-143, April-June 1965.Referenced on Wolfram|Alpha
Cylinder-Cylinder IntersectionCite this as:
Weisstein, Eric W. "Cylinder-Cylinder Intersection." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Cylinder-CylinderIntersection.html