CS 795/895 - Information Visualization
Fall 2012: Tues/Thurs 3-4:15pm, E&CS 2120

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Maps Notes

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Visualize This

  • Ch 8 "Visualizing Spatial Relationships", example code (zip)

Visualizing Data

Links and Examples

Protovis Examples from A Tour through the Visualization Zoo

Map Creation

Map Projections

(Many thanks to Paul Anderson for these links and references!)

Why do we need map projection? We have a 3D globe (sphere) that we want to display in a 2D format as a map.

From wikipedia:

  • Different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties.
  • Any mathematical function transforming coordinates from the curved surface to the plane is a projection.
  • A sphere cannot be represented on a plane without distortion. Since any map projection is a representation of a sphere's surface on a plane, all map projections distort. Every distinct map projection distorts in a distinct way. The study of map projections is the characterization of these distortions.
  • Many properties can be measured on the Earth's surface independently of its geography. Some of these properties are:
    • Area
    • Shape
    • Direction
    • Bearing
    • Distance
    • Scale
  • Map projections can be constructed to preserve one or more of these properties, though not all of them simultaneously. Each projection preserves or compromises or approximates basic metric properties in different ways. The purpose of the map determines which projection should form the base for the map. Because many purposes exist for maps, many projections have been created to suit those purposes.
  • The mathematics of projection do not permit any particular map projection to be "best" for everything. Something will always get distorted. Therefore a diversity of projections exists to service the many uses of maps and their vast range of scales.
  • Modern national mapping systems typically employ a transverse Mercator or close variant for large-scale maps in order to preserve conformality and low variation in scale over small areas.
  • For smaller-scale maps, such as those spanning continents or the entire world, many projections are in common use according to their fitness for the purpose.

Basic Rules - from http://mapmaker.rutgers.edu/355/AndersonProjectionPointers.html

  • If you want to display a country or region on or near the Equator, use a Cylindrical.
  • If you want to display a country or region in the temporate zones use a Conic.
  • If you wish to display a country or region near the poles use an Azimuthal.

Notes from Paul Anderson

Links

Fun with Map Projections

This graphic is one created in error when trying to recreate a particular Conic developed by a cartographer named Nell in the 1890s. To my dismay I did not have access to a set of tables that were needed to construct it. However, a particular image just jumped out at me so I cleaned it up and named it Mickey. In the past when I have been asked to do a Map Projection presentation here at ODU I use this one to break the ice: http://www.galleryofmapprojections.com/images/Mickey.pdf

In regard to the Mecca Map listed in the text file I passed on to you previously, this one is a variation of the same math formulas. I offered it, with further enhancement, as a tee shirt design to the Geography Department when ODU started the football program. At the time it was offered there was no funding available to follow through on developing it as a tee shirt: http://www.galleryofmapprojections.com/images/craig_retro_az.pdf

This one is a Map Projection I made for my second son when he was working as a commerical artist at IDAmerica.com http://www.galleryofmapprojections.com/images/seashell.pdf

This one gave Australia the 'OZ' nickname. An Albers Equal-area Conic with Australia centered was developed and used in the 1950s by Australian Cartographers. I constructed this modern version using G.projector software and Global Mapper software. Note: The NASA Blue Marble Graphic looks really good on a computer screen, but, it appears to be too dark on an overhead projector:

I made this graphic to show the visual differences between the Robinson projection and the Winkel Tripel projection http://www.galleryofmapprojections.com/images/Overlay.pdf

Made back in 2001, here are graphics for more comparisons between the Robinson and Winkel Tripel. There are a few external links broken on the page at this late date - http://www.csiss.org/map-projections/microcam/mapnews.htm

A Usage example. This book cover is from an actual textbook that has been used in the ODU Political Science Department and it uses one of the graphics from my website. The latest version of the Textbook uses the Lambert Cylindrical Equal-area on the cover, also from my website.

