mapproj(3tcl) Tcl Library mapproj(3tcl)______________________________________________________________________________NAMEmapproj - 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_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
_________________________________________________________________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_0 phi_0 lambda phi
Converts to the plate carr['e]e (cylindrical equidistant) pro‐
jection.
::mapproj::fromPlateCarree lambda_0 phi_0 x y
Converts from the plate carr['e]e (cylindrical equidistant) pro‐
jection.
::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. pro‐
jection.
::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) projec‐
tion.
::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 projec‐
tion. (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 projec‐
tion. (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.)
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 pro‐
jections, this figure is also the reference meridian of the pro‐
jection.
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.
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, mea‐
sured 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 projec‐
tion 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 Lam‐
bert azimuthal equal-area projection, the Albers equal-area conic pro‐
jection, and several of the world-map projections (Miller Cylindrical,
Mollweide, Eckert IV, Eckert VI, Robinson, and Hammer). If the signifi‐
cant 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['e]e, 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. Appro‐
priate choices are azimuthal equidistant, azimuthal equal-area, stereo‐
graphic, and perhaps orthographic.
Next, consider how much of the Earth your map will cover, and the gen‐
eral shape of the area of interest. For maps of the entire Earth, the
cylindrical equal area, Eckert IV and VI, Mollweide, Robinson, and Ham‐
mer 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 dis‐
tortion 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 scien‐
tific data, since other projections have moe useful geometric proper‐
ties.
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 refer‐
ence 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 con‐
formal projection; Lambert cylindrical equal-area and sinusoidal pro‐
jections are good equal-area projections; and the plate carr['e]e 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 pos‐
sible 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 proper‐
ties. 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 sur‐
face) 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).
KEYWORDS
geodesy, map, projection
COPYRIGHT
Copyright (c) 2007 Kevin B. Kenny <kennykb@acm.org>
mapproj 0.1 mapproj(3tcl)
