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I have $2$ arbitrary points in space, $p_1$ and $p_2$, that both lie on a sphere of known radius $r$.

The center of the sphere is such that if a line were drawn around the sphere through both points $p_1$ and $p_2$, the line would also cross through the bottom most point of the sphere and would create a slice of the sphere of the maximum size circle.

How can I find the center of the sphere $p$? And the equation that defines the circle that would represent the line drawn around it?

Bryce Bangerter
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  • Define what “the bottom most point of the sphere” is, please. – Michael Hoppe Dec 03 '17 at 12:15
  • Sure. The bottom most point is the point of the sphere with the smallest y value. Y being the axis representing up/down in my scenario. So a sphere of radius 1, at origin, the bottom most point would be 0,-1,0. Given my other condition of "maximum size circle" this also means my circle would cross through the top most point of the sphere, or 0,1,0 in my example here. – Bryce Bangerter Dec 04 '17 at 03:02

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