Perspective Projection

General Perspective Projections project the surface of the sphere onto a tangential image plane  t  in the main point  H  by central projection. In this case the projection centre  Z  (also called point of perspective) lies anywhere onto the main axis through H and M, inside as well as outside the sphere.

If the main axis stands vertical on the image plane  t , we talk about a Vertical Perspective Projection. The Vertical Perspective Projections are azimuthal (see figure 1).
Otherwise we have a Tilted Perspective Projection, which are not azimuthal.

The distance between the projection centre  Z  and the centre  M  of the sphere takes place as a multiple  d  of the radius of the sphere. Figure 1 shows the construction with  d = 2.

The Stereographic (d = –1), the Gnomonic (d = 0) and the Orthographic (d → ∞) projections are special cases of the Vertical Perspective Projections (see the following figures).

Vertical Perspective Projection (Construction with  d = 2)


Figure 1


Stereographic Projection (Construction with  d = –1)


Figure 2


Gnomonic Projection (Construction with  d = 0)


Figure 3


Orthographic Projection (Construction with  d → ∞)


Figure 4

  
See also
  
Map projection animations Map projection animations