A sphere on a plane

The picture below is a 2D representation of a unit sphere, viewed from a particular point on that sphere. Try changing the viewer position by dragging the green points around in the different 2D cross-sectional planes.

Viewer Position

Your current position is .
Change it by dragging the green points below.

in the xy plane:
in the xz plane:
in the yz plane:

Notice how you can only move the position in each cross-sectional plane in a circular motion, otherwise the third dimension would be affected.