Question

Which one of the following is NOT a geometric method of map projection?

• A. Polyconic
• B. Gnomonic
• C. Stereographic
• D. Orthographic

Hint:

Check whether each projection can be constructed by tracing straight light rays from one fixed source onto one developable surface.

Answer 1

The Correct Option is A

Step 1: Recall what defines a "geometric" (perspective) method of map projection.
Map projections are broadly classified by the method used to derive them. A geometric or perspective projection is one that can be visualised, and in the classical sense mathematically constructed, as projecting points from the surface of the reference globe onto a flat plane (azimuthal/planar projections) using rays from a chosen viewpoint, such as the centre of the globe, the antipodal point on the surface, or a point at infinity.
Step 2: Classify each option by this test.
Gnomonic projection (option B) projects rays from the centre of the globe onto a tangent plane, a true perspective construction. Stereographic projection (option C) projects rays from the point on the globe diametrically opposite the point of tangency onto the tangent plane, also a true perspective construction. Orthographic projection (option D) projects rays from a point at infinity (parallel rays) perpendicular onto the tangent plane, again a true perspective construction. All three, Gnomonic, Stereographic, and Orthographic, belong to the classical family of azimuthal perspective projections generated by a light source at a specific point relative to the globe.
Step 3: Examine the Polyconic projection.
The Polyconic projection is instead a mathematically/analytically developed projection. Each parallel of latitude is treated as if it were developed from a separate cone tangent to the globe at that particular latitude, and the meridians are then drawn as curves through points computed from spherical trigonometric formulae, not by projecting light rays from any single point onto a plane. There is no true perspective viewpoint from which the Polyconic projection can be geometrically constructed, it is fundamentally a computational/mathematical projection rather than a geometric one.
Step 4: Conclude.
Since Gnomonic, Stereographic, and Orthographic are all genuine perspective (geometric) azimuthal projections while Polyconic is not derived by any such geometric projection technique, the projection that is NOT a geometric method is the Polyconic projection.
\[ \boxed{\text{Option (A): Polyconic}} \]