Deep Stuff

Gerald I Evenden (PROJ.4 - Map Projection source code in 'C') and I have exchanged ideas and Map Projection formulas in source code. Map Projection Formulas Manual (pdf)

Gnomonic Map Projection

  • Classified by its Graticule shape as an Azimuthal (or Planar) Map projection - http://www.csiss.org/map-projections/Azimuthal/Gnomonic.pdf
  • An ancient map projection of unknown origin named from 'Gnomon' the a Vertical part of a Sun Dial. Used in Navigation, this Map Projection [sometime called a Polar Projection] has the property of showing 'Great Circles' as straight lines.

Mercator Projection

  • Classified by its Graticule shape as a Cylindrical Map projection - http://www.csiss.org/map-projections/Cylindrical/Mercator.pdf
  • A conformal Cylindrical Map Projection invented by Gerardus Mercator in 1659. This projection has the property of displaying 'Rhumb Lines' [Lines of Constant Bearing] as straight lines. Its primary use is in Navigation but it has also found its way into many US classrooms in spite of it being Conformal.
Modern Use of the Mercator and Gnomonic Projections
When the Quartermasters on a US Navy Ship are asked to plot a transoceanic course using a great circle route, the first thing they plot the course on is a Gnomonic projection. The Quartermasters then use their compasses and dividers to pick off the lines of latitude and Longitude that this initial plot crosses and they take those values and plot them again on a Mercator Map [actually called a Chart in this case]. The plot drawn on the Mercator is what the Bridge Officers navigate by. See gtcirrte.gif

Space Oblique Mercator

  • Classified by its Graticule shape as a Cylindrical Map projection.
  • Originally developed by C. S. Peirce in 1894, this Oblique Conformal projection has been modified mathematically by John Parr Snyder and others so that modern satellite tracks can be accurately determined on the ground - http://www.csiss.org/map-projections/Cylindrical/Oblique_Mercator.pdf

Cylindrical-Satellite

Various map projections associated with Navigation

The Azimuthal Equidistant Projection is classified by its Graticule shape as an Azimuthal Map projection. Its property is that all directions and distances are true 'only' from the projection's center point.

The Bonne Projection, classified by its Graticule shape as a Pseudoconic Map projection was sometimes used in the form of a Portolan Chart. It is a mathematical variation of Ptolemy's 2nd Projection - http://www.csiss.org/map-projections/Pseudoconic/Bonne.pdf

The Botley Map Projection (1951) is an Oblique Plate CarreÈ Projection (or Simple Equidistant Cylindrical projection). London has been rotated to the Normal North Pole position at the center of the map. In this case all distances from the center of the map (London) to all other points on the map are correct - http://www.csiss.org/map-projections/Cylindrical/Botley.pdf

The Mecca Map was developed by an Egyptian named J.I. Craig in 1909. It is classified by its Graticule as a Retroazimuthal Projection. At the center of this map is Mecca and as an Azimuthal variation all directions from the center of the map are true. Also known as a Qibla map it was used to help Muslims orient themselves toward Mecca for Prayer. A later parody variation of this map was made with Wall Street in its center - http://www.csiss.org/map-projections/Azimuthal/Craig.pdf

Arden-Close Projection is a Transverse Mollweide (pronounced Moll-vie-da) devised by Charles Arden-Close in 1908. Its Graticule classification is Pseudocylindrical and it is Equal-area. Note that the North pole is placed at the 90 degree position along the equator and the central meridian is at 90 degrees East. Note that this variation is seldom seen today - http://www.csiss.org/map-projections/Pseudocylindrical/Close_Transv_Mollweide.pdf

The Atlantis Projection was developed in 1948 by John Bartholomew of Scotland and is a Variation of the above Arden-Close Projection. The only difference in the Map Projection parameters is that Bartholomew chose 30 Degrees West for his Central Meridian. The original purpose of this projection was to show British shipping routes without the lines representing those routes being broken by the map boundaries. This projection is still seen today but displaying Airline Routes - http://www.csiss.org/map-projections/Pseudocylindrical/Atlantis_projection.pdf

