'\"
'\" Generated from file 'mapproj\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2007 Kevin B\&. Kenny <kennykb@acm\&.org>
'\"
.TH "mapproj" n 1\&.1 tcllib "Tcl Library"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
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.if t .wh -1.3i ^B
.nr ^l \n(.l
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.de AP
.ie !"\\$4"" .TP \\$4
.el \{\
.   ie !"\\$2"" .TP \\n()Cu
.   el          .TP 15
.\}
.ta \\n()Au \\n()Bu
.ie !"\\$3"" \{\
\&\\$1 \\fI\\$2\\fP (\\$3)
.\".b
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.el \{\
.br
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.el \{\
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.AS Tcl_Interp Tcl_CreateInterp in/out
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\h'-1.5n'\L'|\\n(^yu-1v'\l'\\n(^lu+3n\(ul'\L'\\n(^tu+1v-\\n(^yu'\l'|0u-1.5n\(ul'
.\}
.el \}\
\h'-1.5n'\L'|\\n(^yu-1v'\h'\\n(^lu+3n'\L'\\n(^tu+1v-\\n(^yu'\l'|0u-1.5n\(ul'
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.\}
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.nr ^x \\n(^tu+1v-\\n(^Yu
\kx\h'-\\nxu'\h'|\\n(^lu+3n'\ky\L'-\\n(^xu'\v'\\n(^xu'\h'|0u'\c
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.de SO
'ie '\\$1'' .ds So \\fBoptions\\fR
'el .ds So \\fB\\$1\\fR
.SH "STANDARD OPTIONS"
.LP
.nf
.ta 5.5c 11c
.ft B
..
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.de SE
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.ft R
.LP
See the \\*(So manual entry for details on the standard options.
..
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.de OP
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.ta 4c
Command-Line Name:	\\fB\\$1\\fR
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.BS
.SH NAME
mapproj \- Map projection routines
.SH SYNOPSIS
package require \fBTcl ?8\&.5 9?\fR
.sp
package require \fBmath::interpolate ?1\&.1?\fR
.sp
package require \fBmath::special ?0\&.2\&.2?\fR
.sp
package require \fBmapproj ?1\&.1?\fR
.sp
\fB::mapproj::toPlateCarree\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromPlateCarree\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toCylindricalEqualArea\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromCylindricalEqualArea\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toMercator\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromMercator\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toMillerCylindrical\fR \fIlambda_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromMillerCylindrical\fR \fIlambda_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toSinusoidal\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromSinusoidal\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toMollweide\fR \fIlambda_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromMollweide\fR \fIlambda_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toEckertIV\fR \fIlambda_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromEckertIV\fR \fIlambda_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toEckertVI\fR \fIlambda_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromEckertVI\fR \fIlambda_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toRobinson\fR \fIlambda_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromRobinson\fR \fIlambda_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toCassini\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromCassini\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toPeirceQuincuncial\fR \fIlambda_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromPeirceQuincuncial\fR \fIlambda_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toOrthographic\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromOrthographic\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toStereographic\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromStereographic\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toGnomonic\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromGnomonic\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toAzimuthalEquidistant\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromAzimuthalEquidistant\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toLambertAzimuthalEqualArea\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromLambertAzimuthalEqualArea\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toHammer\fR \fIlambda_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromHammer\fR \fIlambda_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toConicEquidistant\fR \fIlambda_0\fR \fIphi_0\fR \fIphi_1\fR \fIphi_2\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromConicEquidistant\fR \fIlambda_0\fR \fIphi_0\fR \fIphi_1\fR \fIphi_2\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toAlbersEqualAreaConic\fR \fIlambda_0\fR \fIphi_0\fR \fIphi_1\fR \fIphi_2\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromAlbersEqualAreaConic\fR \fIlambda_0\fR \fIphi_0\fR \fIphi_1\fR \fIphi_2\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toLambertConformalConic\fR \fIlambda_0\fR \fIphi_0\fR \fIphi_1\fR \fIphi_2\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromLambertConformalConic\fR \fIlambda_0\fR \fIphi_0\fR \fIphi_1\fR \fIphi_2\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toLambertCylindricalEqualArea\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromLambertCylindricalEqualArea\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toBehrmann\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromBehrmann\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toTrystanEdwards\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromTrystanEdwards\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toHoboDyer\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromHoboDyer\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toGallPeters\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromGallPeters\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
.sp
\fB::mapproj::toBalthasart\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
.sp
\fB::mapproj::fromBalthasart\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
.sp
.BE
.SH DESCRIPTION
The \fBmapproj\fR package provides a set of procedures for
converting between world co-ordinates (latitude and longitude) and map
co-ordinates on a number of different map projections\&.
