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mapproj(n) Tcl Library mapproj(n)

____________________________________________________________________________________________________________

NAME
mapproj - Map projection routines

SYNOPSIS
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__ phi__ lambda phi

::mapproj::fromPlateCarree lambda__ phi__ x y

::mapproj::toCylindricalEqualArea lambda__ phi__ lambda phi

::mapproj::fromCylindricalEqualArea lambda__ phi__ x y

::mapproj::toMercator lambda__ phi__ lambda phi

::mapproj::fromMercator lambda__ phi__ x y

::mapproj::toMillerCylindrical lambda__ lambda phi

::mapproj::fromMillerCylindrical lambda__ x y

::mapproj::toSinusoidal lambda__ phi__ lambda phi

::mapproj::fromSinusoidal lambda__ phi__ x y

::mapproj::toMollweide lambda__ lambda phi

::mapproj::fromMollweide lambda__ x y

::mapproj::toEckertIV lambda__ lambda phi

::mapproj::fromEckertIV lambda__ x y

::mapproj::toEckertVI lambda__ lambda phi

::mapproj::fromEckertVI lambda__ x y

::mapproj::toRobinson lambda__ lambda phi

::mapproj::fromRobinson lambda__ x y

::mapproj::toCassini lambda__ phi__ lambda phi

::mapproj::fromCassini lambda__ phi__ x y

::mapproj::toPeirceQuincuncial lambda__ lambda phi

::mapproj::fromPeirceQuincuncial lambda__ x y

::mapproj::toOrthographic lambda__ phi__ lambda phi

::mapproj::fromOrthographic lambda__ phi__ x y

::mapproj::toStereographic lambda__ phi__ lambda phi

::mapproj::fromStereographic lambda__ phi__ x y

::mapproj::toGnomonic lambda__ phi__ lambda phi

::mapproj::fromGnomonic lambda__ phi__ x y

::mapproj::toAzimuthalEquidistant lambda__ phi__ lambda phi

::mapproj::fromAzimuthalEquidistant lambda__ phi__ x y

::mapproj::toLambertAzimuthalEqualArea lambda__ phi__ lambda phi

::mapproj::fromLambertAzimuthalEqualArea lambda__ phi__ x y

::mapproj::toHammer lambda__ lambda phi

::mapproj::fromHammer lambda__ x y

::mapproj::toConicEquidistant lambda__ phi__ phi_1 phi_2 lambda phi

::mapproj::fromConicEquidistant lambda__ phi__ phi_1 phi_2 x y

::mapproj::toAlbersEqualAreaConic lambda__ phi__ phi_1 phi_2 lambda phi

::mapproj::fromAlbersEqualAreaConic lambda__ phi__ phi_1 phi_2 x y

::mapproj::toLambertConformalConic lambda__ phi__ phi_1 phi_2 lambda phi

::mapproj::fromLambertConformalConic lambda__ phi__ phi_1 phi_2 x y

::mapproj::toLambertCylindricalEqualArea lambda__ phi__ lambda phi

::mapproj::fromLambertCylindricalEqualArea lambda__ phi__ x y

::mapproj::toBehrmann lambda__ phi__ lambda phi

::mapproj::fromBehrmann lambda__ phi__ x y

::mapproj::toTrystanEdwards lambda__ phi__ lambda phi

::mapproj::fromTrystanEdwards lambda__ phi__ x y

::mapproj::toHoboDyer lambda__ phi__ lambda phi

::mapproj::fromHoboDyer lambda__ phi__ x y

::mapproj::toGallPeters lambda__ phi__ lambda phi

::mapproj::fromGallPeters lambda__ phi__ x y

::mapproj::toBalthasart lambda__ phi__ lambda phi

::mapproj::fromBalthasart lambda__ phi__ x y

____________________________________________________________________________________________________________

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.

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

::mapproj::toPlateCarree lambda__ phi__ lambda phi
Converts to the plate carr~(C)e (cylindrical equidistant) projection.

::mapproj::fromPlateCarree lambda__ phi__ x y
Converts from the plate carr~(C)e (cylindrical equidistant) projection.

::mapproj::toCylindricalEqualArea lambda__ phi__ lambda phi
Converts to the cylindrical equal-area projection.

::mapproj::fromCylindricalEqualArea lambda__ phi__ x y
Converts from the cylindrical equal-area projection.

::mapproj::toMercator lambda__ phi__ lambda phi
Converts to the Mercator (cylindrical conformal) projection.

::mapproj::fromMercator lambda__ phi__ x y
Converts from the Mercator (cylindrical conformal) projection.

::mapproj::toMillerCylindrical lambda__ lambda phi
Converts to the Miller Cylindrical projection.

::mapproj::fromMillerCylindrical lambda__ x y
Converts from the Miller Cylindrical projection.

::mapproj::toSinusoidal lambda__ phi__ lambda phi
Converts to the sinusoidal (Sanson-Flamsteed) projection. projection.

::mapproj::fromSinusoidal lambda__ phi__ x y
Converts from the sinusoidal (Sanson-Flamsteed) projection. projection.

::mapproj::toMollweide lambda__ lambda phi
Converts to the Mollweide projection.

::mapproj::fromMollweide lambda__ x y
Converts from the Mollweide projection.

::mapproj::toEckertIV lambda__ lambda phi
Converts to the Eckert IV projection.

::mapproj::fromEckertIV lambda__ x y
Converts from the Eckert IV projection.

::mapproj::toEckertVI lambda__ lambda phi
Converts to the Eckert VI projection.

::mapproj::fromEckertVI lambda__ x y
Converts from the Eckert VI projection.

::mapproj::toRobinson lambda__ lambda phi
Converts to the Robinson projection.

::mapproj::fromRobinson lambda__ x y
Converts from the Robinson projection.

