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delphine |
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<?php
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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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/* * *****************************************************************************
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NAME LAMBERT AZIMUTHAL EQUAL-AREA
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PURPOSE: Transforms input longitude and latitude to Easting and
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Northing for the Lambert Azimuthal Equal-Area projection. 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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D. Steinwand, EROS March, 1991
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This function was adapted from the Lambert Azimuthal Equal Area projection
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code (FORTRAN) in the General Cartographic Transformation Package software
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which is available from the U.S. Geological Survey National Mapping Division.
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ALGORITHM REFERENCES
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1. "New Equal-Area Map Projections for Noncircular Regions", John P. Snyder,
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The American Cartographer, Vol 15, No. 4, October 1988, pp. 341-355.
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2. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological
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Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United
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State Government Printing Office, Washington D.C., 1987.
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3. "Software Documentation for GCTP General Cartographic Transformation
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Package", U.S. Geological Survey National Mapping Division, May 1982.
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* ***************************************************************************** */
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class Proj4phpProjLaea {
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protected $S_POLE = 1;
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protected $N_POLE = 2;
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protected $EQUIT = 3;
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protected $OBLIQ = 4;
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protected $P00 = .33333333333333333333;
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protected $P01 = .17222222222222222222;
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protected $P02 = .10257936507936507936;
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protected $P10 = .06388888888888888888;
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protected $P11 = .06640211640211640211;
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protected $P20 = .01641501294219154443;
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/* Initialize the Lambert Azimuthal Equal Area projection
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------------------------------------------------------ */
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public function init() {
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$t = abs( $this->lat0 );
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if( abs( $t - Proj4php::$common->HALF_PI ) < Proj4php::$common->EPSLN ) {
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$this->mode = $this->lat0 < 0. ? $this->S_POLE : $this->N_POLE;
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} else if( abs( $t ) < Proj4php::$common->EPSLN ) {
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$this->mode = $this->EQUIT;
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} else {
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$this->mode = $this->OBLIQ;
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}
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if( $this->es > 0 ) {
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#$sinphi;
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$this->qp = Proj4php::$common->qsfnz( $this->e, 1.0 );
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$this->mmf = .5 / (1. - $this->es);
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$this->apa = $this->authset( $this->es );
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switch( $this->mode ) {
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case $this->N_POLE:
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case $this->S_POLE:
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$this->dd = 1.;
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break;
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case $this->EQUIT:
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$this->rq = sqrt( .5 * $this->qp );
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$this->dd = 1. / $this->rq;
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$this->xmf = 1.;
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$this->ymf = .5 * $this->qp;
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break;
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case $this->OBLIQ:
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$this->rq = sqrt( .5 * $this->qp );
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$sinphi = sin( $this->lat0 );
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$this->sinb1 = Proj4php::$common->qsfnz( $this->e, $sinphi ) / $this->qp;
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$this->cosb1 = sqrt( 1. - $this->sinb1 * $this->sinb1 );
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$this->dd = cos( $this->lat0 ) / (sqrt( 1. - $this->es * $sinphi * $sinphi ) * $this->rq * $this->cosb1);
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$this->ymf = ($this->xmf = $this->rq) / $this->dd;
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$this->xmf *= $this->dd;
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break;
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}
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} else {
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if( $this->mode == $this->OBLIQ ) {
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$this->sinph0 = sin( $this->lat0 );
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$this->cosph0 = cos( $this->lat0 );
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}
