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Extending adaptive composite map projections with Wagner's transformation method

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Abstract

Adaptive composite map projections transform projections as the user changes the scale of the web map. The equal-area version of the original adaptive map projection composite uses the Lambert azimuthal equal-area projection for regional maps, and three equal-area world projections , namely the Hammer, the Eckert-Greifendorff, and the quartic authal-ic projections. These three projections show poles as points. With Wagner’s transformation method, additional projections can be added to the adaptive composite map projections. These additional projections can be transformed to the Lambert azimuthal projection; they are equal-area and they show poles as curved or straight lines.
Extending Adaptive Composite Map
Projections with Wagners Transformation
Bojan Šavrič, CEOAS, Oregon State University
Bernhard Jenny, CEOAS, Oregon State University
ICC 2013, Dresden
August 25 -30, 2013
Adaptive Composite Map Projections
Changes projection on-the-fly when user zooms or pans
A smooth transition between map projections
Equal-area at all scales
Alternative to the web Mercator for web maps
Jenny, B. et al. (2012). Adaptive Composite Map Projections for Web Maps. Presentation at the 32nd Annual Meeting NACIS 2012.
Adaptive Composite Map Projections
Jenny, B. et al. (2012). Adaptive Composite Map Projections for Web Maps. Presentation at the 32nd Annual Meeting NACIS 2012.
Adaptive Composite Map Projections
Aitoff’s transformation method
Poles represented only as points
Pseudocylindrical projections generate less shape distortion
(rotation and skewing)
Wagner’s Transformation Method
Umbeziffernre-numbering method
Latitudes and longitudes are mapped onto a smaller segment of the sphere
Preserves the area distortion characteristics of the parent projection
Aitoff’s method is a special case
3 parameters (m, n, k) instead of one (B)
Wagner, K. (1941). Neue kumenische Netzentwrfe fr die kartographische Praxis. Jahrbuch der Kartographie, p. 176-202
Wagner’s Transformation Method
Wagner, K. (1941). Neue kumenische Netzentwrfe fr die kartographische Praxis. Jahrbuch der Kartographie, p. 176-202
Lambert azimuthal equal-area
Wagner’s Transformation Method
Wagner, K. (1941). Neue kumenische Netzentwrfe fr die kartographische Praxis. Jahrbuch der Kartographie, p. 176-202
Bounding meridian
Wagner’s Transformation Method
Wagner, K. (1941). Neue kumenische Netzentwrfe fr die kartographische Praxis. Jahrbuch der Kartographie, p. 176-202
Bounding parallel
Bounding meridian
Wagner’s Transformation Method
Wagner, K. (1941). Neue kumenische Netzentwrfe fr die kartographische Praxis. Jahrbuch der Kartographie, p. 176-202
Latitudes and longitudes
are mapped onto a smaller
segment of the sphere.
Wagner’s Transformation Method
Wagner, K. (1941). Neue kumenische Netzentwrfe fr die kartographische Praxis. Jahrbuch der Kartographie, p. 176-202
Adding the factor
scales the section to the scale
of the original map.
Wagner’s Transformation Method
Wagner, K. (1941). Neue kumenische Netzentwrfe fr die kartographische Praxis. Jahrbuch der Kartographie, p. 176-202
Adding the factors k and 1/k stretches the projection (while keeping the equal-area property).
Wagner’s Transformation Method
Animation with sliders available on: cartography.oregonstate.edu
Pseudocylindrical Projection Family
Angular Distortion Analysis
Angular Distortion Analysis
The best mean angular distortion
Equator / central meridian ratio: 2.43
Equator / pole line ratio: 1.10 (bounding parallel at 28°)
Scale Distortion Analysis
Scale Distortion Analysis
The best mean scale distortion
Equator / central meridian ratio: 2.02
Equator / pole line ratio: 1.62 (bounding parallel at 57.2°)
Survey Among Experts
44 invited / 27 participated
http://cartography.geo.oregonstate.edu/Survey/projection.html
Experts’ Suggestions
Experts’ Suggestions
Answers and Scale Distortion
Answers and Scale Distortion
Projection from Arithmetic Mean
Answers with mean scale distortion less than 0.39
Equator / central meridian ratio: 2.03
Equator / pole line ratio: 1.82 (bounding parallel at 61.9°)
Answers with Ratio 2
Answers with Ratio 2
Projection from Median
Answers with mean scale distortion less than 0.4
Answers where equator / central meridian ratio is 2
Equator / pole line ratio: 2 (bounding parallel at 65.1°)
Options for Pseudocylindrical Projection
Best angular distortion
Best scale distortion
Median
Arithmetic mean
Options for Pseudocylindrical Projection
Best angular distortion
Best scale distortion
Median
Arithmetic mean
Thank you!
Questions?
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