<?php
class Sourcemap_Proj_Transform_Laea extends Sourcemap_Proj_Transform {
/*******************************************************************************
NAME                  LAMBERT AZIMUTHAL EQUAL-AREA
 
PURPOSE:	Transforms input longitude and latitude to Easting and
		Northing for the Lambert Azimuthal Equal-Area projection.  The
		longitude and latitude must be in radians.  The Easting
		and Northing values will be returned in meters.

PROGRAMMER              DATE            
----------              ----           
D. Steinwand, EROS      March, 1991   

This function was adapted from the Lambert Azimuthal Equal Area projection
code (FORTRAN) in the General Cartographic Transformation Package software
which is available from the U.S. Geological Survey National Mapping Division.
 
ALGORITHM REFERENCES

1.  "New Equal-Area Map Projections for Noncircular Regions", John P. Snyder,
    The American Cartographer, Vol 15, No. 4, October 1988, p$p-> 341-355.

2.  Snyder, John P., "Map Projections--A Working Manual", U.S. Geological
    Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United
    State Government Printing Office, Washington D.C., 1987.

3.  "Software Documentation for GCTP General Cartographic Transformation
    Package", U.S. Geological Survey National Mapping Division, May 1982.
*******************************************************************************/
  
    public $S_POLE = 1;
    public $N_POLE = 2;
    public $EQUIT = 3;
    public $OBLIQ = 4;
    
    /* determine latitude from authalic latitude */
    public $P00 = .33333333333333333333;
    public $P01 = .17222222222222222222;
    public $P02 = .10257936507936507936;
    public $P10 = .06388888888888888888;
    public $P11 = .06640211640211640211;
    public $P20 = .01641501294219154443;
  


    # Initialize the Lambert Azimuthal Equal Area projection
    public function init() {
        $t = abs($this->lat0);
        if(abs(t - Sourcemap_Proj::HALF_PI) < Sourcemap_Proj::EPSLN) {
            $this->mode = $this->lat0 < 0.0 ? $this->S_POLE : $this->N_POLE;
        } else if(abs(t) < Sourcemap_Proj::EPSLN) {
            $this->mode = $this->EQUIT;
        } else {
            $this->mode = $this->OBLIQ;
        }
        if($this->es > 0) {
            $sinphi;

            $this->qp = Sourcemap_Proj::qsfnz($this->e, 1.0);
            $this->mmf = .5 / (1.0 - $this->es);
            $this->apa = $this->authset($this->es);
            switch ($this->mode) {
                case $this->N_POLE:
                case $this->S_POLE:
                    $this->dd = 1.0;
                    break;
                case $this->EQUIT:
                    $this->rq = sqrt(.5 * $this->qp);
                    $this->dd = 1.0 / $this->rq;
                    $this->xmf = 1.0;
                    $this->ymf = .5 * $this->qp;
                    break;
                case $this->OBLIQ:
                    $this->rq = sqrt(.5 * $this->qp);
                    $sinphi = sin($this->lat0);
                    $this->sinb1 = Sourcemap_Proj::qsfnz($this->e, sinphi) / $this->qp;
                    $this->cosb1 = sqrt(1.0 - $this->sinb1 * $this->sinb1);
                    $this->dd = cos($this->lat0) / (sqrt(1.0 - $this->es * $sinphi * $sinphi) * $this->rq * $this->cosb1);
                    $this->ymf = ($this->xmf = $this->rq) / $this->dd;
                    $this->xmf *= $this->dd;
                    break;
            }
        } else {
            if($this->mode == $this->OBLIQ) {
                $this->sinph0 = sin($this->lat0);
                $this->cosph0 = cos($this->lat0);
            }
        }
    }

    # Lambert Azimuthal Equal Area forward equations--mapping lat,long to x,y
    public function forward($p) {

        /* Forward equations
           -----------------*/
        $lam=$p->x;
        $phi=$p->y;
        $lam = Sourcemap_Proj::adjust_lon($lam - $this->long0);

