Although the earth is (nearly) spherical in shape, humans (and computer programs such as MicroStation) prefer to work in a two- or three-dimensional Cartesian coordinate system. A cartographic projection is required to convert spatial data coordinates, which are latitude and longitude, to a Cartesian coordinate system.
The simplest Geographic Coordinate System is to simply using latitude/longitude values as Cartesian coordinates. The problem is that the results of that transformation process do not provide a meaningful way to visualize distances, areas, or angular relationships between geographic features.
To see why this is so, observe that on the Earth, distance between lines of longitude (easting) decreases as one moves from the equator toward the poles. Latitude (northing) values remain equally spaced, Therefore if you simple use longitude as the X Cartesian value and latitude as the Y Cartesian value, the resulting map is quite distorted, as you can see from looking at this map of North America plotted with an such an "unprojected" coordinate system.
No meaningful decisions could be made based on information obtained from this map. Distances cannot be measured, shapes are not accurate, and areas are not reliable. While there may be situations in which you will want to use latitude and longitude coordinates in your data system, the analysis, interpretation and decision making process requires that the spherical geographic data be flattened by a cartographic process.
Using well-designed cartographic projections, we can transform longitude and latitude to Cartesian coordinates with much lower distortion of distances, shapes, and areas. Compare the map of North America below with the unprojected map and you will readily see the difference.
A good way to understand this concept is to forget about the idea of a map and focus on the projection. Imagine the earth as a wire mesh globe, with a huge flash bulb positioned at the center.
To obtain an image of the round Earth on a flat piece of photographic film, we could simply hold the film up to the surface of the globe and expose the film by flashing the light source. If we could actually perform such a process, the resulting photograph would appear. As you can see, the lines defining the features of the globe are clean and crisp where the film was very close to the surface of the globe. Where the film was a significant distance from the surface of the globe, the lines on our photograph are fuzzy. As the distance between the photographic film and the surface of the globe increases, the fuzziness increases until we reach a point at which the lines completely disappear.
The process of projecting spherical geographic data on to a flat map is the same. The technique we have just visualized is essentially what happens, mathematically, when an Azimuthal projection is produced. In such a projection, the area around the origin of the projection is distortion free. The distortion introduced by the projection increases with distance from the origin.
In order to create a more accurate map, we need to get more of the photographic film closer to the surface we are mapping.
Gerardus Mercator did exactly this in 1569. His idea was to take our film and wrap it around the Earth in the form of a cylinder. In so doing, the film actually touched the earth on the whole extent of the equator.
Anywhere close to the equator, the lines are crisp and clean, indicating a minimum of projection distortion. As we move away from the equator, the lines begin to get fuzzy. As we approach the poles, the lines disappear altogether. These are the underlying features of the standard Mercator projection which has been used for years to create maps of the entire world.
We can take a flat piece of photographic film and make a cylinder out of it. Once this cylindrical shaped film is positioned on the Earth, a picture can be taken. Unrolling the cylinder produces a flat surface, which becomes our map. The important concept here is that a cylinder, while round in one dimension, can be easily converted to a perfectly flat surface. A surface which has this characteristic is said to be a developed surface.
A Transverse Cylinder (Transverse Mercator) can be used to produce a cylindrical image from the globe. Wrap the cylinder around the earth with the film touching it at the equator. The open ends of the cylinder are oriented toward the north and south poles.
Since the Earth is nearly a sphere, there are other ways in which our photographic cylinder can be wrapped around the Earth. We can rotate our cylinder 90 degrees so that the open ends are to the left and right and expose the film.
The crisp clean lines still represent the regions where the photographic film was close to the Earth. Instead of an east/west direction, the crisp clean lines follow a great circle of longitude in a north/south direction. There is little distortion as we proceed north and south close to the center, while distortion increases as we move to the east and to the west. This projection is known as the Transverse Mercator projection.
By rotating a cylinder so that it is neither aligned along lines of latitude or longitude, maps can be created that have oblique lines which are free from projection distortion.
Another model that can represent a spherical surface is the cone. A cone is round horizontally, but since it is flat vertically it is also developed. Just cut it on a vertical line and it will be perfectly flat.
To visualize this, we take some photographic film, make a cone and place it on the Earth.
Notice the clean crisp lines now follow a certain line of latitude around the earth; the parallel of latitude at which the photographic cone actually touched the surface of the Earth. As we proceed either north or south from this parallel of latitude, the lines start to get fuzzy and soon disappear altogether.
These are the three forms of map projections: the Azimuthal, the Cylindrical (Mercator), and the Conic. These three forms represent the techniques or projections used in almost all mapping. Now, we will look at some common variations of these forms.
Each projection gives us a different set of distortion free lines. By using different projection techniques, we have achieved different distributions of projection distortion across our map. Depending on our local situation, we will choose a projection that minimizes distortion for our area.