::mapproj::toCassini lambda__ phi__ lambda phi
Converts to the Cassini (transverse cylindrical equidistant) projection.

::mapproj::fromCassini lambda__ phi__ x y
Converts from the Cassini (transverse cylindrical equidistant) projection.

::mapproj::toPeirceQuincuncial lambda__ lambda phi
Converts to the Peirce Quincuncial Projection.

::mapproj::fromPeirceQuincuncial lambda__ x y
Converts from the Peirce Quincuncial Projection.

::mapproj::toOrthographic lambda__ phi__ lambda phi
Converts to the orthographic projection.

::mapproj::fromOrthographic lambda__ phi__ x y
Converts from the orthographic projection.

::mapproj::toStereographic lambda__ phi__ lambda phi
Converts to the stereographic (azimuthal conformal) projection.

::mapproj::fromStereographic lambda__ phi__ x y
Converts from the stereographic (azimuthal conformal) projection.

::mapproj::toGnomonic lambda__ phi__ lambda phi
Converts to the gnomonic projection.

::mapproj::fromGnomonic lambda__ phi__ x y
Converts from the gnomonic projection.

::mapproj::toAzimuthalEquidistant lambda__ phi__ lambda phi
Converts to the azimuthal equidistant projection.

::mapproj::fromAzimuthalEquidistant lambda__ phi__ x y
Converts from the azimuthal equidistant projection.

::mapproj::toLambertAzimuthalEqualArea lambda__ phi__ lambda phi
Converts to the Lambert azimuthal equal-area projection.

::mapproj::fromLambertAzimuthalEqualArea lambda__ phi__ x y
Converts from the Lambert azimuthal equal-area projection.

::mapproj::toHammer lambda__ lambda phi
Converts to the Hammer projection.

::mapproj::fromHammer lambda__ x y
Converts from the Hammer projection.

::mapproj::toConicEquidistant lambda__ phi__ phi_1 phi_2 lambda phi
Converts to the conic equidistant projection.

::mapproj::fromConicEquidistant lambda__ phi__ phi_1 phi_2 x y
Converts from the conic equidistant projection.

::mapproj::toAlbersEqualAreaConic lambda__ phi__ phi_1 phi_2 lambda phi
Converts to the Albers equal-area conic projection.

::mapproj::fromAlbersEqualAreaConic lambda__ phi__ phi_1 phi_2 x y
Converts from the Albers equal-area conic projection.

::mapproj::toLambertConformalConic lambda__ phi__ phi_1 phi_2 lambda phi
Converts to the Lambert conformal conic projection.

::mapproj::fromLambertConformalConic lambda__ phi__ 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__ phi__ lambda phi
Converts to the Lambert cylindrical equal area projection. (standard parallel is the Equator.)

::mapproj::fromLambertCylindricalEqualArea lambda__ phi__ x y
Converts from the Lambert cylindrical equal area projection. (standard parallel is the Equa-tor.) Equator.)
tor.)

::mapproj::toBehrmann lambda__ phi__ lambda phi
Converts to the Behrmann cylindrical equal area projection. (standard parallels are 30 degrees
North and South)

::mapproj::fromBehrmann lambda__ phi__ x y
Converts from the Behrmann cylindrical equal area projection. (standard parallels are 30
degrees North and South.)

::mapproj::toTrystanEdwards lambda__ phi__ lambda phi
Converts to the Trystan Edwards cylindrical equal area projection. (standard parallels are
37.4 degrees North and South)

::mapproj::fromTrystanEdwards lambda__ phi__ x y
Converts from the Trystan Edwards cylindrical equal area projection. (standard parallels are
37.4 degrees North and South.)

::mapproj::toHoboDyer lambda__ phi__ lambda phi
Converts to the Hobo-Dyer cylindrical equal area projection. (standard parallels are 37.5
degrees North and South)

::mapproj::fromHoboDyer lambda__ phi__ x y
Converts from the Hobo-Dyer cylindrical equal area projection. (standard parallels are 37.5
degrees North and South.)

::mapproj::toGallPeters lambda__ phi__ lambda phi
Converts to the Gall-Peters cylindrical equal area projection. (standard parallels are 45
degrees North and South)

::mapproj::fromGallPeters lambda__ phi__ x y
Converts from the Gall-Peters cylindrical equal area projection. (standard parallels are 45
degrees North and South.)

::mapproj::toBalthasart lambda__ phi__ lambda phi
Converts to the Balthasart cylindrical equal area projection. (standard parallels are 50
degrees North and South)

::mapproj::fromBalthasart lambda__ phi__ x y
Converts from the Balthasart cylindrical equal area projection. (standard parallels are 50
degrees North and South.)

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

phi__ 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.

RESULTS
For all of the procedures whose names begin with 'to', the return value is a list comprising an x co-ordinate coordinate
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.

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 equal area projections include the various
cylindrical equal area projections, the sinusoidal projection, the Lambert azimuthal equal-area pro-jection, projection,
jection, 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 carr~(C)e, Cassini, azimuthal equidistant, or conic equidis-tant. equidistant.
tant. 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 inter-est. interest.
est. For maps of the entire Earth, the cylindrical equal area, Eckert IV and VI, Mollweide, Robin-son, Robinson,
son, 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 tradi-tional traditional
tional 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 equidis-tant, equidistant,
tant, 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 carr~(C)e is a good equidistant projec-tion. projection.
tion.

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 pro-jections projections
jections are possible choices for equal-area projections. A good conformal projection in this situa-tion situation
tion 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 projec-tion projection
tion 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 distor-tions distortions
tions of shape and area, and can display only a limited area of the Earth (substantially less than a
hemisphere).

KEYWORDS
geodesy, map, projection

mapproj 0.1 mapproj(n)

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