Geography Reference
In-Depth Information
Making Projections with Light
Although most projections are calculated mathematically, the underlying transformation from
a three-dimensional to a two-dimensional representation of all projections can be physically
constructed with the aid of few common items: a light (flashlight or lamp), a two-liter plastic
bottle, a lampshade, and a piece of wax paper or flat plastic you can draw on. You will write
on all of these items, so you need to be sure they are no longer needed.
To make the construction surfaces, you will need to prepare the plastic bottle by cutting
off the top and bottom carefully with a scissors or knife. The lampshade and the flat wax
paper or plastic are ready to be used as they are. On each of these objects you should mark
a series of horizontal and vertical lines. On the lampshade and piece of wax paper or plastic,
they should radiate from the center. On the lampshade, they should, if extended, meet each
other at an imaginary point above the top of the lampshade; on the wax paper or plastic, they
should radiate from a circle located at the center.
The construction surfaces you made correspond to the developable surfaces used in
cylindrical, conic, and planar types of projections. To show how each developable surface is
used, take a flashlight or light placed at the middle of the bottle or lampshade or behind the
wax paper or plastic surface and shine the light source at a nearby wall or piece of paper. (It
usually helps to dim the room lights when you do this.)
What you see on the wall or paper is the projected surface that corresponds to each type
of projection. Try moving the light, the paper, and the construction surface to see how the
changes affect each projection. These changes correspond to parameters used in the con-
struction of map projections discussed in this chapter.
The shortest route for an airplane high above the Earth's surface is not a
straight line, but a line on a sphere, called the “great circle distance.”
Different projections are used for maps with different roles. The size of
the area to be mapped, the desired projection properties, and the character-
istics of the geographic information and map are the key determinants. The
size of the area distinguishes basically between the whole world, a continent,
a state or province, a region, a county or city, and still smaller units. Differ-
ent projections fit different areas better or worse, depending on their use.
The Mercator projection is quite inaccurate because of size distortion for
world maps, but quite useful for maps of smaller areas used in navigation. A
projection property refers to whether the projection represents angles,
areas, or distances (from one or two points) as they are found on the surface.
No projection retains both angles and areas. Most projections compromise
properties, but a projection can retain one projection property—for example,
the Mercator projection preserves angles. All transverse (turned 90
to be
oriented north-south) Mercator projected geographic information and
maps are useful for mapping north-south-orientated small areas because this
projection is conformal and also preserves shapes over small areas along the
line of tangency where the projection theoretically touches the earth's sur-
°
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