0. Lecture 02: A Transformational View of Cartography - Map Projections - Real Maps vs. Virtual Maps
Geography 128
Spring 2007
Department of Geography
University of California, Santa Barbara

1. Waldo Tobler’s Classic Paper, 1979
“…the entire process of making, and using a map can be viewed as a sequence of transformations”.
Types of Cartographic Transformation
Geometrical Transformations: to “manipulate the locative aspects of the geographical data”
Map Projections
Substantive Transformations: to “modify the substantive geographical data”
Map Generalization

2. Examples of Cartographic Transformation
ESRI, Understanding Map Projections
John Krygier and Denis Wood, Making Maps:
a visual guide to map design for GIS

3. Cartographic Transformations
The base of Computer Cartography
The core of Analytical Cartography
Forms of Cartographic Transformation
Geometry
Attribute
Symbolization
Scale
Data Structure and Data Model
Map Type …

4. Invertibility
“…whether or not a Cartographic Transformation can be undone or reversed to produce the initial starting conditions” – K. C. Clarke, 1995
Stable Transformation
invertible
“controllable and therefore are effectively programmed and modeled, especially with respect to the error introduced”
Unstable Transformation
NOT invertible
“the inverse transformation produces chaos”

5. The Focuses of this lecture
Map Projections
Real Maps vs. Virtual Maps

6. Earth Shape: Sphere and Ellipsoid (Spheroid)

7. Earth as Oblate Ellipsoid
Flatter, longer
Curved,
shorter

8. The Spheroid and Ellipsoid
The sphere is about 40 million meters in circumference.
An ellipsoid is an ellipse rotated in three dimensions about its shorter axis.
The earth's ellipsoid is only about 1/297 off from a sphere.
Many ellipsoids have been measured, and maps based on each. Examples are WGS84 (World Geodetic System) and GRS80 (Geodetic Reference System).

9. Earth as Ellipsoid

10. The Datum
“While a spheroid approximates the shape of the earth, a datum defines the position of the spheroid relative to the center of the earth. A datum provides a frame of reference for measuring locations on the surface of the earth. It defines the origin and orientation of latitude and longitude lines” - ESRI, Understanding Map Projections
An ellipsoid gives the base elevation for mapping, called a datum.
Examples are NAD27 and NAD83 (North American Datum ).

11. The Datum
ESRI, Understanding Map Projections

12. The Geoid
The Geoid is a figure that adjusts the best ellipsoid and the variation of gravity locally.
It is the most accurate, and is used more in geodesy than GIS and cartography.
The Geoid (exaggerated!)

13. The Geoid

14. Earth Models and Datums

15. Map Scale
Map scale is based on the representative fraction, the ratio of a distance on the map to the same distance on the ground.
Most maps in GIS fall between 1:1 million and 1:1000.
A computer map is scaleless because maps can be enlarged and reduced and plotted at many scales other than that of the original data.
To compare or edge-match maps, both maps MUST be at the same scale and have the same extent.

16. Scale of a baseball earth
Baseball circumference = 226 mm
Earth circumference approx 40 million meters
RF is : 1:177 million

17. Length of the Equator at Scale

18. Geographic Coordinates
Geographic coordinates are the earth's latitude and longitude system, ranging from 90 degrees south to 90 degrees north in latitude and 180 degrees west to 180 degrees east in longitude.

19. Geographic Coordinates
A line with a constant latitude running east to west is called a parallel.
A line with constant longitude running from the north pole to the south pole is called a meridian.
The zero-longitude meridian is called the prime meridian and passes through Greenwich, England.
A grid of parallels and meridians shown as lines on a map is called a graticule.

20. The International Meridian Conference (1884: Washington DC)
“That it is the opinion of this Congress that it is desirable to adopt a single prime meridian for all nations, in place of the multiplicity of initial meridians which now exist.”
“That the Conference proposes to the Governments here represented the adoption of the meridian passing through the center of the transit instrument at the Observatory of Greenwich as the initial meridian for longitude.”
“That from this meridian longitude shall be counted in two
directions up to 180 degrees, east longitude being plus and
west longitude minus.”

21. The Prime Meridian (1884)

22. Geographic Coordinates

23. Geographic Coordinates as Data

24. Map Projections
A transformation of the spherical or ellipsoidal earth onto a flat map is called a map projection.
The map projection can be onto a flat surface or a surface that can be made flat by cutting, such as a cylinder or a cone.

25. Types of Map projections

26. Standard parallels
If the globe, after scaling, cuts the surface, the projection is called secant. Lines where the cuts take place or where the surface touches the globe have no projection distortion.

27. Evolution of Projection Techniques
Gulf of Maine Aquarium, 2005
Gigawiz Ltd. Co., 2007

28. Types of Map Projections I
Projections can be based on axes parallel to the earth's rotation axis - equatorial
Or at 90 degrees to it - transverse
Or at any other angle - oblique
Figure 2.9 Variations on the Mercator (pseudocylindrical) projection shown as secant

29. Types of Map Projections II
A projection that preserves the shape of features across the map is called conformal.
A projection that preserves the area of a feature across the map is called equal area or equivalent.
No flat map can be both equivalent and conformal. Most fall between the two as compromises.
To compare or edge-match maps, both maps MUST be in the same projection.

30. No flat map can be both equivalent and conformal!
Map Projection Websites:

31. Real Maps and Virtual Maps
Joel Morrison (1974) called for an expanded definition of map in a computer era
Harold Moellering (1977, 1980, and 1984)
Two crucial characteristics
Whether a map is directly viewable as a cartographic image
Whether it has a permanent tangible reality

32. Classes of Real & Virtual Maps
Moellering, 1984, Real Maps, Virtual Maps and Interactive Cartography

33. Transformations between Real & Virtual Maps
Moellering, 1984, Real Maps, Virtual Maps and Interactive Cartography
Moellering, 2000, The Scope and Conceptual Content of Analytical Cartography

34. Next Lecture
Geocoding and Data Capture