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}
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}
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/* Lambert Azimuthal Equal Area forward equations--mapping lat,long to x,y
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----------------------------------------------------------------------- */
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public function forward( $p ) {
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/* Forward equations
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----------------- */
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#$x;
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#$y;
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$lam = $p->x;
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$phi = $p->y;
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$lam = Proj4php::$common->adjust_lon( $lam - $this->long0 );
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if( $this->sphere ) {
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/*
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$coslam;
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$cosphi;
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$sinphi;
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*/
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$sinphi = sin( $phi );
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$cosphi = cos( $phi );
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$coslam = cos( $lam );
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switch( $this->mode ) {
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case $this->OBLIQ:
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case $this->EQUIT:
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$y = ($this->mode == $this->EQUIT) ? 1. + $cosphi * $coslam : 1. + $this->sinph0 * $sinphi + $this->cosph0 * $cosphi * $coslam;
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if( y <= Proj4php::$common->EPSLN ) {
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Proj4php::reportError( "laea:fwd:y less than eps" );
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return null;
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}
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$y = sqrt( 2. / $y );
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$x = $y * cosphi * sin( $lam );
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$y *= ($this->mode == $this->EQUIT) ? $sinphi : $this->cosph0 * $sinphi - $this->sinph0 * $cosphi * $coslam;
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break;
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case $this->N_POLE:
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$coslam = -$coslam;
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case $this->S_POLE:
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if( abs( $phi + $this->phi0 ) < Proj4php::$common->EPSLN ) {
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Proj4php::reportError( "laea:fwd:phi < eps" );
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return null;
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}
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$y = Proj4php::$common->FORTPI - $phi * .5;
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$y = 2. * (($this->mode == $this->S_POLE) ? cos( $y ) : sin( $y ));
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$x = $y * sin( $lam );
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$y *= $coslam;
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break;
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}
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} else {
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/*
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$coslam;
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$sinlam;
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$sinphi;
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$q;
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*/
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$sinb = 0.0;
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$cosb = 0.0;
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$b = 0.0;
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$coslam = cos( $lam );
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$sinlam = sin( $lam );
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$sinphi = sin( $phi );
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$q = Proj4php::$common->qsfnz( $this->e, $sinphi );
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if( $this->mode == $this->OBLIQ || $this->mode == $this->EQUIT ) {
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$sinb = $q / $this->qp;
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$cosb = sqrt( 1. - $sinb * $sinb );
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}
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switch( $this->mode ) {
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case $this->OBLIQ:
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$b = 1. + $this->sinb1 * $sinb + $this->cosb1 * $cosb * $coslam;
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break;
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case $this->EQUIT:
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$b = 1. + $cosb * $coslam;
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break;
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case $this->N_POLE:
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$b = Proj4php::$common->HALF_PI + $phi;
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$q = $this->qp - $q;
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break;
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case $this->S_POLE:
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$b = $phi - Proj4php::$common->HALF_PI;
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$q = $this->qp + $q;
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break;
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}
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if( abs( $b ) < Proj4php::$common->EPSLN ) {
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Proj4php::reportError( "laea:fwd:b < eps" );
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return null;
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}
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switch( $this->mode ) {
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case $this->OBLIQ:
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case $this->EQUIT:
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$b = sqrt( 2. / $b );
