Cartographic Foundation (Chapter 7 in Peterson)

A.Map Scale Issues B.Map Projections C.Data Classification D.Linear Simplification

A.Map Scale Issues

Three are three ways of depicting map scale: 1)Representative Fraction (RF) (e.g., 1:24,000) Expresses the ratio of map distance to Earth distance

Three ways of depicting map scale: 2) Verbal Scale A spoken description of the relationship between map distance and Earth distance e.g., “One inch represents one mile”

Three ways of depicting map scale: 3) Bar Scale (or Scale Bar) An expression of scale that uses a graphical element resembling a small ruler

Examples of Bar Scales (From Chapter 11, p. 200 of Slocum et al., 2009, Thematic Cartography and Geovisualization)

“Bad” Examples of Bar Scales (From Chapter 11, p. 200 of Slocum et al., 2009, Thematic Cartography and Geovisualization)

Key Point: Bar scales can be used as map scale changes.

How do we differentiate between small-scale and large-scale maps?

Distance Measurements Map service providers often provide automated procedures for measuring distance, but you should also be able to do this by hand. Typical problem: Two points are 5 cm apart on the map and the scale of the map is 1:24,000. What is the distance between the points in km on the Earth?

Distance Measurements Another problem: Two points are 2.2 inches apart on the map and the scale of the map is 1:30,000. What is the distance between the points in miles on the Earth?

Computing an RF for a Bar Scale Typical problem: Using a bar scale, you determine that 5 miles on the Earth is equal to 3.3 inches on the map. What is the RF?

B. Map Projections

Definition of map projection A transformation of the spherical Earth’s graticule and landmasses to a flat surface A key point is that we cannot maintain correct areal relations, angles, distances, and directions at the same time

Equal-area projection Maintains correct areal relationships (From Slocum et al., 2009, p. 160)

Conformal projection Maintains angular relationships around points (From Slocum et al., 2009, p. 160)

Areal vs. conformal projections and dot mapping

Equidistant projection Shows distances correctly (e.g., from one point to surrounding points) (From Slocum et al., 2009, p. 149) Azimuthal Equidistant

Azimuthal projections Shows directions correctly from a point (From Slocum et al., 2009, p. 150) Orthographic

Why the Mercator projection for the Web ? 1)Ideally suited for the rectangular display of the computer monitor 2) Tiling is more straightforward when lines of latitude and longitude are straight 3) Allows for easier panning and zooming

Why Web Mercator?

(From Battersby et al., 2014, Cartographica, p. 87)

(From Battersby et al., 2014, Cartographica, p. 88)

Winkel Tripel: An example of a compromise projection. (From Slocum et al., 2009, p. 145)

C. Data Classification

Why do we class data?

Some Classification Methods Equal Interval Quantiles Maximum Breaks

Equal Interval Method Places an equal portion (or equal interval) of the data range in each class Identical to the method for creating a grouped-frequency table in statistics classes It is a five-step process

1, 2, 10, 11, 12, 13, 20, 21, 22, 47, 50 Step 1. Determine the class interval, or width that each class occupies along the number line. 1, 2, 10, 11, 12, 13, 20, 21, 22, 47, 50

Step 1. Determine the class interval, or width that each class occupies along the number line. 1, 2, 10, 11, 12, 13, 20, 21, 22, 47, 50

Step 2. Determine the upper limit of each class. (This is part of the Calculated Limits.)

Step 3. Determine the lower limit of each class. (This is also part of the Calculated Limits.)

Step 4. Specify the class limits actually shown in the legend. (These are the Legend Limits.) 1, 2, 10, 11, 12, 13, 20, 21, 22, 47, 50

Step 5. Determine which observations fall in each class. 1, 2, 10, 11, 12, 13, 20, 21, 22, 47, 50

Advantages of the Equal Interval method? Ease of computation and understanding For certain kinds of data (e.g., percentage data ranging from 0 to 100), the class intervals are often easy to interpret.

Key disadvantage: Class limits may not reflect how data are distributed along the number line Our hypothetical data: 1, 2, 10, 11, 12, 13, 20, 21, 22, 47, 50 Another hypothetical data set: 1, 2, 12, 13, 14, 15, 16, 17, 18, 19, 50

Quantiles Method Places an equal number of observations in each class Can be viewed as a 4-step process

Step 1. Be sure that the data are ranked from low to high 1, 2, 10, 11, 12, 13, 20, 21, 22, 47, 50

Step 2. Compute the ideal number of observations in each class. 1, 2, 10, 11, 12, 13, 20, 21, 22, 47, 50

Step 3. Determine which observations fall in each class. Class Data 1 1, 2, 10, , 13, 20, , 47, 50 1, 2, 10, 11, 12, 13, 20, 21, 22, 47, 50

Step 4. Specify the Legend Limits. Class Data Legend Limits 1 1, 2, 10, , 13, 20, , 47,

Advantages of the Quantiles method? Ease of computation and understanding Useful for map comparison (each class will have roughly the same area) Useful for ordinal data

Our hypothetical data: 1, 2, 10, 11, 12, 13, 20, 21, 22, 47, 50 Another hypothetical data set: 1, 2, 12, 13, 14, 15, 16, 17, 18, 19, 50 Key disadvantage: Class limits may not reflect how data are distributed along the number line

Maximum Breaks Method The differences between adjacent ranked values are computed and the largest of these differences serve as class breaks. (Uses a “microscope” rather than a “macroscope”)

Computations for Maximum Breaks

Computations for Maximum Breaks Class Limits 1 – 2 10 – – 50

Advantages of Maximum Breaks? Ease of computation and understanding It seems to pay attention to the distribution of the data along the number line

D. Linear Simplification

Linear Simplification Can be viewed as one of many potential map generalization operators “Generalization is the process of reducing the information content of maps because of scale change, map purpose, intended audience, and/or technical constraints.”

Fundamental operators of generalization (Courtesy of Philippe Thibault, see p. 102 of Slocum et al.).

Why simplify linear features? Eliminate duplicate (or near duplicate) points Speed processing Avoid bleeding when scale is reduced

Local vs. Global Processing Algorithms Some algorithms look at a small portion of the line at a time (they are local), while others consider the entire line (they are global)

An Example of a Local Algorithm (From McMaster, 1987, “Automated Line Generalization,” Cartographica)

The Douglas-Peucker Global Algorithm (From McMaster, 1987, “Automated Line Generalization,” Cartographica)

Images on slide 9 are from the web site for Peterson’s bookweb site for Peterson’s book Images on slides 7,8,16,17,18,19,20,21,26,28, and 52 are from the web site for Slocum et al.’s bookweb site for Slocum et al.’s book