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Diffstat (limited to 'funtools/wcs/proj.c')
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diff --git a/funtools/wcs/proj.c b/funtools/wcs/proj.c new file mode 100644 index 0000000..c0264b8 --- /dev/null +++ b/funtools/wcs/proj.c @@ -0,0 +1,4527 @@ +/*============================================================================ +* +* WCSLIB - an implementation of the FITS WCS proposal. +* Copyright (C) 1995-2002, Mark Calabretta +* +* This library is free software; you can redistribute it and/or +* modify it under the terms of the GNU Lesser General Public +* License as published by the Free Software Foundation; either +* version 2 of the License, or (at your option) any later version. +* +* This library is distributed in the hope that it will be useful, +* but WITHOUT ANY WARRANTY; without even the implied warranty of +* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +* Lesser General Public License for more details. +* +* You should have received a copy of the GNU Lesser General Public +* License along with this library; if not, write to the Free Software +* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA +* +* Correspondence concerning WCSLIB may be directed to: +* Internet email: mcalabre@atnf.csiro.au +* Postal address: Dr. Mark Calabretta, +* Australia Telescope National Facility, +* P.O. Box 76, +* Epping, NSW, 2121, +* AUSTRALIA +* +*============================================================================= +* +* C implementation of the spherical map projections recognized by the FITS +* "World Coordinate System" (WCS) convention. +* +* Summary of routines +* ------------------- +* Each projection is implemented via separate functions for the forward, +* *fwd(), and reverse, *rev(), transformation. +* +* Initialization routines, *set(), compute intermediate values from the +* projection parameters but need not be called explicitly - see the +* explanation of prj.flag below. +* +* prjset prjfwd prjrev Driver routines (see below). +* +* azpset azpfwd azprev AZP: zenithal/azimuthal perspective +* szpset szpfwd szprev SZP: slant zenithal perspective +* tanset tanfwd tanrev TAN: gnomonic +* stgset stgfwd stgrev STG: stereographic +* sinset sinfwd sinrev SIN: orthographic/synthesis +* arcset arcfwd arcrev ARC: zenithal/azimuthal equidistant +* zpnset zpnfwd zpnrev ZPN: zenithal/azimuthal polynomial +* zeaset zeafwd zearev ZEA: zenithal/azimuthal equal area +* airset airfwd airrev AIR: Airy +* cypset cypfwd cyprev CYP: cylindrical perspective +* ceaset ceafwd cearev CEA: cylindrical equal area +* carset carfwd carrev CAR: Cartesian +* merset merfwd merrev MER: Mercator +* sflset sflfwd sflrev SFL: Sanson-Flamsteed +* parset parfwd parrev PAR: parabolic +* molset molfwd molrev MOL: Mollweide +* aitset aitfwd aitrev AIT: Hammer-Aitoff +* copset copfwd coprev COP: conic perspective +* coeset coefwd coerev COE: conic equal area +* codset codfwd codrev COD: conic equidistant +* cooset coofwd coorev COO: conic orthomorphic +* bonset bonfwd bonrev BON: Bonne +* pcoset pcofwd pcorev PCO: polyconic +* tscset tscfwd tscrev TSC: tangential spherical cube +* cscset cscfwd cscrev CSC: COBE quadrilateralized spherical cube +* qscset qscfwd qscrev QSC: quadrilateralized spherical cube +* +* +* Driver routines; prjset(), prjfwd() & prjrev() +* ---------------------------------------------- +* A set of driver routines are available for use as a generic interface to +* the specific projection routines. The interfaces to prjfwd() and prjrev() +* are the same as those of the forward and reverse transformation routines +* for the specific projections (see below). +* +* The interface to prjset() differs slightly from that of the initialization +* routines for the specific