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if( $this->mode == $this->OBLIQ ) {
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$y = $this->ymf * $b * ($this->cosb1 * $sinb - $this->sinb1 * $cosb * $coslam);
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} else {
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$y = ($b = sqrt( 2. / (1. + $cosb * $coslam) )) * $sinb * $this->ymf;
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}
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$x = $this->xmf * $b * $cosb * $sinlam;
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break;
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case $this->N_POLE:
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case $this->S_POLE:
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if( q >= 0. ) {
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$x = ($b = sqrt( $q )) * $sinlam;
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$y = $coslam * (($this->mode == $this->S_POLE) ? $b : -$b);
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} else {
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$x = $y = 0.;
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}
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break;
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}
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}
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//v 1.0
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/*
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$sin_lat=sin(lat);
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$cos_lat=cos(lat);
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$sin_delta_lon=sin(delta_lon);
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$cos_delta_lon=cos(delta_lon);
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$g =$this->sin_lat_o * sin_lat +$this->cos_lat_o * cos_lat * cos_delta_lon;
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if (g == -1.0) {
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Proj4php::reportError("laea:fwd:Point projects to a circle of radius "+ 2.0 * R);
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return null;
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}
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$ksp = $this->a * sqrt(2.0 / (1.0 + g));
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$x = ksp * cos_lat * sin_delta_lon + $this->x0;
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$y = ksp * ($this->cos_lat_o * sin_lat - $this->sin_lat_o * cos_lat * cos_delta_lon) + $this->y0;
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*/
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$p->x = $this->a * $x + $this->x0;
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$p->y = $this->a * $y + $this->y0;
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return $p;
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}
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/* Inverse equations
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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 -= $this->y0;
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$x = $p->x / $this->a;
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$y = $p->y / $this->a;
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if( $this->sphere ) {
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$cosz = 0.0;
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#$rh;
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$sinz = 0.0;
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$rh = sqrt( $x * $x + $y * $y );
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$phi = $rh * .5;
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if( $phi > 1. ) {
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Proj4php::reportError( "laea:Inv:DataError" );
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return null;
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}
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$phi = 2. * asin( $phi );
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if( $this->mode == $this->OBLIQ || $this->mode == $this->EQUIT ) {
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$sinz = sin( $phi );
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$cosz = cos( $phi );
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}
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switch( $this->mode ) {
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case $this->EQUIT:
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$phi = (abs( $rh ) <= Proj4php::$common->EPSLN) ? 0. : asin( $y * $sinz / $rh );
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$x *= $sinz;
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$y = $cosz * $rh;
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break;
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case $this->OBLIQ:
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$phi = (abs( $rh ) <= Proj4php::$common->EPSLN) ? $this->phi0 : asin( $cosz * $this->sinph0 + $y * $sinz * $this->cosph0 / $rh );
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$x *= $sinz * $this->cosph0;
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$y = ($cosz - sin( $phi ) * $this->sinph0) * $rh;
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break;
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case $this->N_POLE:
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$y = -$y;
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$phi = Proj4php::$common->HALF_PI - $phi;
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break;
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case $this->S_POLE:
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$phi -= Proj4php::$common->HALF_PI;
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break;
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}
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$lam = ($y == 0. && ($this->mode == $this->EQUIT || $this->mode == $this->OBLIQ)) ? 0. : atan2( $x, $y );
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} else {
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/*
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$cCe;
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$sCe;
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$q;
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$rho;
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*/
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$ab = 0.0;
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switch( $this->mode ) {
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case $this->EQUIT:
