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About: Sphere–cylinder intersection     Goto   Sponge   NotDistinct   Permalink

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In the theory of analytic geometry for real three-dimensional space, the curve formed from 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 ) satisfy We also assume that the sphere, with radius is centered at a point on the positive x-axis, at point . Its points satisfy The intersection is the collection of points satisfying both equations.