Map Projections

Visualization of Projections

The mathematical manipulations of projections are best understood by imagining a clear globe with the graticule printed on its surface, a light bulb used to illuminate the globe, and a large sheet of paper on which to project the lines from the globe using the light bulb. The positioning of the paper and the placement of the bulb in relationship to the globe provide for diverse configurations of the projected grid. This example depicts the categorization of projections.

The first of the variables in these models is the placement of the light bulb, providing different viewpoints. For the gnomonic position, the light [Page 1842]bulb is in the center of the globe. The placement of the bulb against the side of the globe makes the stereographic position. The light bulb can also be placed at infinity for the orthographic projection.

A second variable is the shape formed from the paper. The result provides a developable surface for the projection and drawing of the grid lines. The paper can be left as a flat surface to be planar. It can be wrapped into a cylinder to make the category of the projection cylindrical. A third configuration is to form a cone from the paper. This approach yields the development surface classified as conic.

A third variable is the aspect or the orientation of the paper or the developable surface to the globe. Regular orientations result in the simplest lines and are standardized based on the form made of the paper. For a planar projection, the paper is placed at a pole. For a cylindrical projection, the paper is wrapped around the equator. The conic version places the point of the cone at a pole. Rotating these placements 90° is a transverse orientation. An oblique orientation is any other placement.

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