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| <?php |
| |
| /** |
| * Author : Julien Moquet |
| * |
| * Inspired by Proj4js from Mike Adair madairATdmsolutions.ca |
| * and Richard Greenwood rich@greenwoodmap.com |
| * License: LGPL as per: http://www.gnu.org/copyleft/lesser.html |
| */ |
| class Proj4phpCommon { |
| |
| public $PI = M_PI; #3.141592653589793238; //Math.PI, |
| public $HALF_PI = M_PI_2; #1.570796326794896619; //Math.PI*0.5, |
| public $TWO_PI = 6.283185307179586477; //Math.PI*2, |
| public $FORTPI = 0.78539816339744833; |
| public $R2D = 57.29577951308232088; |
| public $D2R = 0.01745329251994329577; |
| public $SEC_TO_RAD = 4.84813681109535993589914102357e-6; /* SEC_TO_RAD = Pi/180/3600 */ |
| public $EPSLN = 1.0e-10; |
| public $MAX_ITER = 20; |
| // following constants from geocent.c |
| public $COS_67P5 = 0.38268343236508977; /* cosine of 67.5 degrees */ |
| public $AD_C = 1.0026000; /* Toms region 1 constant */ |
| |
| /* datum_type values */ |
| public $PJD_UNKNOWN = 0; |
| public $PJD_3PARAM = 1; |
| public $PJD_7PARAM = 2; |
| public $PJD_GRIDSHIFT = 3; |
| public $PJD_WGS84 = 4; // WGS84 or equivalent |
| public $PJD_NODATUM = 5; // WGS84 or equivalent |
| |
| const SRS_WGS84_SEMIMAJOR = 6378137.0; // only used in grid shift transforms |
| |
| // ellipoid pj_set_ell.c |
| |
| public $SIXTH = .1666666666666666667; /* 1/6 */ |
| public $RA4 = .04722222222222222222; /* 17/360 */ |
| public $RA6 = .02215608465608465608; /* 67/3024 */ |
| public $RV4 = .06944444444444444444; /* 5/72 */ |
| public $RV6 = .04243827160493827160; /* 55/1296 */ |
| |
| |
| /* meridinal distance for ellipsoid and inverse |
| * * 8th degree - accurate to < 1e-5 meters when used in conjuction |
| * * with typical major axis values. |
| * * Inverse determines phi to EPS (1e-11) radians, about 1e-6 seconds. |
| */ |
| protected $C00 = 1.0; |
| protected $C02 = .25; |
| protected $C04 = .046875; |
| protected $C06 = .01953125; |
| protected $C08 = .01068115234375; |
| protected $C22 = .75; |
| protected $C44 = .46875; |
| protected $C46 = .01302083333333333333; |
| protected $C48 = .00712076822916666666; |
| protected $C66 = .36458333333333333333; |
| protected $C68 = .00569661458333333333; |
| protected $C88 = .3076171875; |
| |
| /** |
| * Function to compute the constant small m which is the radius of |
| * a parallel of latitude, phi, divided by the semimajor axis. |
| * |
| * @param type $eccent |
| * @param type $sinphi |
| * @param type $cosphi |
| * @return type |
| */ |
| public function msfnz( $eccent, $sinphi, $cosphi ) { |
| |
| $con = $eccent * $sinphi; |
| |
| return $cosphi / (sqrt( 1.0 - $con * $con )); |
| } |
| |
| /** |
| * Function to compute the constant small t for use in the forward |
| * computations in the Lambert Conformal Conic and the Polar |
| * Stereographic projections. |
| * |
| * @param type $eccent |
| * @param type $phi |
| * @param type $sinphi |
| * @return type |
| */ |
| public function tsfnz( $eccent, $phi, $sinphi ) { |
| |
| $con = $eccent * $sinphi; |
| $com = 0.5 * $eccent; |
| $con = pow( ((1.0 - $con) / (1.0 + $con) ), $com ); |
| |
| return (tan( .5 * (M_PI_2 - $phi) ) / $con); |
| } |
| |
| /** |
| * Function to compute the latitude angle, phi2, for the inverse of the |
| * Lambert Conformal Conic and Polar Stereographic projections. |
