Planet Mapping 2D/3D conversion

Discussion in 'Earth Science' started by jumpjack, Sep 15, 2007.

  1. jumpjack Registered Member

    Messages:
    30
    I want to build my own earthglobe. I found that I need just two things: a ball, and a map.
    The first is quite easy to find... the second is very difficult: I need an UTM Projection of the whole world, like this one (see bottom of page):
    "h t tp :/ /ww w.geog.ubc.ca/courses/geog376/notes/georeferencing/coordinates.html"


    The above image is too low res to be useful: I need a more detailed map, or a software which allows CREATING it: can anybody help finding them? :shrug:
     
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  3. ntgr Registered Senior Member

    Messages:
    70
    It's probably too late, but here is some basic cartography+geodesy:

    The Earth's physical surface is very irregular.
    To describe it (3d) we use the geoid -also irregular- but smoother. It is an equipotential surface and gravity measurements are used to define it. It is the most accurate we have. Very complicated math.

    The second best thing to describe the earth is an ellipsoid of revolution. Even less accurate, math and calculations are simpler but still complicated. Because of the Earth's rotation it resembles an oblate spheroid. For precise measurements we stick to the ellipsoid.

    Since the Earth's flattening is very small, apr. 1/300, we use the sphere where the math is even simpler. At the expense of precision again.

    (Note that none of the above 3 surfaces exist physically)

    To create a map, we have to transform X,Y,Z or long/lat coordinates to x,y map coordinates (3d to 2d). We use projections for the above transformation (the correct word is mathematical functions because not all these functions are projections). The problem is that the sphere is not a developable surface, so we cannot move to a plane without some kind of distortion.
    Most of the times we move to an intermediate developable surface (cylinder, cone etc) and then go to a plane.
    Different projections are used for different purposes.
    The field which studies the mathematical part of all this, is called analytical cartography.

    You can see now that in a globe the 3d to 2d transformation is not necessary since the body is already three dimensional! But since you have to first print the map there is no way to avoid it.

    The UTM you are referring to, Universal Transverse Mercator, is cylindrical and uses different projections for different zones. However, you CANNOT use these zones in one map. UTM was designed to map objects within one zone at a time.

    Instead the way to do it is print an interrupted map with sections (called lobes or gores). The more gores in the map the less distortion you have but more paper discontinuities. In my opinion, choose a compromise projection with no major area, angle or distance distortion instead of eg. an equidistant.
    And print the map in a flexible material instead of paper if you can before gluing it to the sphere.
     
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