Projection System

Maps are flat, but the surfaces they represent are curved. Transforming, three-dimensional space onto a two dimensional map is called "projection". This process inevitably distorts at least one of the following properties:

Theoretically map projection might be defined as "a systematic drawing of parallels of latitude and meridians of longitudes on a plane surface for the whole earth or a part of it on a certain scale so that any point on the earth surface may correspond to that on the drawing."

**Necessity of Map Projection**

An ordinary globe is rendered useless for reference to a small country. It is not possible to make a globe on a very large scale. Say, if anyone wants to make a globe on a scale of one inch to a mile, the radius will be 330 ft. It is difficult to make and handle such a globe and uncomfortable to carry it in the field for reference. Not only topographical maps of different scales but also atlas and wall maps would not have been possibly made without the use of certain projections. So a globe is least useful or helpful in the field of practical purposes. Moreover it is neither easy to compare different regions over the globe in detail, nor convenient to measure distances over it. Therefore for different types of maps different projections have been evolved in accordance with the scale and purpose of the map.

**Selection of Map Projection**

There is no ideal map projection, but representation for a given purpose can be achieved. The selection of projection is made on the basis of the following:

The location and the extension of the feature of the globe.**Classification **

Potentially there exits an unlimited number of map projections possessing one property or the other. The natures of these properties are so complex that they often possess one or more common properties. There is no projection, which can be grouped, in a single class. Moreover, if one attempts to obtain a rational classification of map projection, it will be rather difficult to achieve it. There can be as many classifications as many bases.

Depending on different bases the following classifications may be suggested:

**Classification based on preserved qualities**

While transferring the globe on a plane surface some facts should be kept in view:**Classification based on developable surface area **

There are some surfaces over which the sphere may be projected. After projection such surfaces may be cut open onto flat surface. These developable surfaces include**Cylindrical Projection **

When the graticule is prepared on the surface of a hollow cylinder it is called Cylindrical Projection.**Conical Projection **

A cone may be imagined to touch the globe of a convenient size along any circle (other than a great circle) but the most useful case will be the normal one in which the apex of the cone will lie vertically above the pole on the earth's axis produced and the surface of the cone will be tangent to the sphere along some parallel of latitude. It is called 'standard parallel'.

If the selected parallel (SP) is nearer the pole the vertex of the cone will be closer to it and subsequently the angle at the apex will be increasing proportionately. When the pole itself becomes the selected parallel, the angle of the apex will become 180 degrees, and the surface of the cone will be similar to the tangent plane of Zenithal Projection.

On the other hand, when the selected parallel is nearer to the equator, the vertex of the cone will be moving farther away from the pole. in case equator is the selected parallel, the vertex will be at an infinite distance, and the cone will become a cylinder.

Thus the Cylindrical and Zenithal Projections may be regarded as special cases of Conical Projections.

__Properties__

**Zenithal Projection**

In Zenithal Projection a flat paper is supposed to touch the globe at one point and the light may be kept at another point so as to reflect or project the lines of latitude and longitude on the plane. Here the globe is viewed from a point vertically above it, so these are called Zenithal Projections. They are also called 'azimuthal' because the bearings are all true from the central point.

In respect of the plane's position touching the globe, Zenithal Projection is of three main classes :-__ Properties__

- Shape,
- Area,
- Distance,
- Direction, and often more.

Theoretically map projection might be defined as "a systematic drawing of parallels of latitude and meridians of longitudes on a plane surface for the whole earth or a part of it on a certain scale so that any point on the earth surface may correspond to that on the drawing."

An ordinary globe is rendered useless for reference to a small country. It is not possible to make a globe on a very large scale. Say, if anyone wants to make a globe on a scale of one inch to a mile, the radius will be 330 ft. It is difficult to make and handle such a globe and uncomfortable to carry it in the field for reference. Not only topographical maps of different scales but also atlas and wall maps would not have been possibly made without the use of certain projections. So a globe is least useful or helpful in the field of practical purposes. Moreover it is neither easy to compare different regions over the globe in detail, nor convenient to measure distances over it. Therefore for different types of maps different projections have been evolved in accordance with the scale and purpose of the map.

There is no ideal map projection, but representation for a given purpose can be achieved. The selection of projection is made on the basis of the following:

The location and the extension of the feature of the globe.

- The shape of the boundary to be projected.
- The deformations or distortions of a map to be minimized.
- The mathematical model to be applied to preserve some identity of graphical features.

Based on these characteristics the utility of the projection is ascertained.

**Some Interesting Links :**

- Map Projection Overview

An Article by Peter H. Dana

- Map Projections

An Article by Brian Klinkenberg

- Map Projection

By Worlfram Research

- Map Projection Tutorial

Why are map projections an issue in GIS? - British Columbia

Potentially there exits an unlimited number of map projections possessing one property or the other. The natures of these properties are so complex that they often possess one or more common properties. There is no projection, which can be grouped, in a single class. Moreover, if one attempts to obtain a rational classification of map projection, it will be rather difficult to achieve it. There can be as many classifications as many bases.