.SH COMMANDS
The following commands convert between world co-ordinates and
map co-ordinates:
.TP
\fB::mapproj::toPlateCarree\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
Converts to the \fIplate carrée\fR (cylindrical equidistant)
projection\&.
.TP
\fB::mapproj::fromPlateCarree\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
Converts from the \fIplate carrée\fR (cylindrical equidistant)
projection\&.
.TP
\fB::mapproj::toCylindricalEqualArea\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
Converts to the cylindrical equal-area projection\&.
.TP
\fB::mapproj::fromCylindricalEqualArea\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
Converts from the cylindrical equal-area projection\&.
.TP
\fB::mapproj::toMercator\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
Converts to the Mercator (cylindrical conformal) projection\&.
.TP
\fB::mapproj::fromMercator\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
Converts from the Mercator (cylindrical conformal) projection\&.
.TP
\fB::mapproj::toMillerCylindrical\fR \fIlambda_0\fR \fIlambda\fR \fIphi\fR
Converts to the Miller Cylindrical projection\&.
.TP
\fB::mapproj::fromMillerCylindrical\fR \fIlambda_0\fR \fIx\fR \fIy\fR
Converts from the Miller Cylindrical projection\&.
.TP
\fB::mapproj::toSinusoidal\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
Converts to the sinusoidal (Sanson-Flamsteed) projection\&.
projection\&.
.TP
\fB::mapproj::fromSinusoidal\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
Converts from the sinusoidal (Sanson-Flamsteed) projection\&.
projection\&.
.TP
\fB::mapproj::toMollweide\fR \fIlambda_0\fR \fIlambda\fR \fIphi\fR
Converts to the Mollweide projection\&.
.TP
\fB::mapproj::fromMollweide\fR \fIlambda_0\fR \fIx\fR \fIy\fR
Converts from the Mollweide projection\&.
.TP
\fB::mapproj::toEckertIV\fR \fIlambda_0\fR \fIlambda\fR \fIphi\fR
Converts to the Eckert IV projection\&.
.TP
\fB::mapproj::fromEckertIV\fR \fIlambda_0\fR \fIx\fR \fIy\fR
Converts from the Eckert IV projection\&.
.TP
\fB::mapproj::toEckertVI\fR \fIlambda_0\fR \fIlambda\fR \fIphi\fR
Converts to the Eckert VI projection\&.
.TP
\fB::mapproj::fromEckertVI\fR \fIlambda_0\fR \fIx\fR \fIy\fR
Converts from the Eckert VI projection\&.
.TP
\fB::mapproj::toRobinson\fR \fIlambda_0\fR \fIlambda\fR \fIphi\fR
Converts to the Robinson projection\&.
.TP
\fB::mapproj::fromRobinson\fR \fIlambda_0\fR \fIx\fR \fIy\fR
Converts from the Robinson projection\&.
.TP
\fB::mapproj::toCassini\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
Converts to the Cassini (transverse cylindrical equidistant)
projection\&.
.TP
\fB::mapproj::fromCassini\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
Converts from the Cassini (transverse cylindrical equidistant)
projection\&.
.TP
\fB::mapproj::toPeirceQuincuncial\fR \fIlambda_0\fR \fIlambda\fR \fIphi\fR
Converts to the Peirce Quincuncial Projection\&.
.TP
\fB::mapproj::fromPeirceQuincuncial\fR \fIlambda_0\fR \fIx\fR \fIy\fR
Converts from the Peirce Quincuncial Projection\&.
