1. Lecture 07: Coordinate Transformation I
Overview:
Coordinate system for Earth: Ellipsoids and Datums
Map projections (3D to 2D)
Planar coordinate transformation (2D to 2D)
Geocoding (discrete to continuous)
Topics:
Ellipsoids and Datums
Map projections (3D to 2D)
References:
Chapter 3 in Jan Van Sickle’s Basic GIS Coordinates (2004)
Chapter 5 in Robinson et al (1995) pp

2. Lecture 06: Digital Terrain Analysis II
Outlines
1. Ellipsoids and Datums:
A coordinate system for Earth needs Ellipsoid and Datum
1.1 Ellipsoids
A shape used to approximation the shape of earth
Parameters of a biaxial ellipsoid:
(The biaxial ellipsoid figure)
Common Ellipsoids:
Clarke1866
WGS (world geodetic system) 72 and 84
Airy Britain
GRS80 – U.S.

3. 1.2 Datums:
1) A datum is an actual coordinate system:
2) Creation of a datum (definition of a datum):
(1) Steps:
definition of an ellipsoid (a, b)
attaching the ellipsoid to earth
Initial point and orientation
(five parameters)
realization
(2) Methods:
(a) the old approach
definition of an ellipsoid
attaching the ellipsoid to Earth
through an initial point
with an azimuth to another reference point
Survey of monuments

4. 1.2 Datums: (continued…)
Drawbacks: regional and nongeocentric
(The nongeocentric Ellipsoids Figure)
Common datums:
NAD27 (Clarke 1866)
(b) The new approach
Definition of an ellipsoid (Geocentric)
Attaching the ellipsoid to Earth
Mass center of the earth
Three dimensional
(The Three Dimensional Figure)
GPS positions of monuments
Advantage: global, geocentric, 3-dementional (with Z)
NAD83 (GRS80), NAD83/91
WGS84 (WGS84), WGS84(G730) WGS84(G873)

5. 1.3 Coordinate transformation between datums
1) Molodenski transformation:
(The Molodenski Transformation Figure)
2) Seven-parameter transformation:
(three translation, three rotation, one scale)
(The Seven-parameter Transformation Figure)
3) Surface fitting:
NAD27 to NAD83
(The Surface Fitting Figure)

6. 2. Map Projection: (3D to 2D)
1) Purpose:
2) Difficulty: Shape of the earth
3) Distortion:
Size (Equivalence) v.s. shape (Conformality)
4) Type of projections:
(1) The UTM Projection:
(The Transverse Mercator Figure)
(2) Conformal:
angular relationships are maintained
(The Lambert Conformal Figure)
(3) Equal area:
(The Albers’ Equal Area Figure)
(4) The State Plane Coordinate System:
varies between states.