term% cat index.txt MAP(3X) MAP(3X)
NAME
orient, normalize - map projections
SYNOPSIS
orient(lat, lon, rot)
float lat, lon, rot;
struct place {
float latrad, latsin, latcos;
float lonrad, lonsin, loncos;
};
normalize(p)
struct place *p;
int (*projection())()
int project(p, xptr, yptr)
struct place p;
float *xptr, *yptr;
DESCRIPTION
These functions are loaded with ld(1) option -lmap. Most of them cal‐
culate maps for a spherical earth. Each map projection is available in
one standard form, into which data must be normalized for transverse or
nonpolar projections. The projection is specified by invoking one of
the following functions, known collectively as projection. Each func‐
tion returns the name project of a function that will do the actual
work of calculating coordinates, or 0 if the required projection is not
available. The short summaries of properties pertain to standard maps
of the earth in standard orientation.
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
cylequalarea(lat0) equally spaced straight meridians, equal-
area, true scale on lat0
cylindrical() central projection on tangent cylinder
rectangular() equally spaced straight parallels and meridians
mollweide() (homalographic) equal-area, hemisphere is a circle
Azimuthal projections centered on the North Pole. Parallels are con‐
centric 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 dist earth radii from center of earth
orthographic() viewed from infinity
stereographic() conformal, viewed from opposite pole
laue() radius = tan(2×colatitude), used in xray crystallography
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
bonne(lat0) equally spaced parallels, equal-area, parallel lat0
developed from tangent cone
lambert(lat0,lat1) conformal, true scale on lat0 and lat1
albers(lat0,lat1) equal-area, true scale on lat0 and lat1
Projections with bilateral symmetry about the Prime Meridian and the
equator.
polyconic() parallels developed from tangent cones uniformly
distributed along Prime Meridian
aitoff() equal-area projection of globe onto 2-to-1 ellipse,
based on azimuthal equal area projection
gilbert() conformal, maps whole sphere into a circle
bicentric(lon0) points plotted at true azimuth from two centers
on the equator at longitudes ±lon0, great circles are straight
lines (a stretched gnomonic projection)
elliptic(lon0) points are plotted at true distance from two cen‐
ters on the equator at longitude ±lon0
Doubly periodic projections.
guyou() conformal, W and E hemispheres are square
square() conformal, world is square with Poles at diagonally op‐
posite corners
tetra() conformal map onto regular tetrahedron with an edge tan‐
gent to the Prime Meridian at the South Pole, developed into
equilateral triangle
hex() conformal map onto a hexagon centered on North Pole, N and
S hemispheres are equilateral triangles
Miscellaneous.
mecca(lat0) equally spaced vertical meridians, straight line
from any point to `Mecca' (lat0 on the Prime Meridian) has the
true bearing of Mecca
Maps based on the spheroid. Of geodetic quality, these projections do
not make sense for tilted orientations (see below). For descriptions,
see corresponding maps above.
sp_mercator()
sp_albers(lat0,lat1)
The project functions return a value 1 for a good point, 0 for a point
on a wrong sheet (for example the back of the world in a perspective
projection), and -1 for a point that is deemed unplottable.
Each standard projection is displayed with the Prime Meridian being a
straight vertical line, along which North is up. The orientation of
nonstandard projections is specified by orient. 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 co‐
incides with meridian lon on the globe. Then tilt the North Pole of
the overlay along its Prime Meridian to latitude lat on the globe. Fi‐
nally again turn the overlay about its `North Pole' so that its Prime
Meridian coincides with the previous position of meridian rot. Project
the desired map in the standard form appropriate to the overlay, but
presenting information from the underlying globe.
Normalize converts latitude-longitude coordinates on the globe to coor‐
dinates on the overlaid grid. The coordinates and their sines and
cosines are input to normalize in a structure pointed to by p. Trans‐
formed coordinates and their sines and cosines are returned in the same
structure.
The project functions convert normalized coordinates in the structure
pointed to by p to x-y coordinates for the desired map. Scaling may be
determined from the x-y coordinates of selected points.
Latitudes and longitudes are measured in degrees for ease of specifica‐
tion for orient and projection, but in radians for ease of calculation
for normalize and project. In either case latitude is measured posi‐
tive north of the equator, and longitude positive west of Greenwich.
Radian longitude should be limited to the range -pi <= lon < pi.
SEE ALSO
map(7), map(5), plot(3)
local MAP(3X)