mapproj(n) Tcl Library mapproj(n) 







mapproj - Map projection routines








package require Tcl ?8.4?


package require math::interpolate ?1.0?


package require math::special ?0.2.1?


package require mapproj ?1.0?


::mapproj::toPlateCarree lambda_0 phi_0
    lambda phi


::mapproj::fromPlateCarree lambda_0 phi_0
    x y


::mapproj::toCylindricalEqualArea lambda_0
    phi_0 lambda phi


::mapproj::fromCylindricalEqualArea lambda_0
    phi_0 x y


::mapproj::toMercator lambda_0 phi_0
    lambda phi


::mapproj::fromMercator lambda_0 phi_0
    x y


::mapproj::toMillerCylindrical lambda_0
    lambda phi


::mapproj::fromMillerCylindrical lambda_0 x
    y


::mapproj::toSinusoidal lambda_0 phi_0
    lambda phi


::mapproj::fromSinusoidal lambda_0 phi_0
    x y


::mapproj::toMollweide lambda_0 lambda
    phi


::mapproj::fromMollweide lambda_0 x
  y


::mapproj::toEckertIV lambda_0 lambda
    phi


::mapproj::fromEckertIV lambda_0 x
  y


::mapproj::toEckertVI lambda_0 lambda
    phi


::mapproj::fromEckertVI lambda_0 x
  y


::mapproj::toRobinson lambda_0 lambda
    phi


::mapproj::fromRobinson lambda_0 x
  y


::mapproj::toCassini lambda_0 phi_0
    lambda phi


::mapproj::fromCassini lambda_0 phi_0
    x y


::mapproj::toPeirceQuincuncial lambda_0
    lambda phi


::mapproj::fromPeirceQuincuncial lambda_0 x
    y


::mapproj::toOrthographic lambda_0 phi_0
    lambda phi


::mapproj::fromOrthographic lambda_0 phi_0
    x y


::mapproj::toStereographic lambda_0 phi_0
    lambda phi


::mapproj::fromStereographic lambda_0 phi_0
    x y


::mapproj::toGnomonic lambda_0 phi_0
    lambda phi


::mapproj::fromGnomonic lambda_0 phi_0
    x y


::mapproj::toAzimuthalEquidistant lambda_0
    phi_0 lambda phi


::mapproj::fromAzimuthalEquidistant lambda_0
    phi_0 x y


::mapproj::toLambertAzimuthalEqualArea lambda_0
    phi_0 lambda phi


::mapproj::fromLambertAzimuthalEqualArea lambda_0
    phi_0 x y


::mapproj::toHammer lambda_0 lambda
    phi


::mapproj::fromHammer lambda_0 x y


::mapproj::toConicEquidistant lambda_0 phi_0
    phi_1 phi_2 lambda phi


::mapproj::fromConicEquidistant lambda_0
    phi_0 phi_1 phi_2 x y


::mapproj::toAlbersEqualAreaConic lambda_0
    phi_0 phi_1 phi_2 lambda phi


::mapproj::fromAlbersEqualAreaConic lambda_0
    phi_0 phi_1 phi_2 x y


::mapproj::toLambertConformalConic lambda_0
    phi_0 phi_1 phi_2 lambda phi


::mapproj::fromLambertConformalConic lambda_0
    phi_0 phi_1 phi_2 x y


::mapproj::toLambertCylindricalEqualArea lambda_0
    phi_0 lambda phi


::mapproj::fromLambertCylindricalEqualArea lambda_0
    phi_0 x y


::mapproj::toBehrmann lambda_0 phi_0
    lambda phi


::mapproj::fromBehrmann lambda_0 phi_0
    x y


::mapproj::toTrystanEdwards lambda_0 phi_0
    lambda phi


::mapproj::fromTrystanEdwards lambda_0 phi_0
    x y


::mapproj::toHoboDyer lambda_0 phi_0
    lambda phi


::mapproj::fromHoboDyer lambda_0 phi_0
    x y


::mapproj::toGallPeters lambda_0 phi_0
    lambda phi


::mapproj::fromGallPeters lambda_0 phi_0
    x y


::mapproj::toBalthasart lambda_0 phi_0
    lambda phi


::mapproj::fromBalthasart lambda_0 phi_0
    x y












The mapproj package provides a set of procedures for
    converting between world co-ordinates (latitude and longitude) and map
    co-ordinates on a number of different map projections.








The following commands convert between world co-ordinates and map
    co-ordinates:



  
::mapproj::toPlateCarree lambda_0 phi_0 lambda
    phi

  
Converts to the plate carrée (cylindrical equidistant)
      projection.

