mapproj - Map projection routines

Arguments

       The following arguments are accepted by the projection commands:

       lambda Longitude of the point to be projected, in degrees.

       phi    Latitude of the point to be projected, in degrees.

       lambda_0
              Longitude of the center of the sheet, in degrees.  For many projections, this figure is  also  the
              reference meridian of the projection.

       phi_0  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.

       phi_1  Latitude of the first reference parallel, for projections that use reference parallels.

       phi_2  Latitude of the second reference parallel, for projections that use reference parallels.

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

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

Choosing A Projection

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 equalarea 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
platecarrée, 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 platecarrée 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).

Commands

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

::mapproj::toPlateCarreelambda_0phi_0lambdaphi
Converts to the platecarrée (cylindrical equidistant) projection.

::mapproj::fromPlateCarreelambda_0phi_0xy
Converts from the platecarrée (cylindrical equidistant) projection.

::mapproj::toCylindricalEqualArealambda_0phi_0lambdaphi
Converts to the cylindrical equal-area projection.

::mapproj::fromCylindricalEqualArealambda_0phi_0xy
Converts from the cylindrical equal-area projection.

::mapproj::toMercatorlambda_0phi_0lambdaphi
Converts to the Mercator (cylindrical conformal) projection.

::mapproj::fromMercatorlambda_0phi_0xy
Converts from the Mercator (cylindrical conformal) projection.

::mapproj::toMillerCylindricallambda_0lambdaphi
Converts to the Miller Cylindrical projection.

::mapproj::fromMillerCylindricallambda_0xy
Converts from the Miller Cylindrical projection.

::mapproj::toSinusoidallambda_0phi_0lambdaphi
Converts to the sinusoidal (Sanson-Flamsteed) projection. projection.

::mapproj::fromSinusoidallambda_0phi_0xy
Converts from the sinusoidal (Sanson-Flamsteed) projection. projection.

::mapproj::toMollweidelambda_0lambdaphi
Converts to the Mollweide projection.

::mapproj::fromMollweidelambda_0xy
Converts from the Mollweide projection.

::mapproj::toEckertIVlambda_0lambdaphi
Converts to the Eckert IV projection.

::mapproj::fromEckertIVlambda_0xy
Converts from the Eckert IV projection.

::mapproj::toEckertVIlambda_0lambdaphi
Converts to the Eckert VI projection.

::mapproj::fromEckertVIlambda_0xy
Converts from the Eckert VI projection.

::mapproj::toRobinsonlambda_0lambdaphi
Converts to the Robinson projection.

::mapproj::fromRobinsonlambda_0xy
Converts from the Robinson projection.

::mapproj::toCassinilambda_0phi_0lambdaphi
Converts to the Cassini (transverse cylindrical equidistant) projection.

::mapproj::fromCassinilambda_0phi_0xy
Converts from the Cassini (transverse cylindrical equidistant) projection.

::mapproj::toPeirceQuincunciallambda_0lambdaphi
Converts to the Peirce Quincuncial Projection.

::mapproj::fromPeirceQuincunciallambda_0xy
Converts from the Peirce Quincuncial Projection.

::mapproj::toOrthographiclambda_0phi_0lambdaphi
Converts to the orthographic projection.

::mapproj::fromOrthographiclambda_0phi_0xy
Converts from the orthographic projection.

::mapproj::toStereographiclambda_0phi_0lambdaphi
Converts to the stereographic (azimuthal conformal) projection.

::mapproj::fromStereographiclambda_0phi_0xy
Converts from the stereographic (azimuthal conformal) projection.

::mapproj::toGnomoniclambda_0phi_0lambdaphi
Converts to the gnomonic projection.

::mapproj::fromGnomoniclambda_0phi_0xy
Converts from the gnomonic projection.

::mapproj::toAzimuthalEquidistantlambda_0phi_0lambdaphi
Converts to the azimuthal equidistant projection.

::mapproj::fromAzimuthalEquidistantlambda_0phi_0xy
Converts from the azimuthal equidistant projection.

::mapproj::toLambertAzimuthalEqualArealambda_0phi_0lambdaphi
Converts to the Lambert azimuthal equal-area projection.

::mapproj::fromLambertAzimuthalEqualArealambda_0phi_0xy
Converts from the Lambert azimuthal equal-area projection.

::mapproj::toHammerlambda_0lambdaphi
Converts to the Hammer projection.

::mapproj::fromHammerlambda_0xy
Converts from the Hammer projection.

::mapproj::toConicEquidistantlambda_0phi_0phi_1phi_2lambdaphi
Converts to the conic equidistant projection.

::mapproj::fromConicEquidistantlambda_0phi_0phi_1phi_2xy
Converts from the conic equidistant projection.

::mapproj::toAlbersEqualAreaConiclambda_0phi_0phi_1phi_2lambdaphi
Converts to the Albers equal-area conic projection.

::mapproj::fromAlbersEqualAreaConiclambda_0phi_0phi_1phi_2xy
Converts from the Albers equal-area conic projection.

::mapproj::toLambertConformalConiclambda_0phi_0phi_1phi_2lambdaphi
Converts to the Lambert conformal conic projection.

::mapproj::fromLambertConformalConiclambda_0phi_0phi_1phi_2xy
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::toLambertCylindricalEqualArealambda_0phi_0lambdaphi
Converts to the Lambert cylindrical equal area projection. (standard parallel is the Equator.)

::mapproj::fromLambertCylindricalEqualArealambda_0phi_0xy
Converts from the Lambert cylindrical equal area projection. (standard parallel is the Equator.)

