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How Can Real-World Data Be Translated onto a Two-Dimensional Surface?
to perfectly translate from a three-dimensional object to a two-dimensional
surface. In fact, the only representation of the world that would accurately
capture all features would be a globe. Since it’s hard to keep a globe in the
glove compartment of the car, we’re going to have to make due with a flat
surface representation of the world (like a folded map) and realize that the
map is going to have some sort of distortions built into it, simply because it’s
a two-dimensional version of a three-dimensional construct. One or more of
the following will be distorted in a map projection: the shape of objects, the
size of objects, the distance between objects, or the direction that objects are
in. Some map projections may retain the shape of continents but warp their
size. Other projections may keep the land area correct but throw the shapes
out of place.
An example of this is the Mercator projection (Figure 2.4), a common
type of map that was developed in 1569 for use as a navigation aid—it was
designed so that every straight line on the map was a line of constant direction. The Mercator projection encompasses the whole globe and while it
keeps the shapes of areas intact (that is, the continents look the way they
should), the sizes (that is, the areas of land masses) are completely distorted,
particularly the further you go from the Equator. For example, take a look at
Greenland and Africa—they look to be about the same size on the map, even
though Africa is really more than 13 times larger in area than Greenland.
Similar problems can be seen with Antarctica or Russia which (while they
have the right shape) look overwhelming in land area compared to their actual size.
Think of a projection like this—you have a see-through globe of Earth
with the various landforms and lines of latitude and longitude painted on it.
If you could place a light bulb inside the globe and turn it on, you’d see the
shadows of the latitude, longitude, and continents projected onto the walls
of the room you’re in. In essence, you’ve “projected” the three-dimensional
FIGURE 2.4 The
Mercator projection, which
retains the shapes of
countries and continents,
but greatly warps their
sizes.
How Can Real-World Data Be Translated onto a Two-Dimensional Surface?
to perfectly translate from a three-dimensional object to a two-dimensional
surface. In fact, the only representation of the world that would accurately
capture all features would be a globe. Since it’s hard to keep a globe in the
glove compartment of the car, we’re going to have to make due with a flat
surface representation of the world (like a folded map) and realize that the
map is going to have some sort of distortions built into it, simply because it’s
a two-dimensional version of a three-dimensional construct. One or more of
the following will be distorted in a map projection: the shape of objects, the
size of objects, the distance between objects, or the direction that objects are
in. Some map projections may retain the shape of continents but warp their
size. Other projections may keep the land area correct but throw the shapes
out of place.
An example of this is the Mercator projection (Figure 2.4), a common
type of map that was developed in 1569 for use as a navigation aid—it was
designed so that every straight line on the map was a line of constant direction. The Mercator projection encompasses the whole globe and while it
keeps the shapes of areas intact (that is, the continents look the way they
should), the sizes (that is, the areas of land masses) are completely distorted,
particularly the further you go from the Equator. For example, take a look at
Greenland and Africa—they look to be about the same size on the map, even
though Africa is really more than 13 times larger in area than Greenland.
Similar problems can be seen with Antarctica or Russia which (while they
have the right shape) look overwhelming in land area compared to their actual size.
Think of a projection like this—you have a see-through globe of Earth
with the various landforms and lines of latitude and longitude painted on it.
If you could place a light bulb inside the globe and turn it on, you’d see the
shadows of the latitude, longitude, and continents projected onto the walls
of the room you’re in. In essence, you’ve “projected” the three-dimensional
FIGURE 2.4 The
Mercator projection, which
retains the shapes of
countries and continents,
but greatly warps their
sizes.