Coordinate System

coordinate system

Global 3D coordinates are ok, but ...

Have you ever seen them?

Usually 3D location is split up into

• 2D horizontal

• 1D height

coordinate system

The shape of the earth

How to fix a coordinate surface to the Earth?approximate the real shape of the earth by an ellipsoid:

•fix the dimensions of the ellipsoid define its location with respect to the shape of the earth

Geodetic Horizontal Datum

Approximations of the Earth

Transformation of Scale Factor

It defines the origin and orientation of latitude and longitude lines. A local datum aligns its spheroid to closely fit the Earth’s surface in a particular area and its 'origin point' is located on the surface of the Earth. The coordinates of the 'origin point' are fixed and all other points are calculated from this control point. The coordinate system origin of a local datum is not at the center of the Earth. NAD27 and the European Datum of 1950 are local datums.

local ellipsoid:

global best-fitted ellipsoid: In the last fifteen years, satellite data has provided geodesists with new measurements to define the best Earth-fitting ellipsoid, which relates coordinates to the Earth’s center of mass. An Earth-centered, or geocentric, datum does not have an initial point of origin like a local datum. The Earth’s center of mass is, in a sense, the origin. The most recently developed and widely used datum is the World Geodetic System of 1984 (WGS84). It serves as the framework for supporting locational measurement worldwide. GPS measurements are based upon the WGS84 datum.

Relation Between Earth’s irregular surface -

Ellipsoid and Geoid

Datum shifts

Datum Ellipsoid dX dY dZ Region of use

Adindian Clarke 1880 -118 -14 218 Mean for Ethopia, Sudan

Arc 1950 Clarke 1880 -143 -90 -294 Mean for Botswana, Lesotho, Malawi, Swaziland, Zaire, Zambia, Zimbabwe

Djarkarta (Batavia) Bessel 1841 -377 682 -50 Indonesia

European Datum 1950

International 1924

-87 -98 -121 Mean for Western Europe

Indian Everest (India 1830)

282 726 254 Bangladesh, India and Nepal

Minna Clarke 1880 -81 -84 115 Cameroon

North American 1927 (NAD 27)

Clarke 1866 -8 160 176 Mean for USA

South American 1969

South American 1969

-57 1 -41 Mean for Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, Guyana, Paraguay, Peru, Trinidad&Tobago, Venezuela

Accuracy ~10 m

Concept of Map Projection and Coordinate System

cylindrical

conical

azimuthal

Map Projections

normal transversal

map projections

Coordinate System

• Locating points relative to one another requires use of concepts of direction an distance. Basically there are two types of coordinate systems.– Geographical Coordinate system– Plane rectangular coordinates (Cartesian

Coordinate system)For larger areas geographical coordinate system is

used and for small areas rectangular coordinate system is used

Geographic coordinates

Geographic coordinates• North south distance called latitude• East west distance called longitude• The one dividing the earth in half,

equidistant between the poles was named, the equator

• The series north of equator is called north-latitude and the series south of equator is called south latitude. Since the earth is an oblate (flattened at the top), the north-south line (meridian) has less curvature at poles and more curvature at equator. 1º difference in latitude near the equator is about 110.6 km and 1º difference in latitude near the poles about 111.7 km near the poles.

• Longitude is defined by infinite set of great circles called meridians arranged perpendicular to the parallels. Since all parallels are concentric circles, they all rotate at the same angular speed 360º per day or 15º per hour. In 1884 it was agreed in an international conference that a meridian passing through Royal Observatory Greenwich, near London will be accepted as reference meridian and 0º longitude.

•advantages of geographic coordinates:•one system for the entire earth•more or less conform to the shape of the earth, so no systematic distortions•easy to map in different map projections

•disadvantages of geographic coordinates:•spherical, not planimetric coordinates•must use spherical trigonometry to measure areas and distances•must project onto flat maps where the grid lines are curved

geographic coordinates

Plane rectangular coordinates (Cartesian Coordinate system)

• A point of origin at the intersection of two conveniently located perpendicular “axes”.

Y- axis

X-axis

Origin

(0,0)

The UTM system

• It is very common

• The area of the earth between 84º N and 80º S latitude is divided into north-south columns 6º of longitude wide called zones. There are numbered 1 to 60 east ward, beginning at the 180 º meridian.

• Each column is divided into quadrilaterals 8 º of latitude high.

• The rows of quadrilaterals are assigned letters c to x consecutively (with 1 and 0 omitted) beginning at 80 º S latitude. Row x is beginning 12 º latitude extending from 72 º N to 84 º N. Each quadrilateral is assigned a number letter combination.

UTM Zone

Georeferencing refers to the location of a layer in space as defined by co-ordinate referencing system. The geo-relational approach involves abstracting geographic information into a series of independently layers or coverage’s each representing a selected set of closely associated geographic features (e.g. roads, landuse, river, etc.). Each layer is a theme of geographic feature and the database is organised in the thematic layers.

That way users can combine simple feature sets representing

complex relationship in the real world. This approach borrows

heavily the concepts of relational DBMS, and is typically closely

integrated with such systems.

Georeferencing

real world map

rotation 2 translations,

scale

object

control point

Georeferencing