Zenithal Map Projections
The zenithal map projections are constructed by projecting the parallels and the meridians of a globe on a plane placed tangentially to it at one of the poles or at its any other point. When the plane is placed tangentially at a point on the equator, the projection is called a zenithal projection (equatorial case). When placed tangentially at a point between a pole and the equator it is called a zenithal projection (oblique case) and when plane is placed tangentially at one of the poles, it is called a zenithal projection (polar case). In our exercise we shall study only the polar cases (Polar zenithal stereographic projection).
Polar Zenithal Stereographic Projection
In this projection, a 2-dimensional plane of projection touches the generating globe at either of the poles. It is a perspective projection, with the source of light lying at the pole diametrically opposite to one at which the projection plane touches the generating globe. The parallels are projected as concentric circles of varying radius while the meridians are projected as straight lines radiating from the poles.
1. Radius of the generating globe, \( R= \) Actual radius of the earth \( \div \) Denominator of \( R \). F.
2. Radius of the various parallels, \( r \Phi=2 R \cdot \tan \left(90^{\circ}-\Phi\right) \)
Fig. 1. Polar Zenithal Stereographic Projection with an extension of \( 0^{\circ} \) to \( 90^{\circ} \mathrm{N} \) latitudes at interval and \( 0^{\circ} \) to \( 180^{\circ} \mathrm{E} \) and W at \( 30^{\circ} \) interval.