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# Map Projections

Introduction
We all have got so used to seeing maps all around us that we probably never stop to think about how they must have been made in the first place. Suppose you were given a cuboid-shaped aquarium and told to draw a map of it on a plane sheet of paper, what would you do? The problem is not as simple as it might sound on the first time. The tank in question will have many different types of objects, not to mention fish, and one or more of these will always be in a state of motion. The more you think about it, the more clearly the following question will stand out: "How do you even begin doing it?" The early cartographers were faced with the same dilemma, and answering this question will take us closer to the process of making maps.

What comes to our rescue is a projection. Some of you might even be familiar with it from school days. But while the school was more to do with clearing the exams at all costs, this time we'll aim for learning. If you consult a good dictionary, you will get a bewildering array of definitions on projection, ranging from the obvious to the most surprising. But the word we are looking for is "representation". Representation of what? Of the Earth's surface.

By now you might be beginning to think that we are merely beating about the bush, but wait. Whoever told you Cartography was easy!

Yes, a map projection is a representation of Earth's surface on a plane, such as a sheet of paper. Even though almost all the atlases in the world follow a common method of representing the maps, there are in fact many different types of projections.

2. Types of Map Projections
Depending on the underlying logic and methodology, there can be many types of map projections, such as:
 Azimuthal projection Cylindrical projection Conic projection Conformal projection Hybrid projection Equidistant projection Gnomonic projection Equal-area projection
And some modified versions:
Pseudo-cylindrical projection
Pseudo-conic projection
Modified azimuthal projection
Then there are tilted and crooked projections, projections from very early days that are no longer existing or useful. Needless to say, the mind reels at even thinking of so many projections. And what if we told you there were as many more . . . ?

But have heart. The good news is that not all of these projections are useful for everyday tasks. Actually, a projection is neither good nor bad. It just is. Every projection has its own use, and commands a lot of respect within its specific application area.

So now we get started on exploring the various types of projections, an learning their particular uses. We'll discuss the most common ones, and those that are interesting. Don't feel overwhelmed just yet. Cartography is interesting, and is to be conquered one step at a time . . .

2.1 Cylindrical Projections

This is the most common of all map projections. Almost all the maps you see around yourself, whether in atlases or elsewhere, were formed from cylindrical projection or some of its variant.

So how is a cylindrical projection achieved? Basically, in a cylindrical projection, the various longitudes are mapped as parallel vertical lines. Yes, we know that definition did not help, but the task will be easier if you imagine the globe to be inside a very long cylinder of exactly the same diameter as the sphere of the globe. All that is now left is plotting the various points on the globe on to the inside curved surface of the cylinder. To achieve this, imagine that there is a point of light inside the globe, which gets obstructed by the continents, but allowed to pass by the water bodies. Such an arrangement would soon illustrate the walls of the cylinder with a particular pattern. And this is the projection we have been looking for! Simple enough it was, no?

Now, if you unwrap this cylinder and spread it out, what do you see? Why, a world map for sure! However, something is not quite right here. Sure enough it is a world map, but it looks weird. If you pay some more attention, you will see that it is not so nicely spaced at the length. This phenomenon is known as "distortion", and is common among the maps produced using cylindrical projections. That is to say, a map produced using this plain-vanilla cylindrical projection is distorted from east to west.

Of course this is not how maps are created. The light sources and un-flattening are merely aid to the imagination. The actual operations are neatly defined by certain mathematical operations, discussing which would be out of scope.

So what did the early cartographers do when they were confronted by this odd-looking world map? Did they just shrug their shoulders and carry on? Not at all. They improvised. The remedy of this map lies in its problem only - distortion. Here's the idea: If the map has a different stretch along the east-west direction, all we need to do is add a similar distortion along the poles. This gives rise to different types of cylindrical projections:

The east-west scale is the same as the north-south scale. This is also known as conformal cylindrical or Mercator projection. One disadvantage of this projection is that the it experiences too much distortion at very high latitudes.

The north-south stretching grows less than the east-west stretching. This is known as Miller cylindrical projection.

