ATRACTOR

Given a fixed point \(O\) on the sphere, which we shall call origin of projection, the stereographic projection of a point \(P\neq O\) of the sphere lies in the plane tangent to the sphere in the antipode point (point that is diametrically opposed) of \(O\). This plane is designated by projection plane. The projection of \(P\) is a result of the intersection of the half line \(OP\) with the plane of projection. Notice that the projection of the origin of projection is not defined. The antipode of the origin of projection, that is, the tangency point between the sphere and the projection plane, is called the center of projection.

The stereographic projection we now present has as origin of projection the South Pole. Therefore, the plane of projection is the plane tangent to the sphere at the North Pole (which is also the center of the projection).

1. On the sphere, we highlight a movable point \(P\) which belongs to the northern hemisphere of the sphere. In order to move it, use the respective cursor. The parallel and meridian that pass through that point are also displayed.
2. On the plane of projection, the projection \(P'\) of the point is marked as well as the projections of the parallel and meridian belonging to the northern hemisphere and that contain point \(P\).