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Sphere–cylinder intersection
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Sphere–cylinder intersection : ウィキペディア英語版
Sphere–cylinder intersection

In the theory of analytic geometry for real three-dimensional space, the intersection between a sphere and a cylinder can be a circle, a point, the empty set, or a special type of curve.
For the analysis of this situation, assume (without loss of generality) that the axis of the cylinder coincides with the ''z''-axis; points on the cylinder (with radius r) satisfy
:x^2 + y^2 = r^2.
We also assume that the sphere, with radius R is centered at a point on the positive x-axis, at point (a, 0, 0). Its points satisfy
:(x-a)^2 + y^2 + z^2 = R^2.
The intersection is the collection of points satisfying both equations.
== Trivial cases ==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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