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case $this->OBLIQ:
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$x /= $this->dd;
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$y *= $this->dd;
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$rho = sqrt( $x * $x + $y * $y );
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if( $rho < Proj4php::$common->EPSLN ) {
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$p->x = 0.;
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$p->y = $this->phi0;
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return $p;
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}
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$sCe = 2. * asin( .5 * $rho / $this->rq );
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$cCe = cos( $sCe );
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$x *= ($sCe = sin( $sCe ));
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if( $this->mode == $this->OBLIQ ) {
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$ab = $cCe * $this->sinb1 + $y * $sCe * $this->cosb1 / $rho;
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$q = $this->qp * $ab;
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$y = $rho * $this->cosb1 * $cCe - $y * $this->sinb1 * $sCe;
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} else {
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$ab = $y * $sCe / $rho;
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$q = $this->qp * $ab;
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$y = $rho * $cCe;
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}
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break;
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case $this->N_POLE:
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$y = -$y;
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case $this->S_POLE:
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$q = ($x * $x + $y * $y);
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if( !$q ) {
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$p->x = 0.;
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$p->y = $this->phi0;
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return $p;
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}
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/*
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q = $this->qp - q;
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*/
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320 |
$ab = 1. - $q / $this->qp;
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321 |
if( $this->mode == $this->S_POLE ) {
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$ab = - $ab;
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}
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324 |
break;
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}
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326 |
$lam = atan2( $x, $y );
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$phi = $this->authlat( asin( $ab ), $this->apa );
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328 |
}
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329 |
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|
330 |
/*
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|
331 |
$Rh = sqrt($p->x *$p->x +$p->y * $p->y);
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|
332 |
$temp = Rh / (2.0 * $this->a);
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|
333 |
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|
334 |
if (temp > 1) {
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|
335 |
Proj4php::reportError("laea:Inv:DataError");
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|
336 |
return null;
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|
|
337 |
}
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|
338 |
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|
339 |
$z = 2.0 * Proj4php::$common.asinz(temp);
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|
340 |
$sin_z=sin(z);
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|
341 |
$cos_z=cos(z);
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|
342 |
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|
343 |
$lon =$this->long0;
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|
|
344 |
if (abs(Rh) > Proj4php::$common->EPSLN) {
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|
|
345 |
$lat = Proj4php::$common.asinz($this->sin_lat_o * cos_z +$this-> cos_lat_o * sin_z *$p->y / Rh);
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|
|
346 |
$temp =abs($this->lat0) - Proj4php::$common->HALF_PI;
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|
|
347 |
if (abs(temp) > Proj4php::$common->EPSLN) {
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|
|
348 |
temp = cos_z -$this->sin_lat_o * sin(lat);
|
|
|
349 |
if(temp!=0.0) lon=Proj4php::$common->adjust_lon($this->long0+atan2($p->x*sin_z*$this->cos_lat_o,temp*Rh));
|
|
|
350 |
} else if ($this->lat0 < 0.0) {
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|
|
351 |
lon = Proj4php::$common->adjust_lon($this->long0 - atan2(-$p->x,$p->y));
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|
|
352 |
} else {
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|
|
353 |
lon = Proj4php::$common->adjust_lon($this->long0 + atan2($p->x, -$p->y));
|
|
|
354 |
}
|
|
|
355 |
} else {
|
|
|
356 |
lat = $this->lat0;
|
|
|
357 |
}
|
|
|
358 |
*/
|
|
|
359 |
//return(OK);
|
|
|
360 |
$p->x = Proj4php::$common->adjust_lon( $this->long0 + $lam );
|
|
|
361 |
$p->y = $phi;
|
|
|
362 |
return $p;
|
|
|
363 |
}
|
|
|
364 |
|
|
|
365 |
/**
|
|
|
366 |
* determine latitude from authalic latitude
|
|
|
367 |
*
|
|
|
368 |
* @param type $es
|
|
|
369 |
* @return type
|
|
|
370 |
*/
|
|
|
371 |
public function authset( $es ) {
|
|
|
372 |
#$t;
|
|
|
373 |
$APA = array( );
|
|
|
374 |
$APA[0] = $es * $this->P00;
|
|
|
375 |
$t = $es * $es;
|
|
|
376 |
$APA[0] += $t * $this->P01;
|
|
|
377 |
$APA[1] = $t * $this->P10;
|
|
|
378 |
$t *= $es;
|
|
|
379 |
$APA[0] += $t * $this->P02;
|
|
|
380 |
$APA[1] += $t * $this->P11;
|
|
|
381 |
$APA[2] = $t * $this->P20;
|
|
|
382 |
return $APA;
|
|
|
383 |
}
|
|
|
384 |
|
|
|
385 |
/**
|
|
|
386 |
*
|
|
|
387 |
* @param type $beta
|
|
|
388 |
* @param type $APA
|
|
|
389 |
* @return type
|
|
|
390 |
*/
|
|
|
391 |
public function authlat( $beta, $APA ) {
|
|
|
392 |
$t = $beta + $beta;
|
|
|
393 |
return($beta + $APA[0] * sin( $t ) + $APA[1] * sin( $t + $t ) + $APA[2] * sin( $t + $t + $t ));
|
|
|
394 |
}
|
|
|
395 |
|
|
|
396 |
}
|
|
|
397 |
|
|
|
398 |
Proj4php::$proj['laea'] = new Proj4phpProjLaea();
|