The two planes that remain stationary in the animation each contain SO and a line tangent to circle C. For tan-colored plane this tangent is at (-r,0,0) and for magenta-colored plane it is at SN which is also (r,0,0). Because these two planes contain the center of the sphere, which need not be in the xy-plane, these stationary planes are not parallel to, or perpendicular to, the xy-plane except for when r is at either limit r = 0, or r = 1.
The point on C where 3 moving planes intersect is P. Blue-colored plane contains SO and a line tangent to the circle at point P. The animation starts with P at (r,0,0) and then moves P along a 180º arc of circle C.
Green-colored plane contains the point P and pivots about an axis as P moves, but this axis is not one of the coordinate axes. It is an axis defined by a line containing the line segment from SO to SN, which is the main or cardinal axis of sphere S.
Yellow-colored plane (or light green) contains points SO and P, and is perpendicular to .