| * |
| * rise up an assertion if there is no convergence. |
| * |
| * @param type $eccent |
| * @param type $ts |
| * @return type |
| */ |
| public function phi2z( $eccent, $ts ) { |
| |
| $eccnth = .5 * $eccent; |
| $phi = M_PI_2 - 2 * atan( $ts ); |
| |
| for( $i = 0; $i <= 15; $i++ ) { |
| $con = $eccent * sin( $phi ); |
| $dphi = M_PI_2 - 2 * atan( $ts * (pow( ((1.0 - $con) / (1.0 + $con) ), $eccnth )) ) - $phi; |
| $phi += $dphi; |
| if( abs( $dphi ) <= .0000000001 ) |
| return $phi; |
| } |
| assert( "false; /* phi2z has NoConvergence */" ); |
| |
| return (-9999); |
| } |
| |
| /** |
| * Function to compute constant small q which is the radius of a |
| * parallel of latitude, phi, divided by the semimajor axis. |
| * |
| * @param type $eccent |
| * @param type $sinphi |
| * @return type |
| */ |
| public function qsfnz( $eccent, $sinphi ) { |
| |
| if( $eccent > 1.0e-7 ) { |
| |
| $con = $eccent * $sinphi; |
| |
| return (( 1.0 - $eccent * $eccent) * ($sinphi / (1.0 - $con * $con) - (.5 / $eccent) * log( (1.0 - $con) / (1.0 + $con) ))); |
| } |
| |
| return (2.0 * $sinphi); |
| } |
| |
| /** |
| * Function to eliminate roundoff errors in asin |
| * |
| * @param type $x |
| * @return type |
| */ |
| public function asinz( $x ) { |
| |
| return asin( |
| abs( $x ) > 1.0 ? ($x > 1.0 ? 1.0 : -1.0) : $x |
| ); |
| |
| #if( abs( $x ) > 1.0 ) { |
| # $x = ($x > 1.0) ? 1.0 : -1.0; |
| #} |
| #return asin( $x ); |
| } |
| |
| /** |
| * following functions from gctpc cproj.c for transverse mercator projections |
| * |
| * @param type $x |
| * @return type |
| */ |
| public function e0fn( $x ) { |
| return (1.0 - 0.25 * $x * (1.0 + $x / 16.0 * (3.0 + 1.25 * $x))); |
| } |
| |
| /** |
| * |
| * @param type $x |
| * @return type |
| */ |
| public function e1fn( $x ) { |
| return (0.375 * $x * (1.0 + 0.25 * $x * (1.0 + 0.46875 * $x))); |
| } |
| |
| /** |
| * |
| * @param type $x |
| * @return type |
| */ |
| public function e2fn( $x ) { |
| return (0.05859375 * $x * $x * (1.0 + 0.75 * $x)); |
| } |
| |
| /** |
| * |
| * @param type $x |
| * @return type |
| */ |
| public function e3fn( $x ) { |
| return ($x * $x * $x * (35.0 / 3072.0)); |
| } |
| |
| /** |
| * |
| * @param type $e0 |
| * @param type $e1 |
| * @param type $e2 |
| * @param type $e3 |
| * @param type $phi |
| * @return type |
| */ |
| public function mlfn( $e0, $e1, $e2, $e3, $phi ) { |
| return ($e0 * $phi - $e1 * sin( 2.0 * $phi ) + $e2 * sin( 4.0 * $phi ) - $e3 * sin( 6.0 * $phi )); |
| } |
| |
| /** |
| * |
| * @param type $esinp |
| * @param type $exp |
| * @return type |
| */ |
| public function srat( $esinp, $exp ) { |
| return (pow( (1.0 - $esinp) / (1.0 + $esinp), $exp )); |
| } |
| |
| /** |
| * Function to return the sign of an argument |
| * |
| * @param type $x |
| * @return type |
| */ |
| public function sign( $x ) { |
| |
| return $x < 0.0 ? -1 : 1; |
| } |
| |
| /** |
| * Function to adjust longitude to -180 to 180; input in radians |
| * |
| * @param type $x |
| * @return type |
| */ |
| public function adjust_lon( $x ) { |
| |
| return (abs( $x ) < M_PI) ? $x : ($x - ($this->sign( $x ) * $this->TWO_PI) ); |
| } |
| |
| /** |
| * IGNF - DGR : algorithms used by IGN France |
| * Function to adjust latitude to -90 to 90; input in radians |
| * |
| * @param type $x |