Depending on different bases the following classifications may be suggested:

Basis |
Classes |

1. Method of Construction | 1. Perspective 2. Non-perspective |

2. Preserved qualities | 1. Homolographic / Equal Area 2. Orthomorphic / Conformal |

3. Developable surface area | 1. Cylindrical 2. Conical 3. Azimuthal / Zenithal 4. Conventional |

4. Position of tangent surface | 1. Polar 2. Equation/Normal 3. Oblique |

5. Position of viewpoint or light | 1. Gnomonic 2. Stereographic 3. Orthographic 4. Others |

**Classification based on methods of construction**

Mathematically the term 'projection' means the determination of points on the plane as viewed from a fixed point. But in cartography it may not be necessarily restricted to 'perspective' or geometrical projection. On the globe the meridians and parallels are circles. When they are transferred on a plane surface, they become intersecting lines, curved or straight. If we stick a flat paper over the globe, it will not coincide with it over a large surface without being creased. The paper will touch the globe only at one point, so that the other sectors will be projected over plane in a distorted form. The projection with the help of light will give a shadowed picture of the globe which is distorted in those parts which are farther from the point where the paper touches it. The amount of distortion increases with the increase in distance from the tangential point. But only a few of the projections imply this perspective method.

The majority of projections represent an arrangement of lines of latitude and longitude in conformity with some principles so as to minimize the amount of distortion. With the help of mathematical calculations true relation between latitude and longitudes is maintained. Thus various processes of non-perspective projections have been devised.

**Some Interesting Links :**

- Classification of Map Projection

An Article from University of Waterloo

While transferring the globe on a plane surface some facts should be kept in view:

- Preservation of area,
- Preservation of shape,
- Preservation of bearing i.e. direction and distance.

It is, however, very difficult to make such a projection even for a small country, in which all the above qualities may be well preserved. Any one quality may be thoroughly achieved by a certain map projection only at the cost of others.

**According to the quality they preserve, projections may be classified into three groups :-**

- Equal area (Homolographic projection),
- Correct shape (Orthomorphic or Conformal projection),
- True bearing (Azimuthal projection).

There are some surfaces over which the sphere may be projected. After projection such surfaces may be cut open onto flat surface. These developable surfaces include

- Cylinder and
- Cone.

When the graticule is prepared on the surface of a hollow cylinder it is called Cylindrical Projection.

- Normal Cylindrical Projection - This is a perspective cylindrical projection. When a cylinder is wrapped round the globe so as to touch it along the equator, and the light is placed at the centre, the true cylindrical projection is obtained.

Limitations:

The scale is true only along the equator. The exaggeration of the parallel scale as well as the meridian scale would be very greatly increasing away from the equator. The poles can't be shown, because their distances from the equator becomes infinite.

- Simple Cylindrical Projection - It is also called Equidistant Cylindrical Projection as both the parallels and meridians are equidistant. The whole network represents a series of equal squares. All the parallels are equal to the equator and all the meridians are half of the equator in length. The projection is neither equal area nor orthomorphic.

Limitations :

The scale along the equator is true. The meridian scale is correct everywhere because the parallels are drawn at their true distances. Latitudinal scale increases away from the equator. This leads to great distortion in shape and exaggeration of area in high latitudes.

- Cylindrical Equal Area Projection - This cylindrical projection was introduced by Lambert. The properties are almost the same. The area between two parallels is made equal to the corresponding surface on the sphere at the cost of great distortion in shape towards higher latitudes; this is why it is an equal area projection.

Limitations: Same as (ii).

**General Properties of Cylindrical Projection**

- Cylindricals are true at the equator and the distortion increases as on moves towards the poles.
- Good for areas in the tropics

A cone may be imagined to touch the globe of a convenient size along any circle (other than a great circle) but the most useful case will be the normal one in which the apex of the cone will lie vertically above the pole on the earth's axis produced and the surface of the cone will be tangent to the sphere along some parallel of latitude. It is called 'standard parallel'.

If the selected parallel (SP) is nearer the pole the vertex of the cone will be closer to it and subsequently the angle at the apex will be increasing proportionately. When the pole itself becomes the selected parallel, the angle of the apex will become 180 degrees, and the surface of the cone will be similar to the tangent plane of Zenithal Projection.

On the other hand, when the selected parallel is nearer to the equator, the vertex of the cone will be moving farther away from the pole. in case equator is the selected parallel, the vertex will be at an infinite distance, and the cone will become a cylinder.

Thus the Cylindrical and Zenithal Projections may be regarded as special cases of Conical Projections.

- Conics are true along some parallel somewhere between the equator and the pole and the distortion increases away from this standard.
- Good for Temperate Zone areas

In Zenithal Projection a flat paper is supposed to touch the globe at one point and the light may be kept at another point so as to reflect or project the lines of latitude and longitude on the plane. Here the globe is viewed from a point vertically above it, so these are called Zenithal Projections. They are also called 'azimuthal' because the bearings are all true from the central point.

In respect of the plane's position touching the globe, Zenithal Projection is of three main classes :-

- Normal or Equatorial Zenithal (where the plane touches the globe at equator),
- Polar Zenithal (where the plane touches the globe at pole),
- Oblique Zenithal (where the plane touches the globe at any other point).

- Gnomonic / Central (view point lies at the centre of the globe),
- Stereographic (view point lies at the opposite pole)
- Orthographic (view point lies at the infinity).

- Azimuthals are true only at their centre point, but generally distortion is worst at the edge of the map.
- Good for polar areas.

Source: GIS Development (http://www.gisdevelopment.net/tutorials/tuman007.htm)