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mapproject

Apply a Map Projection

Description

Converts latitude and longitude into projected coordinates.

Usage

mapproject(x, y, projection="", parameters=NULL, orientation=NULL)

Arguments

x,y

two vectors giving longitude and latitude coordinates of points on the earth's surface to be projected. A list containing components named x and y, giving the coordinates of the points to be projected may also be given. Missing values (NAs) are allowed. The coordinate system is degrees of longitude east of Greenwich (so the USA is bounded by negative longitudes) and degrees north of the equator.

projection

optional character string that names a map projection to use. If the string is "" then the previous projection is used, with parameters modified by the next two arguments.

parameters

optional numeric vector of parameters for use with the projection argument. This argument is optional only in the sense that certain projections do not require additional parameters. If a projection does require additional parameters, these must be given in the parameters argument.

orientation

An optional vector c(latitude,longitude,rotation) which describes where the "North Pole" should be when computing the projection. Normally this is c(90,0), which is appropriate for cylindrical and conic projections. For a planar projection, you should set it to the desired point of tangency. The third value is a clockwise rotation (in degrees), which defaults to the midrange of the longitude coordinates in the map. This means that two maps plotted with their own default orientation may not line up. To avoid this, you should not specify a projection twice but rather default to the previous projection using projection="". See the examples.

Details

Each standard projection is displayed with the Prime Meridian (longitude 0) being a straight vertical line, along which North is up. The orientation of nonstandard projections is specified by the three parameters=c(lat,lon,rot). Imagine a transparent gridded sphere around the globe. First turn the overlay about the North Pole so that the Prime Meridian (longitude 0) of the overlay coincides with meridian lon on the globe. Then tilt the North Pole of the overlay along its Prime Meridian to latitude lat on the globe. Finally again turn the overlay about its "North Pole" so that its Prime Meridian coincides with the previous position of (the overlay) meridian rot. Project the desired map in the standard form appropriate to the overlay, but presenting information from the underlying globe.

In the descriptions that follow each projection is shown as a function call; if it requires parameters, these are shown as arguments to the function. The descriptions are grouped into families.

Equatorial projections centered on the Prime Meridian (longitude 0). Parallels are straight horizontal lines.

mercator()

equally spaced straight meridians, conformal, straight compass courses

sinusoidal()

equally spaced parallels, equal-area, same as bonne(0)

cylequalarea(lat0)

equally spaced straight meridians, equal-area, true scale on lat0

cylindrical()

central projection on tangent cylinder

rectangular(lat0)

equally spaced parallels, equally spaced straight meridians, true scale on lat0

gall(lat0)

parallels spaced stereographically on prime meridian, equally spaced straight meridians, true scale on lat0

mollweide()

(homalographic) equal-area, hemisphere is a circle

gilbert()

sphere conformally mapped on hemisphere and viewed orthographically

Azimuthal projections centered on the North Pole. Parallels are concentric circles. Meridians are equally spaced radial lines.

azequidistant()

equally spaced parallels, true distances from pole

azequalarea()

equal-area

gnomonic()

central projection on tangent plane, straight great circles

perspective(dist)

viewed along earth's axis dist earth radii from center of earth

orthographic()

viewed from infinity

stereographic()

conformal, projected from opposite pole

laue()

radius = tan(2 * colatitude) used in xray crystallography

fisheye(n)

stereographic seen through medium with refractive index n

newyorker(r)

radius = log(colatitude/r) map from viewing pedestal of radius r degrees

Polar conic projections symmetric about the Prime Meridian. Parallels are segments of concentric circles. Except in the Bonne projection, meridians are equally spaced radial lines orthogonal to the parallels.

conic(lat0)

central projection on cone tangent at lat0

simpleconic(lat0,lat1)

equally spaced parallels, true scale on lat0 and lat1

lambert(lat0,lat1)

conformal, true scale on lat0 and lat1

albers(lat0,lat1)

equal-area, true scale on lat0 and lat1

bonne(lat0)

equally spaced parallels, equal-area, parallel lat0 developed from tangent cone

Projections with bilateral symmetry about the Prime Meridian and the equator.

polyconic()

parallels developed from tangent cones, equally spaced along Prime Meridian

aitoff()

equal-area projection of globe onto 2-to-1 ellipse, based on azequalarea

lagrange()

conformal, maps whole sphere into a circle

bicentric(lon0)

points plotted at true azimuth from two centers on the equator at longitudes +lon0 and -lon0, great circles are straight lines (a stretched gnomonic projection)

elliptic(lon0)

points are plotted at true distance from two centers on the equator at longitudes +lon0 and -lon0

globular()

hemisphere is circle, circular arc meridians equally spaced on equator, circular arc parallels equally spaced on 0- and 90-degree meridians

vandergrinten()

sphere is circle, meridians as in globular, circular arc parallels resemble mercator

eisenlohr()

conformal with no singularities, shaped like polyconic

Doubly periodic conformal projections.