| * @return type |
| */ |
| public function adjust_lat( $x ) { |
| |
| $x = (abs( $x ) < M_PI_2) ? $x : ($x - ($this->sign( $x ) * M_PI) ); |
| |
| return $x; |
| } |
| |
| /** |
| * Latitude Isometrique - close to tsfnz ... |
| * |
| * @param type $eccent |
| * @param float $phi |
| * @param type $sinphi |
| * @return string |
| */ |
| public function latiso( $eccent, $phi, $sinphi ) { |
| |
| if( abs( $phi ) > M_PI_2 ) |
| return +NaN; |
| if( $phi == M_PI_2 ) |
| return INF; |
| if( $phi == -1.0 * M_PI_2 ) |
| return -1.0 * INF; |
| |
| $con = $eccent * $sinphi; |
| |
| return log( tan( (M_PI_2 + $phi) / 2.0 ) ) + $eccent * log( (1.0 - $con) / (1.0 + $con) ) / 2.0; |
| } |
| |
| /** |
| * |
| * @param type $x |
| * @param type $L |
| * @return type |
| */ |
| public function fL( $x, $L ) { |
| return 2.0 * atan( $x * exp( $L ) ) - M_PI_2; |
| } |
| |
| /** |
| * Inverse Latitude Isometrique - close to ph2z |
| * |
| * @param type $eccent |
| * @param type $ts |
| * @return type |
| */ |
| public function invlatiso( $eccent, $ts ) { |
| |
| $phi = $this->fL( 1.0, $ts ); |
| $Iphi = 0.0; |
| $con = 0.0; |
| |
| do { |
| $Iphi = $phi; |
| $con = $eccent * sin( $Iphi ); |
| $phi = $this->fL( exp( $eccent * log( (1.0 + $con) / (1.0 - $con) ) / 2.0 ), $ts ); |
| } while( abs( $phi - $Iphi ) > 1.0e-12 ); |
| |
| return $phi; |
| } |
| |
| /** |
| * Grande Normale |
| * |
| * @param type $a |
| * @param type $e |
| * @param type $sinphi |
| * @return type |
| */ |
| public function gN( $a, $e, $sinphi ) { |
| $temp = $e * $sinphi; |
| return $a / sqrt( 1.0 - $temp * $temp ); |
| } |
| |
| /** |
| * code from the PROJ.4 pj_mlfn.c file; this may be useful for other projections |
| * |
| * @param type $es |
| * @return type |
| */ |
| public function pj_enfn( $es ) { |
| |
| $en = array( ); |
| $en[0] = $this->C00 - $es * ($this->C02 + $es * ($this->C04 + $es * ($this->C06 + $es * $this->C08))); |
| $en[1] = es * ($this->C22 - $es * ($this->C04 + $es * ($this->C06 + $es * $this->C08))); |
| $t = $es * $es; |
| $en[2] = $t * ($this->C44 - $es * ($this->C46 + $es * $this->C48)); |
| $t *= $es; |
| $en[3] = $t * ($this->C66 - $es * $this->C68); |
| $en[4] = $t * $es * $this->C88; |
| |
| return $en; |
| } |
| |
| /** |
| * |
| * @param type $phi |
| * @param type $sphi |
| * @param type $cphi |
| * @param type $en |
| * @return type |
| */ |
| public function pj_mlfn( $phi, $sphi, $cphi, $en ) { |
| |
| $cphi *= $sphi; |
| $sphi *= $sphi; |
| |
| return ($en[0] * $phi - $cphi * ($en[1] + $sphi * ($en[2] + $sphi * ($en[3] + $sphi * $en[4])))); |
| } |
| |
| /** |
| * |
| * @param type $arg |
| * @param type $es |
| * @param type $en |
| * @return type |
| */ |
| public function pj_inv_mlfn( $arg, $es, $en ) { |
| |
| $k = (float) 1 / (1 - $es); |
| $phi = $arg; |
| |
| for( $i = Proj4php::$common->MAX_ITER; $i; --$i ) { /* rarely goes over 2 iterations */ |
| $s = sin( $phi ); |
| $t = 1. - $es * $s * $s; |
| //$t = $this->pj_mlfn($phi, $s, cos($phi), $en) - $arg; |
| //$phi -= $t * ($t * sqrt($t)) * $k; |
| $t = ($this->pj_mlfn( $phi, $s, cos( $phi ), $en ) - $arg) * ($t * sqrt( $t )) * $k; |
| $phi -= $t; |
| if( abs( $t ) < Proj4php::$common->EPSLN ) |
| return $phi; |
| } |
| |
| Proj4php::reportError( "cass:pj_inv_mlfn: Convergence error" ); |
| |
| return $phi; |
| } |
| |
| } |