The standard cylindrical (Mercator) gives us minimum distortion around the equator. If one is mapping the temperate zones of the entire earth, it represents a good choice.
The Conic enables us to move the east/west line of minimum distortion from the equator to any other line of latitude. Choosing a cone that touches the earth at about 36 degrees of north latitude would be a good choice for producing a map of Tennessee. Tennessee is much larger east/west than north/south.
The Transverse Cylindrical (Transverse Mercator) produces clean crisp lines in a north/south direction. It is the projection of choice for mapping a state such as New Hampshire. New Hampshire is much larger north/south than east/west.
When choosing the flat surface, the Azimuthal projection provides minimum distortion in all directions for a limited distance and is the projection used for maps of the polar regions
Minimizing the projection distortion in a map of a specific region of the Earth is a matter of choosing the right projection. The general rule of thumb is if the greatest extent of the region to be mapped is east/west, the Conic projection should be used. If the greatest extent of the region is north/south, the Transverse Mercator projection should be used. A cylinder (or a cone) can be tilted to obtain clean crisp lines in any specific direction. Such projections exist for the cylindrical case and are referred to as oblique cylindrical projections. For example, the Hotine Oblique Mercator projection is used to map the panhandle of Alaska.
We have seen that the degree of projection distortion at any given point on a map depends upon how far away the developed surface is from the surface to be mapped. We have seen that we can get the photographic film closer to the surface being mapped by using different shapes.
There is another technique used in cartography to reduce the overall distance between the photographic film and the surface of the earth for a given region. In the case of a cylindrical projection, imagine the result if we could shrink the cylinder into the Earth just a little bit. Some of the cylinder would be inside the Earth and some would be outside. However, for a specific region of the Earth, the largest distance between the photographic film and the globe will be reduced. Further, there would be two lines where the cylinder actually touched the surface thereby giving us two lines where there is zero distortion. This technique enables us to, in general, get more of the film closer to more of the region which we wish to map.
MicroStation supports a large variety of map projections. The purpose of this section is to provide a brief introduction to the named projections.
Standard Cones CylindersPlanes (Azimuthal)Other
The three most common projections used are based on sets of parameters represented by names.
Each Projection has both projected coordinates and geodetic coordinates corresponding to the same point on the earth. These geodetic coordinates are the latitude/longitude values corresponding to locations on the sphere or ellipsoid upon which projections are based.
The earth can be measured in degrees, minutes and seconds. uses the standard system which describes the earth using:
While the distances between east-west lines (lines of latitude) is constant from equator to pole, distances between the lines running north-south (lines of longitude) decreases as the lines of longitude converge at the north poles and the south pole.
During the transform process, mapping coordinates are transformed using the following sequence:
Latitude/Longitude values of one datum (Example: WGS84) are different from other datums (Example: WGS72) for the same point on the earth. In other words, it is not enough to have a "latitude/longitude" value without also knowing the datum upon which it was defined.
Changing latitude/longitude values between the various datums is referred to as "datum shift."
Geographic Latitude/Longitude is not a projection but can be used almost interchangeably as a projection within . When used as a projection, it appears as a cylinder and is known as the Plate Caree projection.
Based on the Transverse Mercator projection.
The U.S. Army selected this as the standard for mapping the world in 1947. UTM is Conformal, meaning that local angles are preserved at the expense of distortion of size. The UTM grid divides the world into 60 zones, each zone being 6 degrees wide. The zones are numbered one to sixty, moving eastward from 180th meridian from Greenwich. Letters are assigned moving south to north. For example, Washington, DC falls in grid zone 18N. Each quadrangle on the grid is further subdivided and measured in meters.
Scale reduction factor is set to 0.9996, producing a 1:2500 reduction.
When mapping regions beyond the six degree width, distortion increases at a faster rate as distance from the central longitude increases. Applying a zone of width greater than 15 degrees is not recommended, as the mathematics of transforming Transverse Mercator coordinates back into latitude/longitude values is not as accurate as the transformation of latitude/longitude values into Transverse Mercator values.
See Transverse Mercator (TM) or South Orientated Transverse Mercator (South Africa) for an example.
Established in the United States in the 1930s. For states that are larger east-west than north-south, Lambert Conformal Conic is most commonly used. For those with a north-south orientation, Transverse Mercator is usually chosen. These projections have largely replaced the Polyconic projections commonly used by the U.S. Geological Survey (and others) in the 19th and early 20th century.
The purpose of the SPCS is to minimize map distortion for each state (or zone within a state), yet limit the number of standards in existence.
Selecting a keyname displays the coordinate system definition located in the dictionary. Datum and Ellipsoid lookups also occur and result in a full set of parameters of a particular projection. Parameter cannot be changed and still be referred to by the same keyname. Even a unit change requires a separate keyname. This works differently from the traditional coordinate system State Plane selection system that allowed certain parameters to be modified.