        if($this->sphere) {
            $sinphi = sin($phi);
            $cosphi = cos($phi);
            $coslam = cos($lam);
            switch ($this->mode) {
                case $this->EQUIT:
                    $y = ($this->mode == $this->EQUIT) ? 1.0 + $cosphi * $coslam : 1.0 + $this->sinph0 * $sinphi + $this->cosph0 * $cosphi * $coslam;
                    if($y <= Sourcemap_Proj::EPSLN) {
                        throw new Exception('Y less than eps.');
                    }
                    $y = sqrt(2. / $y);
                    $x = $y * $cosphi * sin($lam);
                    $y *= ($this->mode == $this->EQUIT) ? $sinphi : $this->cosph0 * $sinphi - $this->sinph0 * $cosphi * $coslam;
                    break;
                case $this->N_POLE:
                    $coslam = -$coslam;
                case $this->S_POLE:
                    if(abs($phi + $this->phi0) < Sourcemap_Proj::EPSLN) {
                        throw new Exception("Phi < eps.");
                    }
                    $y = Sourcemap_Proj::FORTPI - $phi * .5;
                    $y = 2.0 * (($this->mode == $this->S_POLE) ? cos($y) : sin($y));
                    $x = $y * sin($lam);
                    $y *= $coslam;
                    break;
            }
        } else {
            $sinb=0.0;
            $cosb=0.0;
            $b=0.0;

            $coslam = cos($lam);
            $sinlam = sin($lam);
            $sinphi = sin($phi);
            $q = Sourcemap_Proj::qsfnz($this->e, $sinphi);
            if($this->mode == $this->OBLIQ || $this->mode == $this->EQUIT) {
                $sinb = $q / $this->qp;
                $cosb = sqrt(1.0 - $sinb * $sinb);
            }
            switch ($this->mode) {
                case $this->OBLIQ:
                    $b = 1.0 + $this->sinb1 * $sinb + $this->cosb1 * $cosb * $coslam;
                    break;
                case $this->EQUIT:
                    $b = 1.0 + $cosb * $coslam;
                    break;
                case $this->N_POLE:
                    $b = Sourcemap_Proj::HALF_PI + $phi;
                    $q = $this->qp - $q;
                    break;
                case $this->S_POLE:
                    $b = $phi - Sourcemap_Proj::HALF_PI;
                    $q = $this->qp + $q;
                    break;
            }
            if(abs($b) < Sourcemap_Proj::EPSLN) {
                throw new Exception("B < eps.");
            }
            switch ($this->mode) {
                case $this->OBLIQ:
                case $this->EQUIT:
                    $b = sqrt(2.0 / $b);
                    if($this->mode == $this->OBLIQ) {
                        $y = $this->ymf * $b * ($this->cosb1 * $sinb - $this->sinb1 * $cosb * $coslam);
                    } else {
                        $y = ($b = sqrt(2.0 / (1.0 + $cosb * $coslam))) * $sinb * $this->ymf;
                    }
                    $x = $this->xmf * $b * $cosb * $sinlam;
                    break;
                case $this->N_POLE:
                case $this->S_POLE:
                    if($q >= 0.) {
                        $x = ($b = sqrt($q)) * $sinlam;
                        $y = $coslam * (($this->mode == $this->S_POLE) ? $b : -$b);
                    } else {
                        $x = $y = 0.;
                    }
                    break;
            }
        }

        //v 1.0
        /*
           $sin_lat=sin(lat);
           $cos_lat=cos(lat);

           $sin_delta_lon=sin(delta_lon);
           $cos_delta_lon=cos(delta_lon);

           $g =$this->sin_lat_o * sin_lat +$this->cos_lat_o * cos_lat * cos_delta_lon;
           if(g == -1.0) {
           Proj4js.reportError("laea:fwd:Point projects to a circle of radius "+ 2.0 * R);
           return null;
           }
           $ksp = $this->a * sqrt(2.0 / (1.0 + g));
           $x = ksp * cos_lat * sin_delta_lon + $this->x0;
           $y = ksp * ($this->cos_lat_o * sin_lat - $this->sin_lat_o * cos_lat * cos_delta_lon) + $this->y0;
         */
        $p->x = $this->a * $x + $this->x0;
        $p->y = $this->a * $y + $this->y0;
        return $p;
    }

    # Inverse equations
    public function inverse($p) {
        $p->x -= $this->x0;
        $p->y -= $this->y0;
        $x = $p->x/$this->a;
        $y = $p->y/$this->a;

        if($this->sphere) {
            $cosz = 0.0;
            $sinz=0.0;