.TP
\fB::mapproj::toOrthographic\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
Converts to the orthographic projection\&.
.TP
\fB::mapproj::fromOrthographic\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
Converts from the orthographic projection\&.
.TP
\fB::mapproj::toStereographic\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
Converts to the stereographic (azimuthal conformal) projection\&.
.TP
\fB::mapproj::fromStereographic\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
Converts from the stereographic (azimuthal conformal) projection\&.
.TP
\fB::mapproj::toGnomonic\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
Converts to the gnomonic projection\&.
.TP
\fB::mapproj::fromGnomonic\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
Converts from the gnomonic projection\&.
.TP
\fB::mapproj::toAzimuthalEquidistant\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
Converts to the azimuthal equidistant projection\&.
.TP
\fB::mapproj::fromAzimuthalEquidistant\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
Converts from the azimuthal equidistant projection\&.
.TP
\fB::mapproj::toLambertAzimuthalEqualArea\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
Converts to the Lambert azimuthal equal-area projection\&.
.TP
\fB::mapproj::fromLambertAzimuthalEqualArea\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
Converts from the Lambert azimuthal equal-area projection\&.
.TP
\fB::mapproj::toHammer\fR \fIlambda_0\fR \fIlambda\fR \fIphi\fR
Converts to the Hammer projection\&.
.TP
\fB::mapproj::fromHammer\fR \fIlambda_0\fR \fIx\fR \fIy\fR
Converts from the Hammer projection\&.
.TP
\fB::mapproj::toConicEquidistant\fR \fIlambda_0\fR \fIphi_0\fR \fIphi_1\fR \fIphi_2\fR \fIlambda\fR \fIphi\fR
Converts to the conic equidistant projection\&.
.TP
\fB::mapproj::fromConicEquidistant\fR \fIlambda_0\fR \fIphi_0\fR \fIphi_1\fR \fIphi_2\fR \fIx\fR \fIy\fR
Converts from the conic equidistant projection\&.
.TP
\fB::mapproj::toAlbersEqualAreaConic\fR \fIlambda_0\fR \fIphi_0\fR \fIphi_1\fR \fIphi_2\fR \fIlambda\fR \fIphi\fR
Converts to the Albers equal-area conic projection\&.
.TP
\fB::mapproj::fromAlbersEqualAreaConic\fR \fIlambda_0\fR \fIphi_0\fR \fIphi_1\fR \fIphi_2\fR \fIx\fR \fIy\fR
Converts from the Albers equal-area conic projection\&.
.TP
\fB::mapproj::toLambertConformalConic\fR \fIlambda_0\fR \fIphi_0\fR \fIphi_1\fR \fIphi_2\fR \fIlambda\fR \fIphi\fR
Converts to the Lambert conformal conic projection\&.
.TP
\fB::mapproj::fromLambertConformalConic\fR \fIlambda_0\fR \fIphi_0\fR \fIphi_1\fR \fIphi_2\fR \fIx\fR \fIy\fR
Converts from the Lambert conformal conic projection\&.
.PP
Among the cylindrical equal-area projections, there are a number of
choices of standard parallels that have names:
.TP
\fB::mapproj::toLambertCylindricalEqualArea\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
Converts to the Lambert cylindrical equal area projection\&. (standard parallel
is the Equator\&.)
.TP
\fB::mapproj::fromLambertCylindricalEqualArea\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
Converts from the Lambert cylindrical equal area projection\&. (standard parallel
is the Equator\&.)
.TP
\fB::mapproj::toBehrmann\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
Converts to the Behrmann cylindrical equal area projection\&. (standard parallels
are 30 degrees North and South)
.TP
\fB::mapproj::fromBehrmann\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
Converts from the Behrmann cylindrical equal area projection\&. (standard parallels
are 30 degrees North and South\&.)
