V8/usr/man/man3/map.3

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.TH MAP 3X local
.br
.SH NAME
orient, normalize \- map projections
.SH SYNOPSIS
.B orient(lat, lon, rot)
.br
.B float lat, lon, rot;
.PP
.ft B
.nf
struct place {
	float latrad, latsin, latcos;
	float lonrad, lonsin, loncos;
};
.fi
.ft R
.PP
.B normalize(p)
.br
.B struct place *p;
.PP
.B int
.BR (* projection ())()
.PP
.B int
.RB project (p,
.B xptr, yptr)
.br
.B struct place p;
.br
.B float *xptr, *yptr;
.SH DESCRIPTION
These functions are loaded with
.IR ld (1)
option
.BR \-lmap .
Most of them
calculate 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
.I projection.
Each function returns the name
.I 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.
.PP
Equatorial projections centered on the Prime Meridian
(longitude 0).
Parallels are straight horizontal lines.
.IP
.B mercator()
equally spaced straight meridians, conformal,
straight compass courses
.br
.B sinusoidal()
equally spaced parallels,
equal-area
.br
.B cylequalarea(lat0)
equally spaced straight meridians, equal-area,
true scale on
.I lat0
.br
.B cylindrical()
central projection on tangent cylinder
.br
.B rectangular()
equally spaced straight parallels and meridians
.br
.B mollweide()
(homalographic) equal-area, hemisphere is a circle
.PP
Azimuthal projections centered on the North Pole.
Parallels are concentric circles.
Meridians are equally spaced radial lines.
.IP
.B azequidistant()
equally spaced parallels,
true distances from pole
.br
.B azequalarea()
equal-area
.br
.B gnomonic()
central projection on tangent plane,
straight great circles
.br
.B perspective(dist)
viewed
.I dist
earth radii from center of earth
.br
.B orthographic()
viewed from infinity
.br
.B stereographic()
conformal, viewed from opposite pole
.br
.B laue()
radius = tan(2\(mucolatitude), used in xray crystallography
.PP
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.
.IP
.B conic(lat0)
central projection on cone tangent at
.I lat0
.br
.B bonne(lat0)
equally spaced parallels, equal-area,
parallel
.I lat0
developed from tangent cone
.br
.B lambert(lat0,lat1)
conformal, true scale on 
.I lat0
and 
.I lat1
.br
.B albers(lat0,lat1)
equal-area, true scale on
.I lat0
and 
.I lat1
.PP
Projections with bilateral symmetry about
the Prime Meridian
and the equator.
.IP
.B polyconic()
parallels developed from tangent cones
uniformly distributed along Prime Meridian
.br
.B aitoff()
equal-area projection of globe onto 2-to-1
ellipse, based on azimuthal equal area projection
.br
.B gilbert()
conformal, maps whole sphere into a circle
.br
.B bicentric(lon0)
points plotted at true azimuth from two
centers on the equator at longitudes
.I \(+-lon0,
great circles are straight lines
(a stretched gnomonic projection)
.br
.B elliptic(lon0)
points are plotted at true distance from
two centers on the equator at longitude
.I \(+-lon0
.PP
Doubly periodic projections.
.IP
.B guyou()
conformal, W and E hemispheres are square
.br
.B square()
conformal, world is square with Poles
at diagonally opposite corners
.br
.B tetra()
conformal map onto regular tetrahedron with an edge
tangent to the Prime Meridian at the South Pole,
developed into equilateral triangle
.br
.B hex()
conformal map onto a hexagon centered
on North Pole, N and S hemispheres are equilateral
triangles
.PP
Miscellaneous.
.IP
.B mecca(lat0)
equally spaced vertical meridians,
straight line from any point to `Mecca'
.RI ( lat0
on the Prime Meridian)
has the true bearing of Mecca
.PP
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.
.IP
.B sp_mercator()
.br
.B sp_albers(lat0,lat1)
.PP
The
.I 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.
.PP
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
.I 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 coincides with meridian
.I lon
on the globe.
Then tilt the North Pole of the
overlay along its Prime Meridian to latitude
.I lat
on the globe.
Finally again turn the
overlay about its `North Pole' so
that its Prime Meridian coincides with the previous position
of meridian
.I rot.
Project the desired map in
the standard form appropriate to the overlay, but presenting
information from the underlying globe.
.PP
.I Normalize
converts latitude-longitude coordinates on the globe
to coordinates on the overlaid grid.
The coordinates and their sines and cosines
are input to
.I normalize
in a structure pointed to by
.I p.
Transformed coordinates and their sines and cosines
are returned in the same structure.
.PP
The
.I project
functions convert normalized coordinates in the structure pointed to by
.I p
to x-y coordinates
for the desired map.
Scaling may be determined from the x-y coordinates of
selected points.
.PP
Latitudes and longitudes are measured in degrees for
ease of specification for
.I orient 
and
.I projection,
but in radians for ease of calculation 
for
.I normalize
and
.I project.
In either case
latitude is measured positive north of the equator,
and longitude positive west of Greenwich.
Radian longitude should be limited to the range
.if t .I \-\(*p\(<=lon<\(*p.
.if n .I -pi <= lon < pi.
.SH "SEE ALSO"
map(7), map(5), plot(3)