  
::mapproj::fromPlateCarree lambda_0 phi_0 x
    y

  
Converts from the plate carrée (cylindrical equidistant)
      projection.

  
::mapproj::toCylindricalEqualArea lambda_0 phi_0
    lambda phi

  
Converts to the cylindrical equal-area projection.

  
::mapproj::fromCylindricalEqualArea lambda_0 phi_0
    x y

  
Converts from the cylindrical equal-area projection.

  
::mapproj::toMercator lambda_0 phi_0 lambda
    phi

  
Converts to the Mercator (cylindrical conformal) projection.

  
::mapproj::fromMercator lambda_0 phi_0 x
    y

  
Converts from the Mercator (cylindrical conformal) projection.

  
::mapproj::toMillerCylindrical lambda_0 lambda
    phi

  
Converts to the Miller Cylindrical projection.

  
::mapproj::fromMillerCylindrical lambda_0 x
    y

  
Converts from the Miller Cylindrical projection.

  
::mapproj::toSinusoidal lambda_0 phi_0 lambda
    phi

  
Converts to the sinusoidal (Sanson-Flamsteed) projection. projection.

  
::mapproj::fromSinusoidal lambda_0 phi_0 x
    y

  
Converts from the sinusoidal (Sanson-Flamsteed) projection.
    projection.

  
::mapproj::toMollweide lambda_0 lambda
    phi

  
Converts to the Mollweide projection.

  
::mapproj::fromMollweide lambda_0 x y

  
Converts from the Mollweide projection.

  
::mapproj::toEckertIV lambda_0 lambda phi

  
Converts to the Eckert IV projection.

  
::mapproj::fromEckertIV lambda_0 x y

  
Converts from the Eckert IV projection.

  
::mapproj::toEckertVI lambda_0 lambda phi

  
Converts to the Eckert VI projection.

  
::mapproj::fromEckertVI lambda_0 x y

  
Converts from the Eckert VI projection.

  
::mapproj::toRobinson lambda_0 lambda phi

  
Converts to the Robinson projection.

  
::mapproj::fromRobinson lambda_0 x y

  
Converts from the Robinson projection.

  
::mapproj::toCassini lambda_0 phi_0 lambda
    phi

  
Converts to the Cassini (transverse cylindrical equidistant)
    projection.

  
::mapproj::fromCassini lambda_0 phi_0 x
    y

  
Converts from the Cassini (transverse cylindrical equidistant)
    projection.

  
::mapproj::toPeirceQuincuncial lambda_0 lambda
    phi

  
Converts to the Peirce Quincuncial Projection.

  
::mapproj::fromPeirceQuincuncial lambda_0 x
    y

  
Converts from the Peirce Quincuncial Projection.

  
::mapproj::toOrthographic lambda_0 phi_0
    lambda phi

  
Converts to the orthographic projection.

  
::mapproj::fromOrthographic lambda_0 phi_0 x
    y

  
Converts from the orthographic projection.

  
::mapproj::toStereographic lambda_0 phi_0
    lambda phi

  
Converts to the stereographic (azimuthal conformal) projection.

  
::mapproj::fromStereographic lambda_0 phi_0 x
    y

  
Converts from the stereographic (azimuthal conformal) projection.

  
::mapproj::toGnomonic lambda_0 phi_0 lambda
    phi

  
Converts to the gnomonic projection.

  
::mapproj::fromGnomonic lambda_0 phi_0 x
    y

  
Converts from the gnomonic projection.

  
::mapproj::toAzimuthalEquidistant lambda_0 phi_0
    lambda phi

  
Converts to the azimuthal equidistant projection.

  
::mapproj::fromAzimuthalEquidistant lambda_0 phi_0
    x y

  
Converts from the azimuthal equidistant projection.

  
::mapproj::toLambertAzimuthalEqualArea lambda_0 phi_0
    lambda phi

  
Converts to the Lambert azimuthal equal-area projection.

  
::mapproj::fromLambertAzimuthalEqualArea lambda_0
    phi_0 x y

  
Converts from the Lambert azimuthal equal-area projection.

  
::mapproj::toHammer lambda_0 lambda phi

  
Converts to the Hammer projection.

  
::mapproj::fromHammer lambda_0 x y

  
Converts from the Hammer projection.

  
::mapproj::toConicEquidistant lambda_0 phi_0
    phi_1 phi_2 lambda phi

  
Converts to the conic equidistant projection.

