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 Java Applet for live rotation on this page is JavaView, by Konrad Polthier et al. See: http://www.javaview.de/.
The images on this page is generated by the following Mathematica packages:
- “PlaneTiling.m” available at Plane Tiling Mathematica Package.
- “Transform2DPlot.m” available at Geometric Transformation on the Plane.
- Notebook: sphere_proj.nb