High Quality Content by WIKIPEDIA articles! In the theory of analytic geometry for real three-dimensional space, the intersection of a plane and a sphere can be the empty set, a point, or a circle. Distinguishing these cases, and determining equations for the point and circle in the latter cases have use, for example, when calculating ray intersections in ray tracing. For convenience in analysis, choose a coordinate system that places the center of the sphere at the origin; this can be accomplished by a translation. Thus the implicit equation for the sphere with radius r becomes.

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