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).
Figure 1
Figure 2
Figure 3
Figure 4
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Map projection animations |