            $rh = sqrt($x * $x + $y * $y);
            $phi = $rh * .5;
            if($phi > 1.) {
                throw new Exception("Data error.");
            }
            $phi = 2.0 * asin($phi);
            if($this->mode == $this->OBLIQ || $this->mode == $this->EQUIT) {
                $sinz = sin($phi);
                $cosz = cos($phi);
            }
            switch ($this->mode) {
                case $this->EQUIT:
                    $phi = (abs($rh) <= Sourcemap_Proj::EPSLN) ? 0. : asin($y * $sinz / $rh);
                    $x *= $sinz;
                    $y = $cosz * $rh;
                    break;
                case $this->OBLIQ:
                    $phi = (abs($rh) <= Sourcemap_Proj::EPSLN) ? $this->phi0 : asin($cosz * $sinph0 + $y * $sinz * $cosph0 / $rh);
                    $x *= $sinz * $cosph0;
                    $y = ($cosz - sin($phi) * $sinph0) * $rh;
                    break;
                case $this->N_POLE:
                    $y = -$y;
                    $phi = Sourcemap_Proj::HALF_PI - $phi;
                    break;
                case $this->S_POLE:
                    $phi -= Sourcemap_Proj::HALF_PI;
                    break;
            }
            $lam = ($y == 0.0 && ($this->mode == $this->EQUIT || $this->mode == $this->OBLIQ)) ? 0.0 : atan2($x, $y);
        } else {
            $ab=0.0;

            switch ($this->mode) {
                case $this->EQUIT:
                case $this->OBLIQ:
                    $x /= $this->dd;
                    $y *=  $this->dd;
                    $rho = sqrt($x * $x + $y * $y);
                    if($rho < Sourcemap_Proj::EPSLN) {
                        $p->x = 0.0;
                        $p->y = $this->phi0;
                        return $p;
                    }
                    $sCe = 2.0 * asin(.5 * $rho / $this->rq);
                    $cCe = cos($sCe);
                    $x *= ($sCe = sin($sCe));
                    if($this->mode == $this->OBLIQ) {
                        $ab = $cCe * $this->sinb1 + $y * $sCe * $this->cosb1 / $rho;
                        $q = $this->qp * $ab;
                        $y = $rho * $this->cosb1 * $cCe - $y * $this->sinb1 * $sCe;
                    } else {
                        $ab = $y * $sCe / $rho;
                        $q = $this->qp * $ab;
                        $y = $rho * $cCe;
                    }
                    break;
                case $this->N_POLE:
                    $y = -$y;
                case $this->S_POLE:
                    $q = ($x * $x + $y * $y);
                    if(!$q ) {
                        $p->x = 0.0;
                        $p->y = $this->phi0;
                        return $p;
                    }
                    /*
                       q = $this->qp - q;
                     */
                    $ab = 1.0 - $q / $this->qp;
                    if($this->mode == $this->S_POLE) {
                        $ab = - $ab;
                    }
                    break;
            }
            $lam = atan2($x, $y);
            $phi = $this->authlat(asin($ab), $this->apa);
        }

        /*
           $Rh = sqrt($p->x *$p->x +$p->y * $p->y);
           $temp = Rh / (2.0 * $this->a);

           if(temp > 1) {
           Proj4js.reportError("laea:Inv:DataError");
           return null;
           }

           $z = 2.0 * Sourcemap_Proj::asinz(temp);
           $sin_z=sin(z);
           $cos_z=cos(z);

           $lon =$this->long0;
           if(abs(Rh) > Sourcemap_Proj::EPSLN) {
           $lat = Sourcemap_Proj::asinz($this->sin_lat_o * cos_z +$this-> cos_lat_o * sin_z *$p->y / Rh);
           $temp =abs($this->lat0) - Sourcemap_Proj::HALF_PI;
           if(abs(temp) > Sourcemap_Proj::EPSLN) {
           temp = cos_z -$this->sin_lat_o * sin(lat);
           if(temp!=0.0) lon=Sourcemap_Proj::adjust_lon($this->long0+atan2($p->x*sin_z*$this->cos_lat_o,temp*Rh));
           } else if($this->lat0 < 0.0) {
           lon = Sourcemap_Proj::adjust_lon($this->long0 - atan2(-$p->x,$p->y));
           } else {
           lon = Sourcemap_Proj::adjust_lon($this->long0 + atan2($p->x, -$p->y));
           }
           } else {
           lat = $this->lat0;
           }
         */
        //return(OK);
        $p->x = Sourcemap_Proj::adjust_lon($this->long0+$lam);
        $p->y = $phi;
        return $p;
    }
  
    public function authset($es) {
        $APA = aaaaaaaaarray();
        $APA[0] = $es * $this->P00;
        $t = $es * $es;
        $APA[0] += $t * $this->P01;
        $APA[1] = $t * $this->P10;
        $t *= $es;
        $APA[0] += $t * $this->P02;
        $APA[1] += $t * $this->P11;
        $APA[2] = $t * $this->P20;
        return $APA;
    }
  
    public function authlat($beta, $APA) {
        $t = $beta + $beta;
        return($beta + $APA[0] * sin($t) + $APA[1] * sin($t + $t) + $APA[2] * sin($t + $t + $t));
    }
}