The north-south stretching grows faster than the east-west stretching. But this is not a practical projection because the distortion in this case is far worse.

The north-south lines are neither compressed nor stretched.

The north-south distortion is exactly the reciprocal of east-west distortion. This makes for what are known as equal-area cylindrical projections.

The cylindrical projections are good for navigational purposes, especially the Mercator projection, because a straight line drawn on it corresponds to a unique and fixed direction. However, as noted before, the this also results in a lot of distortion at the poles and they can't be shown as a result.

2.2 Conical Projections

We have already seen that the Cylindrical Projections result in significant distortion at the poles. This makes the countries in the higher longitudes a bit difficult to represent, and the poles, impossible. To overcome this difficulty, Conical Projections are used.

How does a conical projection work? This time, the globe can be imagines to be inside a cone than a cylinder. As the different points get projected on the inside of the cone, the lines of latitude get represented by the regular circular arcs, and the meridians get mapped as radial lines that are equally spaced. This gives an accurate representation of the countries closer to the poles, such as Greenland and Canada, and reflects their true shapes more closely.

Another useful concept is that of "standard lines". Standard lines are parallel lines where the sphere touches the cone on the inside. While one of these lines will be point where the two diameters coincide, the other one is set to define the spread of the map. When the map is finally cut open and spread (so to speak), the area of the map will be within these two lines.

Conical projections are not good for creating world maps, but are rather used to create maps of temperate zones.

2.3 Azimuthal Projection

To understand what an Azimuthal Projection is, it is important to first know what an azimuth is. Consider the Earth as a sphere. Now take any point on it. Let us call it point A. From this point, take two points in different directions that are equidistant from it. Now, join both these points to point A. The angle formed between these lines in known as azimuth of the surface.

Now, in an Azimuthal Projection, this angle is preserved. What does it mean? Two things. First, that the azimuth as measured on a map created from the azimuthal projection would be the same as that measured on the sphere. At the same time, it means that the directions are preserved on the final map. This is a great plus actually, as it let us use maps created from these projections to be used for making globes. After all, a globe must accurately represent the Earth.

Depending on the different settings, many types of azimuthal projections are possible. There is only one small problem, though: While such a projection preserves the directions, the shapes can be more than distorted.

2.3.1 Gnomonic Projection

This remains derived from the Azimuthal Projection, and is also known central azimuthal projection. The only difference is that in this type of projection, the light source is imagined to be placed at the exact centre of the sphere, This gives it a surprising about of spread near the edges of the diameter, and doesn't allow the map to represent more than one hemisphere at a time.

But why use this projection at all? As we said earlier, each projection has its own quality, which makes it outshine others in certain cases. The good thing about the Gnomonic Projection is that all the great circles on it (the imaginary planes that cut through the Earth's surface to form the meridians) finally appear as straight lines. This makes it extremely easy to find the shortest distance between two points. The maps do look a bit (or quite) distorted, but that's a small sacrifice when you consider the benefits.

2.4 Other remaining projections

Other projections listed above are merely minor variants of these already listed. For instance, the pseudo-cylindrical and pseudo-conical projections are similar to the cylindrical and conical projections, except that they have curved meridians. A hybrid projection is that which uses many of these projections to produce a map to be used for some specialized purpose.

3. Choosing a Map Projection

Since there is a fair bit of mathematics involved, only the experts can comment on why a particular projection is to be chosen. However, in general, one needs to keep in mind the distortion factor, which is inevitable in any form of projection. Also, one needs to be clear which factor is more important: distances, directions, areas, or the look of the map. For instance, the Robinson projection is a much simpler process that makes the map look very pretty, but can't be used for any other purpose as it has too many deviations from the true representation of the Earth's curved surface. The coordinate origin is another important factor.

4. Conclusion

Earth is spherical in shape. Any attempt to represent it on a plane paper, however clever, will ultimately fail on one count or the other. Thus, map projections are a good but imperfect representation of the Earth. However, having a good knowledge about the various projections makes you better with using maps, and perhaps, lends you an eye for appreciating the complexity and beauty in the process of map creation.

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