.TP
\fB::mapproj::toTrystanEdwards\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
Converts to the Trystan Edwards cylindrical equal area projection\&. (standard parallels
are 37\&.4 degrees North and South)
.TP
\fB::mapproj::fromTrystanEdwards\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
Converts from the Trystan Edwards cylindrical equal area projection\&. (standard parallels
are 37\&.4 degrees North and South\&.)
.TP
\fB::mapproj::toHoboDyer\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
Converts to the Hobo-Dyer cylindrical equal area projection\&. (standard parallels
are 37\&.5 degrees North and South)
.TP
\fB::mapproj::fromHoboDyer\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
Converts from the Hobo-Dyer cylindrical equal area projection\&. (standard parallels
are 37\&.5 degrees North and South\&.)
.TP
\fB::mapproj::toGallPeters\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
Converts to the Gall-Peters cylindrical equal area projection\&. (standard parallels
are 45 degrees North and South)
.TP
\fB::mapproj::fromGallPeters\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
Converts from the Gall-Peters cylindrical equal area projection\&. (standard parallels
are 45 degrees North and South\&.)
.TP
\fB::mapproj::toBalthasart\fR \fIlambda_0\fR \fIphi_0\fR \fIlambda\fR \fIphi\fR
Converts to the Balthasart cylindrical equal area projection\&. (standard parallels
are 50 degrees North and South)
.TP
\fB::mapproj::fromBalthasart\fR \fIlambda_0\fR \fIphi_0\fR \fIx\fR \fIy\fR
Converts from the Balthasart cylindrical equal area projection\&. (standard parallels
are 50 degrees North and South\&.)
.PP
.SH ARGUMENTS
The following arguments are accepted by the projection commands:
.TP
\fIlambda\fR
Longitude of the point to be projected, in degrees\&.
.TP
\fIphi\fR
Latitude of the point to be projected, in degrees\&.
.TP
\fIlambda_0\fR
Longitude of the center of the sheet, in degrees\&.  For many projections,
this figure is also the reference meridian of the projection\&.
.TP
\fIphi_0\fR
Latitude of the center of the sheet, in degrees\&.  For the azimuthal
projections, this figure is also the latitude of the center of the projection\&.
.TP
\fIphi_1\fR
Latitude of the first reference parallel, for projections that use reference
parallels\&.
.TP
\fIphi_2\fR
Latitude of the second reference parallel, for projections that use reference
parallels\&.
.TP
\fIx\fR
X co-ordinate of a point on the map, in units of Earth radii\&.
.TP
\fIy\fR
Y co-ordinate of a point on the map, in units of Earth radii\&.
.PP
.SH RESULTS
For all of the procedures whose names begin with 'to', the return value
is a list comprising an \fIx\fR co-ordinate and a \fIy\fR co-ordinate\&.
The co-ordinates are relative to the center of the map sheet to be drawn,
measured in Earth radii at the reference location on the map\&.
For all of the functions whose names begin with 'from', the return value
is a list comprising the longitude and latitude, in degrees\&.
.SH "CHOOSING A PROJECTION"
This package offers a great many projections, because no single projection
is appropriate to all maps\&.  This section attempts to provide guidance
on how to choose a projection\&.
.PP
First, consider the type of data that you intend to display on the map\&.
If the data are \fIdirectional\fR (\fIe\&.g\&.,\fR winds, ocean currents, or
magnetic fields) then you need to use a projection that preserves
angles; these are known as \fIconformal\fR projections\&.  Conformal
projections include the Mercator, the Albers azimuthal equal-area,
the stereographic, and the Peirce Quincuncial projection\&.  If the
data are \fIthematic\fR, describing properties of land or water, such
as temperature, population density, land use, or demographics; then
you need a projection that will show these data with the areas on the map
proportional to the areas in real life\&.  These so-called \fIequal area\fR
projections include the various cylindrical equal area projections,
the sinusoidal projection, the Lambert azimuthal equal-area projection,
the Albers equal-area conic projection, and several of the world-map
projections (Miller Cylindrical, Mollweide, Eckert IV, Eckert VI, Robinson,
and Hammer)\&. If the significant factor in your data is distance from a
central point or line (such as air routes), then you will do best with
an \fIequidistant\fR projection such as \fIplate carrée\fR,
Cassini, azimuthal equidistant, or conic equidistant\&.  If direction from
a central point is a critical factor in your data (for instance,
air routes, radio antenna pointing), then you will almost surely want to
use one of the azimuthal projections\&. Appropriate choices are azimuthal
equidistant, azimuthal equal-area, stereographic, and perhaps orthographic\&.
