Improving Decision Making
in Choosing a Projection
Michael Braymen
Overview
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Objective
Background
Problem
Proposed Solution
Process
Obstacles
Timeline
Literature
Objective
•To facilitate decision making in choosing
projections.
•Expand the common decision process for
choosing projections
•Create a tool that will allow comparison of
different projections
•Display distortion of various characteristics of
projections both graphically and quantifiably.
•The audience for the tool would be GIS
professionals
•Prepare results in form for non-GIS
professional.
Background
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Early GIS adopters used common
choices and local projections like
UTM and State plane
Now easier and faster to project
Push to combine data into larger
extents
Problem
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Organizations using GIS may not
have expertise in-house to make
good decisions on projection choice
Example: USDA Forest Service
Proposed Solution
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Create tools to assist the decision
making process
• Decision tree for common parameters
and characteristics
• Graphic tool to display distortion of
selected characteristics with quantifiable
values
Process
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Two methods:
• Tissot’s indicatrix
• Grid of equal area polygons
Tissot’s indicatrix
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The theory that at every point on a map
there is a pair of perpendicular lines that
are also perpendicular on the earth
(Snyder 1987).
Infinitely small circles on the earth always
project as perfect ellipses with the ratio of
the major and minor axis related to scale
and angular deformation.
A statistical assessment of distortion can
be done using a series of indicatrices for
an area of interest.
Tissot’s indicatrix
Grid of equal area polygons
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Select equal area projection for
area of interest
Generate grid of equal area
polygons
Project grid to projection of interest
Calculate difference in area from
original, i.e. “true” area
Calculate statistics and display
Generate Grid
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<graphic
Examples>
Example for Pacific NW
Obstacles
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Determining how to calculate Tissot’s
indicatrix for any area of interest and
projection.
Assessing and minimizing additional
distortion due to point to point
projection, e.g. lengths being shorter
than they should be in a projection
because a two vertex line should be
a curve.
Densify Arcs – Preliminary Results
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Original Arc length 10,000 meters
Add vertex every 100 meters
Compare results of projection to Lambert
conformal conic for original and densified
data
Single example –
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3 mm gap
Difference in perimeter = 0.008 meters
Difference in area = 48 square meters
Difference in computed error = 0.00005 %
Estimated Timeline
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JULY - Document process for determining key
characteristics and thresholds
AUGUST - Automate evaluation of area distortion
using equal area grid technique.
AUGUST - Analyze effect of vertex density on
projection distortion
SEPTEMBER - Automate evaluation of shape, scale
and area using Tissot’s indicatrix
OCTOBER - Analyze sensitivity of analysis for
continental and sub-continental extents
NOVEMBER – Format and automate presentation of
results
???? – Present Results
Literature
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Adams, Oscar S. 1919, General Theory of
Polyconic Projections: Washington, Government
Printing Office.
Deetz, Charles and Adams, Oscar S. 1945,
Elements of Map Projection with Applications to
Map and Chart Construction: New York,
Greenwood Press.
Snyder, John Parr, 1987 Map Projections – A
Working Manual, US Geographical Survey
Professional Paper 1395: Washington,
Government Printing Office, ppg 20-21.
Tissot, Nicolas Auguste, 1881, Mémoire sur la
représentation des surfaces et les projections des
cartes géographiques: Paris, Gauthier Villars.
Questions?