guyou

W and E hemispheres are square

square

world is square with Poles at diagonally opposite corners

tetra

map on tetrahedron with edge tangent to Prime Meridian at S Pole, unfolded into equilateral triangle

hex

world is hexagon centered on N Pole, N and S hemispheres are equilateral triangles

Miscellaneous projections.

harrison(dist,angle)

oblique perspective from above the North Pole, dist earth radii from center of earth, looking along the Date Line angle degrees off vertical

trapezoidal(lat0,lat1)

equally spaced parallels, straight meridians equally spaced along parallels, true scale at lat0 and lat1 on Prime Meridian

lune(lat,angle)

conformal, polar cap above latitude lat maps to convex lune with given angle at 90E and 90W

Retroazimuthal projections. At every point the angle between vertical and a straight line to "Mecca", latitude lat0 on the prime meridian, is the true bearing of Mecca.

mecca(lat0)

equally spaced vertical meridians

homing(lat0)

distances to Mecca are true

Maps based on the spheroid. Of geodetic quality, these projections do not make sense for tilted orientations.

sp\_mercator()

Mercator on the spheroid.

sp\_albers(lat0,lat1)

Albers on the spheroid.

Value

list with components named x and y, containing the projected coordinates. NAs project to NAs. Points deemed unprojectable (such as north of 80 degrees latitude in the Mercator projection) are returned as NA. Because of the ambiguity of the first two arguments, the other arguments must be given by name.

Each time mapproject is called, it leaves on frame 0 the dataset .Last.projection, which is a list with components projection, parameters, and orientation giving the arguments from the call to mapproject or as constructed (for orientation). Subsequent calls to mapproject will get missing information from .Last.projection. Since map uses mapproject to do its projections, calls to mapproject after a call to map need not supply any arguments other than the data.

References

Richard A. Becker, and Allan R. Wilks, "Maps in S", AT\&T Bell Laboratories Statistics Research Report, 1991. http://www.research.att.com/areas/stat/doc/93.2.ps

M. D. McIlroy, Documentation from the Tenth Edition UNIX Manual, Volume 1, Saunders College Publishing, 1990.

Examples

library(maps)
# Bonne equal-area projection with state abbreviations
map("state",proj='bonne', param=45)
data(state)
text(mapproject(state.center), state.abb)

# this does not work because the default orientations are different:
map("state",proj='bonne', param=45)
text(mapproject(state.center,proj='bonne',param=45),state.abb)

map("state",proj="albers",par=c(30,40))
map("state",par=c(20,50)) # another Albers projection

map("world",proj="gnomonic",orient=c(0,-100,0)) # example of orient
# see map.grid for more examples

# tests of projections added RSB 091101
projlist <- c("aitoff", "albers", "azequalarea", "azequidist", "bicentric",
 "bonne", "conic", "cylequalarea", "cylindrical", "eisenlohr", "elliptic",
 "fisheye", "gall", "gilbert", "guyou", "harrison", "hex", "homing",
 "lagrange", "lambert", "laue", "lune", "mercator", "mollweide", "newyorker",
 "orthographic", "perspective", "polyconic", "rectangular", "simpleconic",
 "sinusoidal", "tetra", "trapezoidal")
x <- seq(-100, 0, 10)
y <- seq(-45, 45, 10)
xy <- expand.grid(x=x, y=y)
pf <- c(0, 2, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 1, 0, 2, 0, 2,
 0, 0, 1, 0, 1, 0, 1, 2, 0, 0, 2)
res <- vector(mode="list", length=length(projlist))
for (i in seq(along=projlist)) {
 if (pf[i] == 0) res[[i]] <- mapproject(xy$x, xy$y, projlist[i])
 else if (pf[i] == 1) res[[i]] <- mapproject(xy$x, xy$y, projlist[i], 0)
 else res[[i]] <- mapproject(xy$x, xy$y, projlist[i], c(0,0))
}
names(res) <- projlist
lapply(res, function(p) rbind(p$x, p$y))
mapproj

Map Projections

v1.2.7
Lucent Public License
Authors
Doug McIlroy. Packaged for R by Ray Brownrigg and Thomas P Minka, transition to Plan 9 codebase by Roger Bivand.
Initial release
2020-01-31

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