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
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
Examples of Cartographic Transformation
ESRI, Understanding Map Projections
John Krygier and Denis Wood, Making Maps:
a visual guide to map design for GIS
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
…
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”
The Focuses of this lecture
 Map
Projections
 Real
Maps vs. Virtual Maps
Earth Shape: Sphere and Ellipsoid
(Spheroid)
Earth as Oblate Ellipsoid
Flatter, longer
Curved,
shorter
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).
Earth as Ellipsoid
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 ).
The Datum
ESRI, Understanding Map Projections
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!)
The Geoid
Earth Models and Datums
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.
Scale of a baseball earth
 Baseball
circumference =
226 mm
 Earth
circumference
approx 40 million meters
 RF
is : 1:177 million
Length of the Equator at Scale
Rep. Fraction
1:400 Million
1:40,000,000
1:1,000,000
1:100,000
1:24,000
1:1,000
Map Distance
0.10002
Ground Distance
0.328 (3.9 inches)
1.0002
3.28
40.008
131
400.078
1,312
1,666.99
5,469 (1.036 miles)
40,007.8
131,259 (24.86miles)
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.
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.
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.”
The Prime Meridian (1884)
Geographic Coordinates
Geographic Coordinates as Data
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.
Types of Map projections
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.
Evolution of Projection Techniques
Gulf of Maine Aquarium,
2005
http://www.gma.org/surfing/i
maging/mapproj.html
Gigawiz Ltd. Co., 2007
http://www.gigawiz.com/thematic.html
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
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 edgematch maps, both maps
MUST be in the same
projection.
No flat map can
be both
equivalent and
conformal!
Map Projection Websites: http://www.geog.ucsb.edu/~kclarke/G128/projectionsites.html
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
Classes of Real & Virtual Maps
Moellering, 1984, Real Maps, Virtual Maps and Interactive Cartography
Transformations between Real & Virtual Maps
Moellering, 1984, Real Maps, Virtual
Maps and Interactive Cartography
Moellering, 2000, The Scope and Conceptual Content
of Analytical Cartography
Next Lecture
Geocoding and Data Capture