Guyou Projection by …mile Guyou in 1886, This is a conformal projection but its Graticule does not fit in with the normal Classifcation scheme, so it is normally refered to as a Miscellaneous Graticule. While the graphic below shows the the projection as a world map, its original purpose was to show France in a pleasing shape - http://www.csiss.org/map-projections/Miscellaneous/Guyou_Conformal.pdf

Mollweide Projection is an Equal-area Pseudocylindrical map projection that was developed by K. B. Mollweide in 1814 but not used until Jacques Babinet found it and reintroduced it as the Homalographic in 1857. This map projection was breifly used by a number of cartographers who used it, gave it another name, and then stopped using it. In 1916, J. Paul Goode a Geography professor at University of Chicago began experimenting with Interrupted projections. He Interrupted a number of Equal-area Pseudocylindrical map Projections because the straight parallels were ideal for displaying Statistical data, but was not satisfied with them. What he finally hit upon was a combination projection consisting of the Sinusoidal Projection from the Equator to 40 Degrees 44 minutes North and South and the Mollweide projection from both poles to 40 Degrees 44 Minutes. And called it his Homolosine Projection. - http://www.csiss.org/map-projections/Pseudocylindrical/Mollweide_a.pdf

Sinusoidal Projection, Equal-area Pseudocylindrical with the Pole as a Point - http://www.csiss.org/map-projections/Pseudocylindrical/Sinusoidal_a.pdf

The Homolosine Not Interrupted - http://www.csiss.org/map-projections/Pseudocylindrical/Goode_Homolosine_a.pdf

Robinson Projection - In the 1950s Rand McNally comissioned A. H. Robinson to produce a Compromise Pseudocylindrical projection with the pole as a line. National Geographic and others soon adopted it - http://www.csiss.org/map-projections/Pseudocylindrical/Robinson.pdf

  • It had its issues but there was a push in the cartographic community to get schools to switch to it from the Mercator because of its more pleasing shape.

Winkel Tripel - Just before Robinson's passing the National Geographic Society switched to using the Winkel Tripel because they felt it was a more realistic (read: Less Distorted) View of the earth - http://www.csiss.org/map-projections/Azimuthal/Winkel_Tripel_1.pdf

Paul D. Thomas and F. Webster McBryde, for the Coast and Geodetic Survey, produced 5 Equal-area Pseudocylindricals. These were pretty much forgotten until A. H. Robinson reproduced one of them for his Cartography Textbook without attribution. A public war broke out between Robinson and McBryde resulting in F. Webster McBryde applying for a Patent to protect his S3 Map Projection in 1977. McBryde was the last person allowed to patent a map projection Formula.

In 1929 S. Whittmore Boggs commissioned Oscar S. Adams (Mathematicians were called 'Calculators' then) to create a map projection similar to the Goode Homolosine for the Office of the Geographer, US Department of State.

One thing I noticed when researching this material is that when Miller presented his Modified Gall Projection to Boggs he actually used the same parameters as the Kamenetskiy 2 (or BSAM) projection (1937). It appears that he may have hidden the Standard parallels value in additional math so that it would not be noticed.

This may be of interest, they are Gedymin Profiles (Distortion Diagrams) I created for a Textbook by Keith C. Clarke Ph.D. - http://www.galleryofmapprojections.com/gedymin/gedymin_prof.pdf

This one is larger and may be easier to figure out - http://www.galleryofmapprojections.com/gedymin/gedymin_prof_11x17.pdf

The directory actually contains additional source material - http://www.galleryofmapprojections.com/gedymin

Personal Note:

  • John Parr Snyder (passed away in 1997) was a Personal Friend who infected me with the desire to learn all I could about map projections. The ODU library has several of his books. The one I recommend is 'Flattening the Earth: Two Thousand Years of Map Projections'.
  • John Introduced me to F. Webster McBryde about 6 months before 'Web' passed away. However, that was enough time for Web to teach me how to create Interrupted Map Projections with my software.

Update (July 2013)

Paul sent an email with links to some map projection visualizations that had been done in D3.