  
::mapproj::fromConicEquidistant lambda_0 phi_0
    phi_1 phi_2 x y

  
Converts from the conic equidistant projection.

  
::mapproj::toAlbersEqualAreaConic lambda_0 phi_0
    phi_1 phi_2 lambda phi

  
Converts to the Albers equal-area conic projection.

  
::mapproj::fromAlbersEqualAreaConic lambda_0 phi_0
    phi_1 phi_2 x y

  
Converts from the Albers equal-area conic projection.

  
::mapproj::toLambertConformalConic lambda_0 phi_0
    phi_1 phi_2 lambda phi

  
Converts to the Lambert conformal conic projection.

  
::mapproj::fromLambertConformalConic lambda_0 phi_0
    phi_1 phi_2 x y

  
Converts from the Lambert conformal conic projection.




Among the cylindrical equal-area projections, there are a number
    of choices of standard parallels that have names:



  
::mapproj::toLambertCylindricalEqualArea lambda_0
    phi_0 lambda phi

  
Converts to the Lambert cylindrical equal area projection. (standard
      parallel is the Equator.)

  
::mapproj::fromLambertCylindricalEqualArea lambda_0
    phi_0 x y

  
Converts from the Lambert cylindrical equal area projection. (standard
      parallel is the Equator.)

  
::mapproj::toBehrmann lambda_0 phi_0 lambda
    phi

  
Converts to the Behrmann cylindrical equal area projection. (standard
      parallels are 30 degrees North and South)

  
::mapproj::fromBehrmann lambda_0 phi_0 x
    y

  
Converts from the Behrmann cylindrical equal area projection. (standard
      parallels are 30 degrees North and South.)

  
::mapproj::toTrystanEdwards lambda_0 phi_0
    lambda phi

  
Converts to the Trystan Edwards cylindrical equal area projection.
      (standard parallels are 37.4 degrees North and South)

  
::mapproj::fromTrystanEdwards lambda_0 phi_0 x
    y

  
Converts from the Trystan Edwards cylindrical equal area projection.
      (standard parallels are 37.4 degrees North and South.)

  
::mapproj::toHoboDyer lambda_0 phi_0 lambda
    phi

  
Converts to the Hobo-Dyer cylindrical equal area projection. (standard
      parallels are 37.5 degrees North and South)

  
::mapproj::fromHoboDyer lambda_0 phi_0 x
    y

  
Converts from the Hobo-Dyer cylindrical equal area projection. (standard
      parallels are 37.5 degrees North and South.)

  
::mapproj::toGallPeters lambda_0 phi_0 lambda
    phi

  
Converts to the Gall-Peters cylindrical equal area projection. (standard
      parallels are 45 degrees North and South)

  
::mapproj::fromGallPeters lambda_0 phi_0 x
    y

  
Converts from the Gall-Peters cylindrical equal area projection. (standard
      parallels are 45 degrees North and South.)

  
::mapproj::toBalthasart lambda_0 phi_0 lambda
    phi

  
Converts to the Balthasart cylindrical equal area projection. (standard
      parallels are 50 degrees North and South)

  
::mapproj::fromBalthasart lambda_0 phi_0 x
    y

  
Converts from the Balthasart cylindrical equal area projection. (standard
      parallels are 50 degrees North and South.)










The following arguments are accepted by the projection
  commands:



  

  
Longitude of the point to be projected, in degrees.

  

  
Latitude of the point to be projected, in degrees.

  

  
Longitude of the center of the sheet, in degrees. For many projections,
      this figure is also the reference meridian of the projection.

  

  
Latitude of the center of the sheet, in degrees. For the azimuthal
      projections, this figure is also the latitude of the center of the
      projection.

  

  
Latitude of the first reference parallel, for projections that use
      reference parallels.

  

  
Latitude of the second reference parallel, for projections that use
      reference parallels.

  

  
X co-ordinate of a point on the map, in units of Earth radii.

  

  
Y co-ordinate of a point on the map, in units of Earth radii.










For all of the procedures whose names begin with 'to', the return
    value is a list comprising an x co-ordinate and a y
    co-ordinate. The co-ordinates are relative to the center of the map sheet to
    be drawn, measured in Earth radii at the reference location on the map. For
    all of the functions whose names begin with 'from', the return value is a
    list comprising the longitude and latitude, in degrees.








This package offers a great many projections, because no single
    projection is appropriate to all maps. This section attempts to provide
    guidance on how to choose a projection.


