Lecture Notes for Clarke, K. C. Analytical and Computer Cartography

Lecture 10: A Transformational View of Cartography

Transformations and Analytical Cartography.

Transformations can be of :

• Attribute Data
• Locational properties
• Graphics
• Information content of maps

Questions

• Basic questions:
• Is a transformation quantifiable?
• Can the transformation process be automated?
• Is a transformation invertible?
• Is a transformation stable?

Tobler's classic paper "A Transformational View of Cartography"(1979)

• Used map projections (geometric transformation) as an example.
• Extended concept to other dimensions.

Transformations

• Map scale
• Dimension
• Symbolic content
• Data structures

Why Transform?

• We may wish to compare maps collected at different scales.
• We may wish to convert the geometry of the map base.
• We may wish or need to change the map data structure.

Robinson's Classification

Origins of the approach date from Robinson's Classification of symbolization methods and map types.

Levels of Measurement

Robinson's Classification was based on dimension and level of measurement.

Level of measurement idea is from Stevens (1946).

• Nominal data assume only existance and type. An example is a text label on a map.
• Ordinal data assume only ranking. Relations are like "greater than".
• Interval data have an arbitrary numerical value, with relative value. Example: Elevation.
• Ratio data have an absolute zero and scale.

Transformations as Stages in Map Production

• Transformation of level can be shown in making a choropleth map.
• This transformation is not invertible, but can be error measured and minimized.

• Idea was extended by David Unwin.
• Unwin separated issue of data from issues of mapping method, (map type and data type).

State Changes and Transformations

Cartographers are interested in the full set of state transformation.

• each map has an optimal path through the set.
• Design cartography primariliy concentrates on the last, or symbolization transformation.
• Four types of transformations shape the mapping process:
  • Geocoding (transforming entities to objects:levels, dimension, data structure)
  • Map Scale
  • Locational Attributes or Map Base
  • Symbolization

Scale Transformations

• Some transformations "collapse" space: e.g. area to point.
• Map scales of interest to cartography are 1:1,000 to 1:400M.
• Transformations from larger to smaller scale by the process of generalization.
• At the minimum, generalization involves simplification, elimination, combination and displacement.

Generalization Components

Some Generalization Problems

• Length
• Shape
• Topology

• These steps are conducted under specified and consistent rules.
• An example is the set of algorithms for point elimination along a line.
• The inverse of this adds points along a line: enhancement.

Transformations and Algorithms

• In mathematics, transformations are expressed as equations.
• Solutions, inversion as so forth are by algebra, calculus etc.
• In computer science, a set of transformations defining a process is called an algorithm.
• Any process that can be reduced to a set of steps can be automated by an algorithm.
• data structures + transformational algorithms = maps

Keith Clarke Last Change 4/24/97 Copyright Prentice Hall, 1995