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Geographic Coordinate Systems
An Introduction


Prof. David Bernstein
James Madison University

Computer Science Department
bernstdh@jmu.edu

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Overview
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  • Geographic Coordinate System:
    • A coordinate system that enables every location on a planet (e.g., the Earth) to be specified
  • History:
    • Is said to date back to Eratosthenes in the third century BC
The Most Common System
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  • Latitude:
    • Specifies the north-south position using an angular measure
    • Ranges from \(0^\circ\) at the equator to \(90^\circ\) at the North and South poles
    • Denoted by \(\phi\)
  • Longitude:
    • Specifies the east-west position using an angular measure
    • Ranges from \(0^\circ\) at the prime meridian to \(180^\circ\) at the international date line (with positive value to the east and negative values to the west)
    • Denoted by \(\lambda\)
Simplifications and Assumptions
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  • Getting Started:
    • Use a spherical coordinate system
  • A Significant Issue:
    • Planets are not spherical so the spherical coordinates must be mapped onto a reference ellipsoid
  • Other Significant Issues:
    • Planets are not perfect ellipsoids
    • Surfaces of planets are not smooth
    • Points on the surface move relative to each other (e.g., motion of plates, subsidence, tidal movements)
Latitude and Longitude
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images/latitude-and-longitude.png
From Longitude/Latitude to Cartesian Coordinates
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Notation

images/longitude-latitude-to-cartesian.gif
From Longitude/Latitude to Cartesian Coordinates (cont.)
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  • Derivation of the Conversion:
    • \(\cos \phi = d / R \Rightarrow d = R \cos \phi\)
    • \(\cos \lambda = p_{z}/d \Rightarrow p_{z} = d \cos \lambda = R\cos \phi \cos \lambda\)
    • \(\sin \lambda = p_{x}/d \Rightarrow p_{x} = d \sin \lambda = R \cos \phi \sin \lambda\)
    • \(p_{y} = R \sin \phi\)
  • Note:
    • This is very similar to the conversion of spherical coordinates to Cartesian coordinates (but it uses the latitude not the colatitude)
There's Always More to Learn
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