.PP
Next, consider how much of the Earth your map will cover, and the general
shape of the area of interest\&.  For maps of the entire Earth,
the cylindrical equal area, Eckert IV and VI, Mollweide, Robinson, and Hammer
projections are good overall choices\&.  The Mercator projection is traditional,
but the extreme distortions of area at high latitudes make it
a poor choice unless a conformal projection is required\&. The Peirce
projection is a better choice of conformal projection, having less distortion
of landforms\&.  The Miller Cylindrical is a compromise designed to give
shapes similar to the traditional Mercator, but with less polar stretching\&.
The Peirce Quincuncial projection shows all the continents with acceptable
distortion if a reference meridian close to +20 degrees is chosen\&.
The Robinson projection yields attractive maps for things like political
divisions, but should be avoided in presenting scientific data, since other
projections have moe useful geometric properties\&.
.PP
If the map will cover a hemisphere, then choose stereographic,
azimuthal-equidistant, Hammer, or Mollweide projections; these all project
the hemisphere into a circle\&.
.PP
If the map will cover a large area (at least a few hundred km on a side),
but less than
a hemisphere, then you have several choices\&.  Azimuthal projections
are usually good (choose stereographic, azimuthal equidistant, or
Lambert azimuthal equal-area according to whether shapes, distances from
a central point, or areas are important)\&.  Azimuthal projections (and possibly
the Cassini projection) are the only
really good choices for mapping the polar regions\&.
.PP
If the large area is in one of the temperate zones and is round or has
a primarily east-west extent, then the conic projections are good choices\&.
Choose the Lambert conformal conic, the conic equidistant, or the Albers
equal-area conic according to whether shape, distance, or area are the
most important parameters\&.  For any of these, the reference parallels
should be chosen at approximately 1/6 and 5/6 of the range of latitudes
to be displayed\&.  For instance, maps of the 48 coterminous United States
are attractive with reference parallels of 28\&.5 and 45\&.5 degrees\&.
.PP
If the large area is equatorial and is round or has a primarily east-west
extent, then the Mercator projection is a good choice for a conformal
projection; Lambert cylindrical equal-area and sinusoidal projections are
good equal-area projections; and the \fIplate carrée\fR is a
good equidistant projection\&.
.PP
Large areas having a primarily North-South aspect, particularly those
spanning the Equator, need some other choices\&.  The Cassini projection
is a good choice for an equidistant projection (for instance, a Cassini
projection with a central meridian of 80 degrees West produces an
attractive map of the Americas)\&. The cylindrical equal-area, Albers
equal-area conic, sinusoidal, Mollweide and Hammer
projections are possible choices for equal-area projections\&.
A good conformal projection in this situation is the Transverse
Mercator, which alas, is not yet implemented\&.
.PP
Small areas begin to get into a realm where the ellipticity of the
Earth affects the map scale\&.  This package does not attempt to
handle accurate mapping for large-scale topographic maps\&.  If
slight scale errors are acceptable in your application, then any
of the projections appropriate to large areas should work for
small ones as well\&.
.PP
There are a few projections that are included for their special
properties\&.  The orthographic projection produces views of the
Earth as seen from space\&.  The gnomonic projection produces a
map on which all great circles (the shortest distance between
two points on the Earth's surface) are rendered as straight lines\&.
While this projection is useful for navigational planning, it
has extreme distortions of shape and area, and can display
only a limited area of the Earth (substantially less than a hemisphere)\&.
.SH KEYWORDS
geodesy, map, projection
.SH COPYRIGHT
.nf
Copyright (c) 2007 Kevin B\&. Kenny <kennykb@acm\&.org>

.fi
