What is a Map?
Once a reference datum has been determined the elevation of any point can be accurately determined, and it will correlate to the elevation of any point on the earth's surface that has the same elevation and is using the same datum. But…how do you accurately represent the X and Y coordinates of that point? This question leads to one of the fundamental problems of mapmaking…how do you represent all or part of an ellipsoid object on a flat piece of paper? The answer to this question is a bit complicated, but understanding it is fundamental to understanding what maps actually represent (this statement will become clearer shortly).
In order to represent the surface of the earth on a flat piece of paper, the map area is projected onto the paper. There are many different types of projections, each with its own strengths and weaknesses.
The simplest (and easiest to visualize) example of a projection is a planar projection. To understand this type of projection, imagine inserting a piece of paper through the earth along the equator. Now imagine that the earth is semi-transparent and you could shine a flashlight oriented along the (geographic) polar axis through the earth.
The resulting outline on the paper would be a map created using this type of projection (known as a transverse azimuthal or planar projection).
There are three main types of projections, based on the shape of the 'paper' onto which the earth is projected. The example above used an azimuthal (planar) piece of paper.
The other main types, illustrated to the right, are cylindrical and conical projections. These three types of projections can be further modified by the way the 'paper' is oriented when it is inserted into the earth.
In the example above, the plane was oriented along the equator, known as a transverse orientation (hence the 'transverse azimuthal' projection). Projections may also be equatorial (oriented perpendicular to the plane of the equator) or oblique (oriented at some angle that is neither parallel nor perpendicular to the plane of the equator.
Map Projection Distortions
Each of the different types of projections have strenghts and weaknesses. Knowledge of these different advantages and disadvantages for a particular map projection will often help in which map to choose for a particular project. The basic problem inherent in any type of map projection is that it will result in some distortion of the ‘ground truth’ of the area being mapped.
There are four basic characteristics of a map that are distorted to some degree, depending on the projection used. These characteristics include distance, direction, shape, and area. The only place on a map where there is no distortion is along the trace of the line that marks the intersection of our ‘paper’ with the surface of the earth.
Any place on the map that does not lie along this line will suffer some distortion. Fortunately, depending on the type of projection used, at least one of the four characteristics can generally be preserved.
A conformal projection primarily preserves shape, an equidistant projection primarily preserves distance, and an equal-area projection primarily preserves area.
These image show the earth using different projections. Notice how the continents look stretched or squashed depending on the projection. Following are some websites with more information.