Let two spheres of radii R and r be located along the x-axis centered at (0, 0, 0) and (d, 0, 0), respectively. Not surprisingly, the analysis is very similar to the case of the circle-circle intersection. The equations of the two spheres are x^2 + y^2 + z^2 | = | R^2 (x - d)^2 + y^2 + z^2 | = | r^2. Combining (-2) and (-1) gives (x - d)^2 + (R^2 - x^2) = r^2. Multiplying through and rearranging give x^2 - 2d x + d^2 - x^2 = r^2 - R^2.
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