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diff --git a/static/unix-v10/man3/proj.3 b/static/unix-v10/man3/proj.3 new file mode 100644 index 00000000..95a86ac7 --- /dev/null +++ b/static/unix-v10/man3/proj.3 @@ -0,0 +1,370 @@ +.TH PROJ 3X bowell +.CT 2 graphics math +.br +.SH NAME +orient, normalize \- map projections +.SH SYNOPSIS +.B orient(lat, lon, rot) +.br +.B float lat, lon, rot; +.PP +.B normalize(p) +.br +.B struct place *p; +.SH DESCRIPTION +Users of +.IR map (7) +may skip to the description of `Projection generators' +below. +.PP +The functions +.I orient +and +.I normalize +plus a collection of map projection generators +are loaded by +option +.BR -lmap +of +.IR ld (1). +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. +.PP +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 +.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 (the overlay's) meridian +.I rot. +Project the desired map in +the standard form appropriate to the overlay, but presenting +information from the underlying globe. +It is not useful to use +.I orient +without using +.IR normalize . +.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 +.B place +structure. +Transformed coordinates and their sines and cosines +are returned in the same structure. +.PP +.EX +.nr xx \w'12345678' +.ta \n(xxu +\n(xxu +\n(xxu +\n(xxu +\n(xxu +\n(xxu + struct place { + float radianlat, sinlat, coslat; + float radianlon, sinlon, coslon; + }; +.EE +.PP +The projection generators +return a pointer to a function that converts normalized coordinates +to +.I x-y +coordinates for the desired map, or +0 if the required projection +is not available. +The returned function is exemplified by +.I proj +in this example: +.PP +.EX +.ta \n(xxu +\n(xxu +\n(xxu +\n(xxu +\n(xxu +\n(xxu + struct place pt; + int (*proj)() = mercator(); + float x, y; +.EE +.PP +.EX + orient(45.0, 30.0, 180.0); /* set coordinate rotation */ +.EE +.PP +.EX + . . . /* fill in the pt structure */ + normalize(&pt); /* rotate coordinates */ + if((*proj)(&pt, &x, &y) > 0) /* project onto x,y plane */ + plot(x, y); +.EE +.PP +The projection function +.B (*proj)() +returns 1 for a good point, +0 for a point on a wrong +sheet (e.g. the back of the world in a perspective +projection), and \-1 for a point that is deemed +unplottable (e.g. points near the poles on a Mercator projection). +.PP +Scaling may be determined from the +.I x-y +coordinates of +selected points. +Latitudes and longitudes are measured in degrees for +ease of specification for +.I orient +and the projection generators +but in radians for ease of calculation +for +.I normalize +and +.I proj. +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. +.SS Projection generators +Equatorial projections centered on the Prime Meridian +(longitude 0). +Parallels are straight horizontal lines. +.br +.ns +.IP +.B mercator() +equally spaced straight meridians, conformal, +straight compass courses +.br +.B sinusoidal() +equally spaced parallels, +equal-area, same as +.I bonne(0) +.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(lat0) +equally spaced parallels, equally spaced straight meridians, true scale on +.I lat0 +.br +.B gall(lat0) +parallels spaced stereographically on prime meridian, equally spaced straight +meridians, true scale on +.I lat0 +.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. +.br +.ns +.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 along earth's axis +.I dist +earth radii from center of earth +.br +.B orthographic() +viewed from infinity +.br +.B stereographic() +conformal, projected from opposite pole +.br +.B laue() +.IR radius " = tan(2\(mu" colatitude ), +used in xray crystallography +.br +.B fisheye(r) +.IR radius " = log(" colatitude / r ): +.I New Yorker +map from viewing pedestal of radius +.I r +degrees +.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. +.br +.ns +.IP +.B conic(lat0) +central projection on cone tangent at +.I lat0 +.br +.B simpleconic(lat0,lat1) +equally spaced parallels, true scale on +.I lat0 +and +.I lat1 +.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 +.br +.B bonne(lat0) +equally spaced parallels, equal-area, +parallel +.I lat0 +developed from tangent cone +.PP +Projections with bilateral symmetry about +the Prime Meridian +and the equator. +.br +.ns +.IP +.B polyconic() +parallels developed from tangent cones, +equally spaced along Prime Meridian +.br +.B aitoff() +equal-area projection of globe onto 2-to-1 +ellipse, based on +.I azequalarea +.br +.B lagrange() +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 longitudes +.I \(+-lon0 +.br +.B globular() +hemisphere is circle, +circular arc meridians equally spaced on equator, +circular arc parallels equally spaced on 0- and 90-degree meridians +.br +.B vandergrinten() +sphere is circle, +meridians as in +.I globular, +circular arc parallels resemble +.I mercator +.PP +Doubly periodic conformal projections. +.br +.ns +.IP +.B guyou() +W and E hemispheres are square +.br +.B square() +world is square with Poles +at diagonally opposite corners +.br +.B tetra() +map on tetrahedron with edge +tangent to Prime Meridian at S Pole, +unfolded into equilateral triangle +.br +.B hex() +world is hexagon centered +on N Pole, N and S hemispheres are equilateral +triangles +.PP +Miscellaneous projections. +.br +.ns +.IP +.B harrison(dist,angle) +oblique perspective from above the North Pole, +.I dist +earth radii from center of earth, looking +along the Date Line +.I angle +degrees off vertical +.br +.B trapezoidal(lat0,lat1) +equally spaced parallels, +straight meridians equally spaced along parallels, +true scale at +.I lat0 +and +.I lat1 +on Prime Meridian +.PP +Retroazimuthal projections. +At every point the angle between vertical and a straight line to +`Mecca', latitude +.I lat0 +on the prime meridian, +is the true bearing of Mecca. +.br +.ns +.IP +.B mecca(lat0) +equally spaced vertical meridians +.br +.B homing(lat0) +distances to `Mecca' are true +.PP +Maps based on the spheroid. +Of geodetic quality, these projections do not make sense +for tilted orientations. +For descriptions, see corresponding maps above. +.br +.ns +.IP +.B sp_mercator() +.br +.B sp_albers(lat0,lat1) +.SH "SEE ALSO +.IR map (7), +.IR map (5), +.IR plot (3) +.SH BUGS +Only one projection and one orientation can be active at a time. +.br +The west-longitude-positive convention +betrays Yankee chauvinism. |