::mapproj::toBehrmannlambda_0phi_0lambdaphi
Converts to the Behrmann cylindrical equal area projection. (standard parallels are 30 degrees
North and South)

::mapproj::fromBehrmannlambda_0phi_0xy
Converts from the Behrmann cylindrical equal area projection. (standard parallels are 30 degrees
North and South.)

::mapproj::toTrystanEdwardslambda_0phi_0lambdaphi
Converts to the Trystan Edwards cylindrical equal area projection. (standard parallels are 37.4
degrees North and South)

::mapproj::fromTrystanEdwardslambda_0phi_0xy
Converts from the Trystan Edwards cylindrical equal area projection. (standard parallels are 37.4
degrees North and South.)

::mapproj::toHoboDyerlambda_0phi_0lambdaphi
Converts to the Hobo-Dyer cylindrical equal area projection. (standard parallels are 37.5 degrees
North and South)

::mapproj::fromHoboDyerlambda_0phi_0xy
Converts from the Hobo-Dyer cylindrical equal area projection. (standard parallels are 37.5
degrees North and South.)

::mapproj::toGallPeterslambda_0phi_0lambdaphi
Converts to the Gall-Peters cylindrical equal area projection. (standard parallels are 45 degrees
North and South)

::mapproj::fromGallPeterslambda_0phi_0xy
Converts from the Gall-Peters cylindrical equal area projection. (standard parallels are 45
degrees North and South.)

::mapproj::toBalthasartlambda_0phi_0lambdaphi
Converts to the Balthasart cylindrical equal area projection. (standard parallels are 50 degrees
North and South)

::mapproj::fromBalthasartlambda_0phi_0xy
Converts from the Balthasart cylindrical equal area projection. (standard parallels are 50 degrees
North and South.)

Copyright

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

tcllib                                                 1.1                                         mapproj(3tcl)

Description

       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.

Keywords

       geodesy, map, projection

Name

       mapproj - Map projection routines

Results

       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.

Synopsis

       package require Tcl?8.59?

       package require math::interpolate?1.1?

       package require math::special?0.2.2?

       package require mapproj?1.1?::mapproj::toPlateCarreelambda_0phi_0lambdaphi::mapproj::fromPlateCarreelambda_0phi_0xy::mapproj::toCylindricalEqualArealambda_0phi_0lambdaphi::mapproj::fromCylindricalEqualArealambda_0phi_0xy::mapproj::toMercatorlambda_0phi_0lambdaphi::mapproj::fromMercatorlambda_0phi_0xy::mapproj::toMillerCylindricallambda_0lambdaphi::mapproj::fromMillerCylindricallambda_0xy::mapproj::toSinusoidallambda_0phi_0lambdaphi::mapproj::fromSinusoidallambda_0phi_0xy::mapproj::toMollweidelambda_0lambdaphi::mapproj::fromMollweidelambda_0xy::mapproj::toEckertIVlambda_0lambdaphi::mapproj::fromEckertIVlambda_0xy::mapproj::toEckertVIlambda_0lambdaphi::mapproj::fromEckertVIlambda_0xy::mapproj::toRobinsonlambda_0lambdaphi::mapproj::fromRobinsonlambda_0xy::mapproj::toCassinilambda_0phi_0lambdaphi::mapproj::fromCassinilambda_0phi_0xy::mapproj::toPeirceQuincunciallambda_0lambdaphi::mapproj::fromPeirceQuincunciallambda_0xy::mapproj::toOrthographiclambda_0phi_0lambdaphi::mapproj::fromOrthographiclambda_0phi_0xy::mapproj::toStereographiclambda_0phi_0lambdaphi::mapproj::fromStereographiclambda_0phi_0xy::mapproj::toGnomoniclambda_0phi_0lambdaphi::mapproj::fromGnomoniclambda_0phi_0xy::mapproj::toAzimuthalEquidistantlambda_0phi_0lambdaphi::mapproj::fromAzimuthalEquidistantlambda_0phi_0xy::mapproj::toLambertAzimuthalEqualArealambda_0phi_0lambdaphi::mapproj::fromLambertAzimuthalEqualArealambda_0phi_0xy::mapproj::toHammerlambda_0lambdaphi::mapproj::fromHammerlambda_0xy::mapproj::toConicEquidistantlambda_0phi_0phi_1phi_2lambdaphi::mapproj::fromConicEquidistantlambda_0phi_0phi_1phi_2xy::mapproj::toAlbersEqualAreaConiclambda_0phi_0phi_1phi_2lambdaphi::mapproj::fromAlbersEqualAreaConiclambda_0phi_0phi_1phi_2xy::mapproj::toLambertConformalConiclambda_0phi_0phi_1phi_2lambdaphi::mapproj::fromLambertConformalConiclambda_0phi_0phi_1phi_2xy::mapproj::toLambertCylindricalEqualArealambda_0phi_0lambdaphi::mapproj::fromLambertCylindricalEqualArealambda_0phi_0xy::mapproj::toBehrmannlambda_0phi_0lambdaphi::mapproj::fromBehrmannlambda_0phi_0xy::mapproj::toTrystanEdwardslambda_0phi_0lambdaphi::mapproj::fromTrystanEdwardslambda_0phi_0xy::mapproj::toHoboDyerlambda_0phi_0lambdaphi::mapproj::fromHoboDyerlambda_0phi_0xy::mapproj::toGallPeterslambda_0phi_0lambdaphi::mapproj::fromGallPeterslambda_0phi_0xy::mapproj::toBalthasartlambda_0phi_0lambdaphi::mapproj::fromBalthasartlambda_0phi_0xy

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