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<?php
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/*******************************************************************************
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NAME LAMBERT CYLINDRICAL EQUAL AREA
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PURPOSE: Transforms input longitude and latitude to Easting and
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Northing for the Lambert Cylindrical Equal Area projection.
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This class of projection includes the Behrmann and
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Gall-Peters Projections. The
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longitude and latitude must be in radians. The Easting
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and Northing values will be returned in meters.
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PROGRAMMER DATE
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---------- ----
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R. Marsden August 2009
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Winwaed Software Tech LLC, http://www.winwaed.com
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This function was adapted from the Miller Cylindrical Projection in the Proj4php
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library.
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Note: This implementation assumes a Spherical Earth. The (commented) code
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has been included for the ellipsoidal forward transform, but derivation of
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the ellispoidal inverse transform is beyond me. Note that most of the
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Proj4php implementations do NOT currently support ellipsoidal figures.
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Therefore this is not seen as a problem - especially this lack of support
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is explicitly stated here.
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ALGORITHM REFERENCES
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1. "Cartographic Projection Procedures for the UNIX Environment -
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A User's Manual" by Gerald I. Evenden, USGS Open File Report 90-284
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and Release 4 Interim Reports (2003)
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2. Snyder, John P., "Flattening the Earth - Two Thousand Years of Map
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Projections", Univ. Chicago Press, 1993
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****************************************************************************** */
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/**
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* Author : Julien Moquet
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*
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* Inspired by Proj4php from Mike Adair madairATdmsolutions.ca
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* and Richard Greenwood rich@greenwoodma$p->com
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* License: LGPL as per: http://www.gnu.org/copyleft/lesser.html
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*/
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class Proj4phpProjCea {
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/* Initialize the Cylindrical Equal Area projection
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------------------------------------------- */
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public function init() {
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//no-op
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}
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/* Cylindrical Equal Area forward equations--mapping lat,long to x,y
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------------------------------------------------------------ */
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public function forward( $p ) {
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$lon = $p->x;
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$lat = $p->y;
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/* Forward equations
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----------------- */
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$dlon = Proj4php::$common->adjust_lon( $lon - $this->long0 );
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$x = $this->x0 + $this->a * $dlon * cos( $this->lat_ts );
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$y = $this->y0 + $this->a * sin( $lat ) / cos( $this->lat_ts );
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/* Elliptical Forward Transform
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Not implemented due to a lack of a matchign inverse function
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{
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$Sin_Lat = sin(lat);
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$Rn = $this->a * (sqrt(1.0e0 - $this->es * Sin_Lat * Sin_Lat ));
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x = $this->x0 + $this->a * dlon * cos($this->lat_ts);
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y = $this->y0 + Rn * sin(lat) / cos($this->lat_ts);
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}
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*/
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$p->x = $x;
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$p->y = $y;
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return $p;
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}
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/**
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* Cylindrical Equal Area inverse equations--mapping x,y to lat/long
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*
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* @param type $p
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* @return type
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*/
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public function inverse( $p ) {
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$p->x -= $this->x0;
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$p->y -= $this->y0;
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$p->x = Proj4php::$common->adjust_lon( $this->long0 + ($p->x / $this->a) / cos( $this->lat_ts ) );
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$p->y = asin( ($p->y / $this->a) * cos( $this->lat_ts ) );
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return $p;
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}
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}
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Proj4php::$proj['cea'] = new Proj4phpProjCea();
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