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Cartesian Coordinates - GIS and Mapping - Lecture Slides, Slides of Geology

Aliah UniversityGeology

Professor has explained the following concepts in these Lecture Slides : Cartesian Coordinates, Geodetic Coordinates, Dimenional Cartesian System, Spheroid As the Origin, Planar Coordinates, Dimensional Cartesian, False Origin, Digitiser Coordinates, Measuring Distance, Datums

Typology: Slides

2012/2013

Uploaded on 07/23/2013

raksha
raksha 🇮🇳

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Cartesian Coordinates
•Geodetic coordinates are a bit unwieldy for observations
made from satellites, so a 3-dimenional Cartesian system is
sometimes used.
•Treating the centre of the spheroid as the origin, the Z-axis
is aligned with the minor axis of the ellipsoid (i.e. through
the north pole), and the X and Y axes lie on the equatorial
plane. The X-axis intersects the equator at the prime
meridian, and the Y axes is at right angles to it.
• Any point in 3-D space can be expressed relative to the 3
axes.
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Cartesian Coordinates

  • Geodetic coordinates are a bit unwieldy for observations made from satellites, so a 3-dimenional Cartesian system is sometimes used.
  • Treating the centre of the spheroid as the origin, the Z-axis is aligned with the minor axis of the ellipsoid (i.e. through the north pole), and the X and Y axes lie on the equatorial plane. The X-axis intersects the equator at the prime meridian, and the Y axes is at right angles to it.
  • Any point in 3-D space can be expressed relative to the 3 axes.

Digitiser Coordinates

  • If you digitise a paper map using a digitising table, the digitiser will use its own planar coordinate system (i.e. points will be measured in inches (or whatever) from the centre of the table).
  • The digitiser coordinates therefore need to translated into the planar coordinate system used by source map (e.g. Irish Grid).
  • These conversions also need to take account of the displacement of the origin and any angular errors.

Measuring Distance

  • Measuring distance in a Cartesian system is a simple application of Pythagoras’s theorem:
  • However, the distance estimates will vary depending upon the projection used.
  • Measuring distance using geographic coordinates is more complex:
  • The calculations are even more complex for geodetic coordinates.

d ( x 1 x 2 ) ( y 1 y 2 )

2 2 = − + −

d = R cos−^1 [sin φ 1 sinφ 2 +cosφ 1 cosφ 2 cos ( λ 1 − λ 2 )]

National Standards (1)

  • North American maps traditionally used a spheroid defined by Clarke in 1866. This formed part of the North American Datum drawn up in 1927 (NAD27).
  • Different states then adopted different projections with different origins. The standards for each state are referred to as the state planes.
  • Following more accurate data from satellites, a new North American Datum was defined in 1983 (NAD83) based on the world Geodetic Reference System defined in 1980 (GRS80).
  • If working with US maps you need to know whether they use NAD27 or NAD

National Standards (3)

  • The Irish Grid uses a datum called Ireland 1965, based on a spheroid originally defined by Airy in 1830, but modified in 1849.
  • OSGB uses a datum called OSGB36 which uses Airy’s unmodified spheroid.
  • OSI introduced a new planar coordinate system in 2001 called Irish Transverse Mercator. This uses a Transverse Mercator projection and is based on GRS80/ETRF89/ IRENET96 and is therefore more compatible with GPS.