First, consider the type of data that you intend to display on the
    map. If the data are directional (e.g., winds, ocean currents,
    or magnetic fields) then you need to use a projection that preserves angles;
    these are known as conformal projections. Conformal projections
    include the Mercator, the Albers azimuthal equal-area, the stereographic,
    and the Peirce Quincuncial projection. If the data are thematic,
    describing properties of land or water, such as temperature, population
    density, land use, or demographics; then you need a projection that will
    show these data with the areas on the map proportional to the areas in real
    life. These so-called equal area projections include the various
    cylindrical equal area projections, the sinusoidal projection, the Lambert
    azimuthal equal-area projection, the Albers equal-area conic projection, and
    several of the world-map projections (Miller Cylindrical, Mollweide, Eckert
    IV, Eckert VI, Robinson, and Hammer). If the significant factor in your data
    is distance from a central point or line (such as air routes), then you will
    do best with an equidistant projection such as plate
    carrée, Cassini, azimuthal equidistant, or conic equidistant. If
    direction from a central point is a critical factor in your data (for
    instance, air routes, radio antenna pointing), then you will almost surely
    want to use one of the azimuthal projections. Appropriate choices are
    azimuthal equidistant, azimuthal equal-area, stereographic, and perhaps
    orthographic.


Next, consider how much of the Earth your map will cover, and the
    general shape of the area of interest. For maps of the entire Earth, the
    cylindrical equal area, Eckert IV and VI, Mollweide, Robinson, and Hammer
    projections are good overall choices. The Mercator projection is
    traditional, but the extreme distortions of area at high latitudes make it a
    poor choice unless a conformal projection is required. The Peirce projection
    is a better choice of conformal projection, having less distortion of
    landforms. The Miller Cylindrical is a compromise designed to give shapes
    similar to the traditional Mercator, but with less polar stretching. The
    Peirce Quincuncial projection shows all the continents with acceptable
    distortion if a reference meridian close to +20 degrees is chosen. The
    Robinson projection yields attractive maps for things like political
    divisions, but should be avoided in presenting scientific data, since other
    projections have moe useful geometric properties.


If the map will cover a hemisphere, then choose stereographic,
    azimuthal-equidistant, Hammer, or Mollweide projections; these all project
    the hemisphere into a circle.


If the map will cover a large area (at least a few hundred km on a
    side), but less than a hemisphere, then you have several choices. Azimuthal
    projections are usually good (choose stereographic, azimuthal equidistant,
    or Lambert azimuthal equal-area according to whether shapes, distances from
    a central point, or areas are important). Azimuthal projections (and
    possibly the Cassini projection) are the only really good choices for
    mapping the polar regions.


If the large area is in one of the temperate zones and is round or
    has a primarily east-west extent, then the conic projections are good
    choices. Choose the Lambert conformal conic, the conic equidistant, or the
    Albers equal-area conic according to whether shape, distance, or area are
    the most important parameters. For any of these, the reference parallels
    should be chosen at approximately 1/6 and 5/6 of the range of latitudes to
    be displayed. For instance, maps of the 48 coterminous United States are
    attractive with reference parallels of 28.5 and 45.5 degrees.


If the large area is equatorial and is round or has a primarily
    east-west extent, then the Mercator projection is a good choice for a
    conformal projection; Lambert cylindrical equal-area and sinusoidal
    projections are good equal-area projections; and the plate
    carrée is a good equidistant projection.


Large areas having a primarily North-South aspect, particularly
    those spanning the Equator, need some other choices. The Cassini projection
    is a good choice for an equidistant projection (for instance, a Cassini
    projection with a central meridian of 80 degrees West produces an attractive
    map of the Americas). The cylindrical equal-area, Albers equal-area conic,
    sinusoidal, Mollweide and Hammer projections are possible choices for
    equal-area projections. A good conformal projection in this situation is the
    Transverse Mercator, which alas, is not yet implemented.


Small areas begin to get into a realm where the ellipticity of the
    Earth affects the map scale. This package does not attempt to handle
    accurate mapping for large-scale topographic maps. If slight scale errors
    are acceptable in your application, then any of the projections appropriate
    to large areas should work for small ones as well.


There are a few projections that are included for their special
    properties. The orthographic projection produces views of the Earth as seen
    from space. The gnomonic projection produces a map on which all great
    circles (the shortest distance between two points on the Earth's surface)
    are rendered as straight lines. While this projection is useful for
    navigational planning, it has extreme distortions of shape and area, and can
    display only a limited area of the Earth (substantially less than a
    hemisphere).








geodesy, map, projection








Copyright (c) 2007 Kevin B. Kenny <kennykb@acm.org>








  

    0.1
    mapproj