The following are images of stereographic projection.
Suppose you have a beach ball sitting on a elaborately beautifully tiled floor. Now, suppose the top of the beach ball we call it North Pole. Now, Let there be a straight line from the north pole to a point on the floor. Call this point P. This line will intersect the beach ball somewhere, let's call the point of intersection Q. Now, every point P on the floor will then have a corresponding point Q on the ball. This process, of making a image from the floor to the ball is called Stereographic Projection. The following are some examples.
The images on this page is generated by the following Mathematica packages: