1mapproj(n) Tcl Library mapproj(n)
2______________________________________________________________________________
6
8 mapproj - Map projection routines
9
11 package require Tcl ?8.4?
12 package require math::interpolate ?1.0?
14 package require math::special ?0.2.1?
16 package require mapproj ?1.0?
18 ::mapproj::toPlateCarree lambda_0 phi_0 lambda phi
20 ::mapproj::fromPlateCarree lambda_0 phi_0 x y
22 ::mapproj::toCylindricalEqualArea lambda_0 phi_0 lambda phi
24 ::mapproj::fromCylindricalEqualArea lambda_0 phi_0 x y
26 ::mapproj::toMercator lambda_0 phi_0 lambda phi
28 ::mapproj::fromMercator lambda_0 phi_0 x y
30 ::mapproj::toMillerCylindrical lambda_0 lambda phi
32 ::mapproj::fromMillerCylindrical lambda_0 x y
34 ::mapproj::toSinusoidal lambda_0 phi_0 lambda phi
36 ::mapproj::fromSinusoidal lambda_0 phi_0 x y
38 ::mapproj::toMollweide lambda_0 lambda phi
40 ::mapproj::fromMollweide lambda_0 x y
42 ::mapproj::toEckertIV lambda_0 lambda phi
44 ::mapproj::fromEckertIV lambda_0 x y
46 ::mapproj::toEckertVI lambda_0 lambda phi
48 ::mapproj::fromEckertVI lambda_0 x y
50 ::mapproj::toRobinson lambda_0 lambda phi
52 ::mapproj::fromRobinson lambda_0 x y
54 ::mapproj::toCassini lambda_0 phi_0 lambda phi
56 ::mapproj::fromCassini lambda_0 phi_0 x y
58 ::mapproj::toPeirceQuincuncial lambda_0 lambda phi
60 ::mapproj::fromPeirceQuincuncial lambda_0 x y
62 ::mapproj::toOrthographic lambda_0 phi_0 lambda phi
64 ::mapproj::fromOrthographic lambda_0 phi_0 x y
66 ::mapproj::toStereographic lambda_0 phi_0 lambda phi
68 ::mapproj::fromStereographic lambda_0 phi_0 x y
70 ::mapproj::toGnomonic lambda_0 phi_0 lambda phi
72 ::mapproj::fromGnomonic lambda_0 phi_0 x y
74 ::mapproj::toAzimuthalEquidistant lambda_0 phi_0 lambda phi
76 ::mapproj::fromAzimuthalEquidistant lambda_0 phi_0 x y
78 ::mapproj::toLambertAzimuthalEqualArea lambda_0 phi_0 lambda phi
80 ::mapproj::fromLambertAzimuthalEqualArea lambda_0 phi_0 x y
82 ::mapproj::toHammer lambda_0 lambda phi
84 ::mapproj::fromHammer lambda_0 x y
86 ::mapproj::toConicEquidistant lambda_0 phi_0 phi_1 phi_2 lambda phi
88 ::mapproj::fromConicEquidistant lambda_0 phi_0 phi_1 phi_2 x y
90 ::mapproj::toAlbersEqualAreaConic lambda_0 phi_0 phi_1 phi_2 lambda phi
92 ::mapproj::fromAlbersEqualAreaConic lambda_0 phi_0 phi_1 phi_2 x y
94 ::mapproj::toLambertConformalConic lambda_0 phi_0 phi_1 phi_2 lambda
96 phi
97 ::mapproj::fromLambertConformalConic lambda_0 phi_0 phi_1 phi_2 x y
99 ::mapproj::toLambertCylindricalEqualArea lambda_0 phi_0 lambda phi
101 ::mapproj::fromLambertCylindricalEqualArea lambda_0 phi_0 x y
103 ::mapproj::toBehrmann lambda_0 phi_0 lambda phi
105 ::mapproj::fromBehrmann lambda_0 phi_0 x y
107 ::mapproj::toTrystanEdwards lambda_0 phi_0 lambda phi
109 ::mapproj::fromTrystanEdwards lambda_0 phi_0 x y
111 ::mapproj::toHoboDyer lambda_0 phi_0 lambda phi
113 ::mapproj::fromHoboDyer lambda_0 phi_0 x y
115 ::mapproj::toGallPeters lambda_0 phi_0 lambda phi
117 ::mapproj::fromGallPeters lambda_0 phi_0 x y
119 ::mapproj::toBalthasart lambda_0 phi_0 lambda phi
121 ::mapproj::fromBalthasart lambda_0 phi_0 x y
123_________________________________________________________________
125
127 The mapproj package provides a set of procedures for converting between
128 world co-ordinates (latitude and longitude) and map co-ordinates on a
129 number of different map projections.
130
132 The following commands convert between world co-ordinates and map co-
133 ordinates:
134 ::mapproj::toPlateCarree lambda_0 phi_0 lambda phi
136 Converts to the plate carrée (cylindrical equidistant) projec‐
137 tion.
138 ::mapproj::fromPlateCarree lambda_0 phi_0 x y
140 Converts from the plate carrée (cylindrical equidistant) projec‐
141 tion.
142 ::mapproj::toCylindricalEqualArea lambda_0 phi_0 lambda phi
144 Converts to the cylindrical equal-area projection.
145 ::mapproj::fromCylindricalEqualArea lambda_0 phi_0 x y
147 Converts from the cylindrical equal-area projection.
148 ::mapproj::toMercator lambda_0 phi_0 lambda phi
150 Converts to the Mercator (cylindrical conformal) projection.
151 ::mapproj::fromMercator lambda_0 phi_0 x y
153 Converts from the Mercator (cylindrical conformal) projection.
154 ::mapproj::toMillerCylindrical lambda_0 lambda phi
156 Converts to the Miller Cylindrical projection.
157 ::mapproj::fromMillerCylindrical lambda_0 x y
159 Converts from the Miller Cylindrical projection.
160 ::mapproj::toSinusoidal lambda_0 phi_0 lambda phi
162 Converts to the sinusoidal (Sanson-Flamsteed) projection. pro‐
163 jection.
164 ::mapproj::fromSinusoidal lambda_0 phi_0 x y
166 Converts from the sinusoidal (Sanson-Flamsteed) projection.
167 projection.
168 ::mapproj::toMollweide lambda_0 lambda phi
170 Converts to the Mollweide projection.
171 ::mapproj::fromMollweide lambda_0 x y
173 Converts from the Mollweide projection.
174 ::mapproj::toEckertIV lambda_0 lambda phi
176 Converts to the Eckert IV projection.
177 ::mapproj::fromEckertIV lambda_0 x y
179 Converts from the Eckert IV projection.
180 ::mapproj::toEckertVI lambda_0 lambda phi
182 Converts to the Eckert VI projection.
183 ::mapproj::fromEckertVI lambda_0 x y
185 Converts from the Eckert VI projection.
186 ::mapproj::toRobinson lambda_0 lambda phi
188 Converts to the Robinson projection.
189 ::mapproj::fromRobinson lambda_0 x y
191 Converts from the Robinson projection.
192 ::mapproj::toCassini lambda_0 phi_0 lambda phi
194 Converts to the Cassini (transverse cylindrical equidistant)
195 projection.
196 ::mapproj::fromCassini lambda_0 phi_0 x y
198 Converts from the Cassini (transverse cylindrical equidistant)
199 projection.
200 ::mapproj::toPeirceQuincuncial lambda_0 lambda phi
202 Converts to the Peirce Quincuncial Projection.
203 ::mapproj::fromPeirceQuincuncial lambda_0 x y
205 Converts from the Peirce Quincuncial Projection.
206 ::mapproj::toOrthographic lambda_0 phi_0 lambda phi
208 Converts to the orthographic projection.
209 ::mapproj::fromOrthographic lambda_0 phi_0 x y
211 Converts from the orthographic projection.
212 ::mapproj::toStereographic lambda_0 phi_0 lambda phi
214 Converts to the stereographic (azimuthal conformal) projection.
215 ::mapproj::fromStereographic lambda_0 phi_0 x y
217 Converts from the stereographic (azimuthal conformal) projec‐
218 tion.
219 ::mapproj::toGnomonic lambda_0 phi_0 lambda phi
221 Converts to the gnomonic projection.
222 ::mapproj::fromGnomonic lambda_0 phi_0 x y
224 Converts from the gnomonic projection.
225 ::mapproj::toAzimuthalEquidistant lambda_0 phi_0 lambda phi
227 Converts to the azimuthal equidistant projection.
228 ::mapproj::fromAzimuthalEquidistant lambda_0 phi_0 x y
230 Converts from the azimuthal equidistant projection.
231 ::mapproj::toLambertAzimuthalEqualArea lambda_0 phi_0 lambda phi
233 Converts to the Lambert azimuthal equal-area projection.
234 ::mapproj::fromLambertAzimuthalEqualArea lambda_0 phi_0 x y
236 Converts from the Lambert azimuthal equal-area projection.
237 ::mapproj::toHammer lambda_0 lambda phi
239 Converts to the Hammer projection.
240 ::mapproj::fromHammer lambda_0 x y
242 Converts from the Hammer projection.
243 ::mapproj::toConicEquidistant lambda_0 phi_0 phi_1 phi_2 lambda phi
245 Converts to the conic equidistant projection.
246 ::mapproj::fromConicEquidistant lambda_0 phi_0 phi_1 phi_2 x y
248 Converts from the conic equidistant projection.
249 ::mapproj::toAlbersEqualAreaConic lambda_0 phi_0 phi_1 phi_2 lambda phi
251 Converts to the Albers equal-area conic projection.
252 ::mapproj::fromAlbersEqualAreaConic lambda_0 phi_0 phi_1 phi_2 x y
254 Converts from the Albers equal-area conic projection.
255 ::mapproj::toLambertConformalConic lambda_0 phi_0 phi_1 phi_2 lambda
257 phi
258 Converts to the Lambert conformal conic projection.
259 ::mapproj::fromLambertConformalConic lambda_0 phi_0 phi_1 phi_2 x y
261 Converts from the Lambert conformal conic projection.
262 Among the cylindrical equal-area projections, there are a number of
264 choices of standard parallels that have names:
265 ::mapproj::toLambertCylindricalEqualArea lambda_0 phi_0 lambda phi
267 Converts to the Lambert cylindrical equal area projection.
268 (standard parallel is the Equator.)
269 ::mapproj::fromLambertCylindricalEqualArea lambda_0 phi_0 x y
271 Converts from the Lambert cylindrical equal area projection.
272 (standard parallel is the Equator.)
273 ::mapproj::toBehrmann lambda_0 phi_0 lambda phi
275 Converts to the Behrmann cylindrical equal area projection.
276 (standard parallels are 30 degrees North and South)
277 ::mapproj::fromBehrmann lambda_0 phi_0 x y
279 Converts from the Behrmann cylindrical equal area projection.
280 (standard parallels are 30 degrees North and South.)
281 ::mapproj::toTrystanEdwards lambda_0 phi_0 lambda phi
283 Converts to the Trystan Edwards cylindrical equal area projec‐
284 tion. (standard parallels are 37.4 degrees North and South)
285 ::mapproj::fromTrystanEdwards lambda_0 phi_0 x y
287 Converts from the Trystan Edwards cylindrical equal area projec‐
288 tion. (standard parallels are 37.4 degrees North and South.)
289 ::mapproj::toHoboDyer lambda_0 phi_0 lambda phi
291 Converts to the Hobo-Dyer cylindrical equal area projection.
292 (standard parallels are 37.5 degrees North and South)
293 ::mapproj::fromHoboDyer lambda_0 phi_0 x y
295 Converts from the Hobo-Dyer cylindrical equal area projection.
296 (standard parallels are 37.5 degrees North and South.)
297 ::mapproj::toGallPeters lambda_0 phi_0 lambda phi
299 Converts to the Gall-Peters cylindrical equal area projection.
300 (standard parallels are 45 degrees North and South)
301 ::mapproj::fromGallPeters lambda_0 phi_0 x y
303 Converts from the Gall-Peters cylindrical equal area projection.
304 (standard parallels are 45 degrees North and South.)
305 ::mapproj::toBalthasart lambda_0 phi_0 lambda phi
307 Converts to the Balthasart cylindrical equal area projection.
308 (standard parallels are 50 degrees North and South)
309 ::mapproj::fromBalthasart lambda_0 phi_0 x y
311 Converts from the Balthasart cylindrical equal area projection.
312 (standard parallels are 50 degrees North and South.)
313
315 The following arguments are accepted by the projection commands:
316 lambda Longitude of the point to be projected, in degrees.
318 phi Latitude of the point to be projected, in degrees.
320 lambda_0
322 Longitude of the center of the sheet, in degrees. For many pro‐
323 jections, this figure is also the reference meridian of the pro‐
324 jection.
325 phi_0 Latitude of the center of the sheet, in degrees. For the
327 azimuthal projections, this figure is also the latitude of the
328 center of the projection.
329 phi_1 Latitude of the first reference parallel, for projections that
331 use reference parallels.
332 phi_2 Latitude of the second reference parallel, for projections that
334 use reference parallels.
335 x X co-ordinate of a point on the map, in units of Earth radii.
337 y Y co-ordinate of a point on the map, in units of Earth radii.
339
341 For all of the procedures whose names begin with 'to', the return value
342 is a list comprising an x co-ordinate and a y co-ordinate. The co-
343 ordinates are relative to the center of the map sheet to be drawn, mea‐
344 sured in Earth radii at the reference location on the map. For all of
345 the functions whose names begin with 'from', the return value is a list
346 comprising the longitude and latitude, in degrees.
347
349 This package offers a great many projections, because no single projec‐
350 tion is appropriate to all maps. This section attempts to provide
351 guidance on how to choose a projection.
352 First, consider the type of data that you intend to display on the map.
354 If the data are directional (e.g., winds, ocean currents, or magnetic
355 fields) then you need to use a projection that preserves angles; these
356 are known as conformal projections. Conformal projections include the
357 Mercator, the Albers azimuthal equal-area, the stereographic, and the
358 Peirce Quincuncial projection. If the data are thematic, describing
359 properties of land or water, such as temperature, population density,
360 land use, or demographics; then you need a projection that will show
361 these data with the areas on the map proportional to the areas in real
362 life. These so-called equal area projections include the various
363 cylindrical equal area projections, the sinusoidal projection, the Lam‐
364 bert azimuthal equal-area projection, the Albers equal-area conic pro‐
365 jection, and several of the world-map projections (Miller Cylindrical,
366 Mollweide, Eckert IV, Eckert VI, Robinson, and Hammer). If the signifi‐
367 cant factor in your data is distance from a central point or line (such
368 as air routes), then you will do best with an equidistant projection
369 such as plate carrée, Cassini, azimuthal equidistant, or conic equidis‐
370 tant. If direction from a central point is a critical factor in your
371 data (for instance, air routes, radio antenna pointing), then you will
372 almost surely want to use one of the azimuthal projections. Appropriate
373 choices are azimuthal equidistant, azimuthal equal-area, stereographic,
374 and perhaps orthographic.
375 Next, consider how much of the Earth your map will cover, and the gen‐
377 eral shape of the area of interest. For maps of the entire Earth, the
378 cylindrical equal area, Eckert IV and VI, Mollweide, Robinson, and Ham‐
379 mer projections are good overall choices. The Mercator projection is
380 traditional, but the extreme distortions of area at high latitudes make
381 it a poor choice unless a conformal projection is required. The Peirce
382 projection is a better choice of conformal projection, having less dis‐
383 tortion of landforms. The Miller Cylindrical is a compromise designed
384 to give shapes similar to the traditional Mercator, but with less polar
385 stretching. The Peirce Quincuncial projection shows all the continents
386 with acceptable distortion if a reference meridian close to +20 degrees
387 is chosen. The Robinson projection yields attractive maps for things
388 like political divisions, but should be avoided in presenting scien‐
389 tific data, since other projections have moe useful geometric proper‐
390 ties.
391 If the map will cover a hemisphere, then choose stereographic,
393 azimuthal-equidistant, Hammer, or Mollweide projections; these all
394 project the hemisphere into a circle.
395 If the map will cover a large area (at least a few hundred km on a
397 side), but less than a hemisphere, then you have several choices.
398 Azimuthal projections are usually good (choose stereographic, azimuthal
399 equidistant, or Lambert azimuthal equal-area according to whether
400 shapes, distances from a central point, or areas are important).
401 Azimuthal projections (and possibly the Cassini projection) are the
402 only really good choices for mapping the polar regions.
403 If the large area is in one of the temperate zones and is round or has
405 a primarily east-west extent, then the conic projections are good
406 choices. Choose the Lambert conformal conic, the conic equidistant, or
407 the Albers equal-area conic according to whether shape, distance, or
408 area are the most important parameters. For any of these, the refer‐
409 ence parallels should be chosen at approximately 1/6 and 5/6 of the
410 range of latitudes to be displayed. For instance, maps of the 48
411 coterminous United States are attractive with reference parallels of
412 28.5 and 45.5 degrees.
413 If the large area is equatorial and is round or has a primarily east-
415 west extent, then the Mercator projection is a good choice for a con‐
416 formal projection; Lambert cylindrical equal-area and sinusoidal pro‐
417 jections are good equal-area projections; and the plate carrée is a
418 good equidistant projection.
419 Large areas having a primarily North-South aspect, particularly those
421 spanning the Equator, need some other choices. The Cassini projection
422 is a good choice for an equidistant projection (for instance, a Cassini
423 projection with a central meridian of 80 degrees West produces an
424 attractive map of the Americas). The cylindrical equal-area, Albers
425 equal-area conic, sinusoidal, Mollweide and Hammer projections are pos‐
426 sible choices for equal-area projections. A good conformal projection
427 in this situation is the Transverse Mercator, which alas, is not yet
428 implemented.
429 Small areas begin to get into a realm where the ellipticity of the
431 Earth affects the map scale. This package does not attempt to handle
432 accurate mapping for large-scale topographic maps. If slight scale
433 errors are acceptable in your application, then any of the projections
434 appropriate to large areas should work for small ones as well.
435 There are a few projections that are included for their special proper‐
437 ties. The orthographic projection produces views of the Earth as seen
438 from space. The gnomonic projection produces a map on which all great
439 circles (the shortest distance between two points on the Earth's sur‐
440 face) are rendered as straight lines. While this projection is useful
441 for navigational planning, it has extreme distortions of shape and
442 area, and can display only a limited area of the Earth (substantially
443 less than a hemisphere).
444
446 Copyright (c) 2007 Kevin B. Kenny <kennykb@acm.org>
447mapproj 0.1 mapproj(n)