Lecture
3
The
Basics, Part II
This chapter from Principles of
Symbolization for Thematic Cartography and GeoVisualization, 3rd ed. by
Slocum, McMaster, Kessler, and Howard gives a nice
introduction on mapping data to symbols. Its focused on geoscience
visualization but the concepts are very applicable to other forms of
visualization.
Nature of
Geographic Phenomena:
Spatial Dimension
- 0d - point
phenomena located in 2d or 3d space (eg data collected at weather
monitoring stations)
- 1d -
linear phenomena (eg the path an AUV takes while taking measurements)
- 2d - areal
phenomena (eg data collected on the surface of a lake)
- 2.5d -
volumetric phenomena - each x, y position has a single z value
associated with it (eg the maximum depth at any point in the lake)
- 3d -
volumetric phenomena - each x, y, z position has a value associated
with it (eg the ph values collected at various points and depths in the
lake)
Discrete vs Continuous and Abrupt vs
Smooth Phenomena
discrete - occur at distinct locations (and have a
space between them)
continuous - occur throughout a region of interest
abrupt - can change suddenly
smooth - change gradually

Figure 5.1
showing phenomena and appropriate ways of representing them
Distinction
between data that has been collected to represent a phenomenon and the
phenomenon being mapped
ie we are typically collecting data at discrete sites (weather
stations, well sites) or aggregating over small regions (counties,
states) where the actual phenomena is continuous
Type of
visualization used depends both on the nature of the underlying
phenomenon and the purpose of the map
Levels of
Measurement:
qualitative
- nominal - grouping (categorization) but no
ordering of those categories (eg census data on religion)
quantitative
- ordinal - categorization plus ordering of those categories (eg
low, medium, high)
- numerical
- interval - ordering of the data plus
explicit numerical differentiation between those categories (eg
temperature values) with an arbitrary
zero point (eg SAT scores, F, C - eg getting 2x an SAT score doesnt
mean you are twice as smart, the temperature isnt twice as hot from 10
degrees C to 20 degrees C)
- ratio - ordering of the data plus explicit
numerical differentiation between
those categories (eg temperature values) with an nonarbitrary zero point (eg
temperatures in degree kelvin)
Visual Variables:
visual
variables
for qualitative should
reflect only a nominal level of measurement - ie
there shouldn't be a sense that one value is 'more' than another, jsut
that they are different.
- orientation
- direction/orientation of the marks/symbol
- shape -
different shapes are used
- arrangement
- different arrangement of marks making up the symbol
- hue -
different colors are used but careful choices
need to be made here so there is no sense of 'less' to 'more' in the
different hues

visual
variables for quantitative
should reflect ordinal, interval, or ratio
level of measurement
- spacing
(texture) - smaller spacing between marks suggest higher value
- size -
larger symbol or larger marks making up the symbol suggests a higher
value
- perspective
height - higher elevation suggests a higher value (cant be used for 3D
phenomena because all 3 dimensions are already in use)
- color
(hue) - what is the dominant wavelength (red, green, blue, etc but
careful choices need to be made here so there is a sense of 'less' to
'more' in the progression on hues)
- color
(lightness) - how light or dark the color is (light green, dark green)
- color
(saturation) - how far is the intensity is from grey (bright red, muted
red)

There are also
pictographic symbols

Comparison
of choropleth, proportional symbol, isopleth, and dot mapping:
choropleth
- commonly used to portray data collected for units such as
counties or states
- regions are shaded / colored based on the phenomena - in the
example below lightness is used
- good for when values change abruptly at unit boundaries but hides
variation within units, and the boundaries may be artificial in
relation
to the phenomena.
- the units may also be different sizes, so the raw data may need
to be standardized to better show the underlying phenomena - eg
California has much more land mass and more people than Illinois which
has more land mass and people than Rhode Island. The visualization
above showing the raw number of brew pubs may give people the wrong
impression; it might be better to (also) view the number of brew pubs
per million people in each state.
isopleth
(contour map)
- good when data collected was from a smooth continuous phenomenon
- regions are shaded / colored based on the phenomena - in the
example below lightness is used
- interpolating set of isolines between sample points of known
values
- the data should be standardized
- we will be talking about algorithms for this in 2D and 3D next
week
proportional
symbol
- scale symbols in proportion to the magnitude
of the data
- symbol might be a true point (located at a
data collection point) or a conceptual point (at the center of a unit)
- normally used to show raw data
dot mapping
- one dot is
set equal to a certain amount of the phenomenon
- dots
should be placed where the phenomena occurs (much higher level of
accuracy than other maps)

Selecting visual
variables for choropleth maps



Here are some interesting examples from the US Environmental Protection
Agency: http://www.epa.gov/air/airtrends/2008/
and here are some variations of the typical red/blue election map for
the 2008 presidential election
http://www-personal.umich.edu/~mejn/election/2008/
Coming
Next Time
VTK
last
revision 1/22/09 (added in link to red/blu maps)