projections and unlike them it must be invoked +* explicitly to use prjfwd() and prjrev(). +* +* Given: +* pcode[4] const char +* WCS projection code. +* +* Given and/or returned: +* prj prjprm* Projection parameters (see below). +* +* Function return value: +* int Error status +* 0: Success. +* +* +* Initialization routine; *set() +* ------------------------------ +* Initializes members of a prjprm data structure which hold intermediate +* values. Note that this routine need not be called directly; it will be +* invoked by prjfwd() and prjrev() if the "flag" structure member is +* anything other than a predefined magic value. +* +* Given and/or returned: +* prj prjprm* Projection parameters (see below). +* +* Function return value: +* int Error status +* 0: Success. +* 1: Invalid projection parameters. +* +* Forward transformation; *fwd() +* ----------------------------- +* Compute (x,y) coordinates in the plane of projection from native spherical +* coordinates (phi,theta). +* +* Given: +* phi, const double +* theta Longitude and latitude of the projected point in +* native spherical coordinates, in degrees. +* +* Given and returned: +* prj prjprm* Projection parameters (see below). +* +* Returned: +* x,y double* Projected coordinates. +* +* Function return value: +* int Error status +* 0: Success. +* 1: Invalid projection parameters. +* 2: Invalid value of (phi,theta). +* +* Reverse transformation; *rev() +* ----------------------------- +* Compute native spherical coordinates (phi,theta) from (x,y) coordinates in +* the plane of projection. +* +* Given: +* x,y const double +* Projected coordinates. +* +* Given and returned: +* prj prjprm* Projection parameters (see below). +* +* Returned: +* phi, double* Longitude and latitude of the projected point in +* theta native spherical coordinates, in degrees. +* +* Function return value: +* int Error status +* 0: Success. +* 1: Invalid projection parameters. +* 2: Invalid value of (x,y). +* 1: Invalid projection parameters. +* +* Projection parameters +* --------------------- +* The prjprm struct consists of the following: +* +* int flag +* This flag must be set to zero whenever any of p[10] or r0 are set +* or changed. This signals the initialization routine to recompute +* intermediaries. flag may also be set to -1 to disable strict bounds +* checking for the AZP, SZP, TAN, SIN, ZPN, and COP projections. +* +* double r0 +* r0; The radius of the generating sphere for the projection, a linear +* scaling parameter. If this is zero, it will be reset to the default +* value of 180/pi (the value for FITS WCS). +* +* double p[10] +* The first 10 elements contain projection parameters which correspond +* to the PROJPn keywords in FITS, so p[0] is PROJP0, and p[9] is +* PROJP9. Many projections use p[1] (PROJP1) and some also use p[2] +* (PROJP2). ZPN is the only projection which uses any of the others. +* +* The remaining members of the prjprm struct are maintained by the +* initialization routines and should not be modified. This is done for the +* sake of efficiency and to allow an arbitrary number of contexts to be +* maintained simultaneously. +* +* char code[4] +* Three-letter projection code. +* +* double phi0, theta0 +* Native longitude and latitude of the reference point, in degrees. +* +* double w[10] +* int n +* Intermediate values derived from the projection parameters. +* +* int (*prjfwd)() +* int (*prjrev)() +* Pointers to the forward and reverse projection routines. +* +* Usage of the p[] array as it applies to each projection is described in +* the prologue to each trio of projection routines. +* +* Argument checking +* ----------------- +* Forward routines: +* +* The values of phi and theta (the native longitude and latitude) +* normally lie in the range [-180,180] for phi, and [-90,90] for theta. +* However, all forward projections will accept any value of phi and will +* not normalize it. +* +* The forward projection routines do not explicitly check that theta lies +* within the range [-90,90]. They do check for any value of theta which +* produces an invalid argument to the projection equations (e.g. leading +* to division by zero). The forward routines for AZP, SZP, TAN, SIN, +* ZPN, and COP also return error 2 if (phi,theta) corresponds to the +* overlapped (far) side of the projection but also return the +* corresponding value of (x,y). This strict bounds checking may be +* relaxed by setting prj->flag to -1 (rather than 0) when these +* projections are initialized. +* +* Reverse routines: +* +* Error checking on the projected coordinates (x,y) is limited to that +* required to ascertain whether a solution exists. Where a solution does +* exist no check is made that the value of phi and theta obtained lie +* within the ranges [-180,180] for phi, and [-90,90] for theta. +* +* Accuracy +* -------- +* Closure to a precision of at least 1E-10 degree of longitude and latitude +* has been verified for typical projection parameters on the 1 degree grid +* of native longitude and latitude (to within 5 degrees of any latitude +* where the projection may diverge). +* +* Author: Mark Calabretta, Australia Telescope National Facility +* $Id: proj.c,v 2.20 2002/04/03 01:25:29 mcalabre Exp $ +*===========================================================================*/ + +#include <stdlib.h> +#include <string.h> +#include <math.h> +#include "wcslib.h" + +int npcode = 26; +char pcodes[26][4] = + {"AZP", "SZP", "TAN", "STG", "SIN", "ARC", "ZPN", "ZEA", "AIR", "CYP", + "CEA", "CAR", "MER", "COP", "COE", "COD", "COO", "SFL", "PAR", "MOL", + "AIT", "BON", "PCO", "TSC", "CSC", "QSC"}; + +const int AZP = 101; +const int SZP = 102; +const int TAN = 103; +const int STG = 104; +const int SIN = 105; +const int ARC = 106; +const int ZPN = 107; +const int ZEA = 108; +const int AIR = 109; +const int CYP = 201; +const int CEA = 202; +const int CAR = 203; +const int MER = 204; +const int SFL = 301; +const int PAR = 302; +const int MOL = 303; +const int AIT = 401; +const int COP = 501; +const int COE = 502; +const int COD = 503; +const int COO = 504; +const int BON = 601; +const int PCO = 602; +const int TSC = 701; +const int CSC = 702; +const int QSC = 703; + +/* Map error number to error message for each function. */ +const char *prjset_errmsg[] = { + 0, + "Invalid projection parameters"}; + +const char *prjfwd_errmsg[] = { + 0, + "Invalid projection parameters", + "Invalid value of (phi,theta)"}; + +const char *prjrev_errmsg[] = { + 0, + "Invalid projection parameters", + "Invalid value of (x,y)"}; + +#define copysgn(X, Y) ((Y) < 0.0 ? -fabs(X) : fabs(X)) +#define copysgni(X, Y) ((Y) < 0 ? -abs(X) : abs(X)) + +/*==========================================================================*/ + +int prjset(pcode, prj) + +const char pcode[4]; +struct prjprm *prj; + +{ + /* Set pointers to the forward and reverse projection routines. */ + if (strcmp(pcode, "AZP") == 0) { + azpset(prj); + } else if (strcmp(pcode, "SZP") == 0) { + szpset(prj); + } else if (strcmp(pcode, "TAN") == 0) { + tanset(prj); + } else if (strcmp(pcode, "STG") == 0) { + stgset(prj); + } else if (strcmp(pcode, "SIN") == 0) { + sinset(prj); + } else if (strcmp(pcode, "ARC") == 0) { + arcset(prj); + } else if (strcmp(pcode, "ZPN") == 0) { + zpnset(prj); + } else if (strcmp(pcode, "ZEA") == 0) { + zeaset(prj); + } else if (strcmp(pcode, "AIR") == 0) { + airset(prj); + } else if (strcmp(pcode, "CYP") == 0) { + cypset(prj); + } else if (strcmp(pcode, "CEA") == 0) { + ceaset(prj); + } else if (strcmp(pcode, "CAR") == 0) { + carset(prj); + } else if (strcmp(pcode, "MER") == 0) { + merset(prj); + } else if (strcmp(pcode, "SFL") == 0) { + sflset(prj); + } else if (strcmp(pcode, "PAR") == 0) { + parset(prj); + } else if (strcmp(pcode, "MOL") == 0) { + molset(prj); + } else if (strcmp(pcode, "AIT") == 0) { + aitset(prj); + } else if (strcmp(pcode, "COP") == 0) { + copset(prj); + } else if (strcmp(pcode, "COE") == 0) { + coeset(prj); + } else if (strcmp(pcode, "COD") == 0) { + codset(prj); + } else if (strcmp(pcode, "COO") == 0) { + cooset(prj); + } else if (strcmp(pcode, "BON") == 0) { + bonset(prj); + } else if (strcmp(pcode, "PCO") == 0) { + pcoset(prj); + } else if (strcmp(pcode, "TSC") == 0) { + tscset(prj); + } else if (strcmp(pcode, "CSC") == 0) { + cscset(prj); + } else if (strcmp(pcode, "QSC") == 0) { + qscset(prj); + } else { + /* Unrecognized projection code. */ + return 1; + } + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int prjfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + return prj->prjfwd(phi, theta, prj, x, y); +} + +/*--------------------------------------------------------------------------*/ + +int prjrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + return prj->prjrev(x, y, prj, phi, theta); +} + +/*============================================================================ +* AZP: zenithal/azimuthal perspective projection. +* +* Given: +* prj->p[1] Distance parameter, mu in units of r0. +* prj->p[2] Tilt angle, gamma in degrees. +* +* Given and/or returned: +* prj->flag AZP, or -AZP if prj->flag is given < 0. +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "AZP" +* prj->phi0 0.0 +* prj->theta0 90.0 +* prj->w[0] r0*(mu+1) +* prj->w[1] tan(gamma) +* prj->w[2] sec(gamma) +* prj->w[3] cos(gamma) +* prj->w[4] sin(gamma) +* prj->w[5] asin(-1/mu) for |mu| >= 1, -90 otherwise +* prj->w[6] mu*cos(gamma) +* prj->w[7] 1 if |mu*cos(gamma)| < 1, 0 otherwise +* prj->prjfwd Pointer to azpfwd(). +* prj->prjrev Pointer to azprev(). +*===========================================================================*/ + +int azpset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "AZP"); + prj->flag = copysgni (AZP, prj->flag); + prj->phi0 = 0.0; + prj->theta0 = 90.0; + + if (prj->r0 == 0.0) prj->r0 = R2D; + + prj->w[0] = prj->r0*(prj->p[1] + 1.0); + if (prj->w[0] == 0.0) { + return 1; + } + + prj->w[3] = cosdeg (prj->p[2]); + if (prj->w[3] == 0.0) { + return 1; + } + + prj->w[2] = 1.0/prj->w[3]; + prj->w[4] = sindeg (prj->p[2]); + prj->w[1] = prj->w[4] / prj->w[3]; + + if (fabs(prj->p[1]) > 1.0) { + prj->w[5] = asindeg (-1.0/prj->p[1]); + } else { + prj->w[5] = -90.0; + } + + prj->w[6] = prj->p[1] * prj->w[3]; + prj->w[7] = (fabs(prj->w[6]) < 1.0) ? 1.0 : 0.0; + + prj->prjfwd = azpfwd; + prj->prjrev = azprev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int azpfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double a, b, cphi, cthe, r, s, t; + + if (abs(prj->flag) != AZP) { + if (azpset(prj)) return 1; + } + + cphi = cosdeg (phi); + cthe = cosdeg (theta); + + s = prj->w[1]*cphi; + t = (prj->p[1] + sindeg (theta)) + cthe*s; + if (t == 0.0) { + return 2; + } + + r = prj->w[0]*cthe/t; + *x = r*sindeg (phi); + *y = -r*cphi*prj->w[2]; + + /* Bounds checking. */ + if (prj->flag > 0) { + /* Overlap. */ + if (theta < prj->w[5]) { + return 2; + } + + /* Divergence. */ + if (prj->w[7] > 0.0) { + t = prj->p[1] / sqrt(1.0 + s*s); + + if (fabs(t) <= 1.0) { + s = atandeg (-s); + t = asindeg (t); + a = s - t; + b = s + t + 180.0; + + if (a > 90.0) a -= 360.0; + if (b > 90.0) b -= 360.0; + + if (theta < ((a > b) ? a : b)) { + return 2; + } + } + } + } + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int azprev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double a, b, r, s, t, ycosg; + const double tol = 1.0e-13; + + if (abs(prj->flag) != AZP) { + if (azpset(prj)) return 1; + } + + ycosg = y*prj->w[3]; + + r = sqrt(x*x + ycosg*ycosg); + if (r == 0.0) { + *phi = 0.0; + *theta = 90.0; + } else { + *phi = atan2deg (x, -ycosg); + + s = r / (prj->w[0] + y*prj->w[4]); + t = s*prj->p[1]/sqrt(s*s + 1.0); + + s = atan2deg (1.0, s); + + if (fabs(t) > 1.0) { + t = copysgn (90.0,t); + if (fabs(t) > 1.0+tol) { + return 2; + } + } else { + t = asindeg (t); + } + + a = s - t; + b = s + t + 180.0; + + if (a > 90.0) a -= 360.0; + if (b > 90.0) b -= 360.0; + + *theta = (a > b) ? a : b; + } + + return 0; +} + +/*============================================================================ +* SZP: slant zenithal perspective projection. +* +* Given: +* prj->p[1] Distance of the point of projection from the centre of the +* generating sphere, mu in units of r0. +* prj->p[2] Native longitude, phi_c, and ... +* prj->p[3] Native latitude, theta_c, on the planewards side of the +* intersection of the line through the point of projection +* and the centre of the generating sphere, phi_c in degrees. +* +* Given and/or returned: +* prj->flag SZP, or -SZP if prj->flag is given < 0. +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "SZP" +* prj->phi0 0.0 +* prj->theta0 90.0 +* prj->w[0] 1/r0 +* prj->w[1] xp = -mu*cos(theta_c)*sin(phi_c) +* prj->w[2] yp = mu*cos(theta_c)*cos(phi_c) +* prj->w[3] zp = mu*sin(theta_c) + 1 +* prj->w[4] r0*xp +* prj->w[5] r0*yp +* prj->w[6] r0*zp +* prj->w[7] (zp - 1)^2 +* prj->w[8] asin(1-zp) if |1 - zp| < 1, -90 otherwise +* prj->prjfwd Pointer to szpfwd(). +* prj->prjrev Pointer to szprev(). +*===========================================================================*/ + +int szpset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "SZP"); + prj->flag = copysgni (SZP, prj->flag); + prj->phi0 = 0.0; + prj->theta0 = 90.0; + + if (prj->r0 == 0.0) prj->r0 = R2D; + + prj->w[0] = 1.0/prj->r0; + + prj->w[3] = prj->p[1] * sindeg (prj->p[3]) + 1.0; + if (prj->w[3] == 0.0) { + return 1; + } + + prj->w[1] = -prj->p[1] * cosdeg (prj->p[3]) * sindeg (prj->p[2]); + prj->w[2] = prj->p[1] * cosdeg (prj->p[3]) * cosdeg (prj->p[2]); + prj->w[4] = prj->r0 * prj->w[1]; + prj->w[5] = prj->r0 * prj->w[2]; + prj->w[6] = prj->r0 * prj->w[3]; + prj->w[7] = (prj->w[3] - 1.0) * prj->w[3] - 1.0; + + if (fabs(prj->w[3] - 1.0) < 1.0) { + prj->w[8] = asindeg (1.0 - prj->w[3]); + } else { + prj->w[8] = -90.0; + } + + prj->prjfwd = szpfwd; + prj->prjrev = szprev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int szpfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double a, b, cphi, cthe, s, sphi, t; + + if (abs(prj->flag) != SZP) { + if (szpset(prj)) return 1; + } + + cphi = cosdeg (phi); + sphi = sindeg (phi); + cthe = cosdeg (theta); + s = 1.0 - sindeg (theta); + + t = prj->w[3] - s; + if (t == 0.0) { + return 2; + } + + *x = (prj->w[6]*cthe*sphi - prj->w[4]*s)/t; + *y = -(prj->w[6]*cthe*cphi + prj->w[5]*s)/t; + + /* Bounds checking. */ + if (prj->flag > 0) { + /* Divergence. */ + if (theta < prj->w[8]) { + return 2; + } + + /* Overlap. */ + if (fabs(prj->p[1]) > 1.0) { + s = prj->w[1]*sphi - prj->w[2]*cphi; + t = 1.0/sqrt(prj->w[7] + s*s); + + if (fabs(t) <= 1.0) { + s = atan2deg (s, prj->w[3] - 1.0); + t = asindeg (t); + a = s - t; + b = s + t + 180.0; + + if (a > 90.0) a -= 360.0; + if (b > 90.0) b -= 360.0; + + if (theta < ((a > b) ? a : b)) { + return 2; + } + } + } + } + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int szprev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double a, b, c, d, r2, sth1, sth2, sthe, sxy, t, x1, xp, y1, yp, z; + const double tol = 1.0e-13; + + if (abs(prj->flag) != SZP) { + if (szpset(prj)) return 1; + } + + xp = x*prj->w[0]; + yp = y*prj->w[0]; + r2 = xp*xp + yp*yp; + + x1 = (xp - prj->w[1])/prj->w[3]; + y1 = (yp - prj->w[2])/prj->w[3]; + sxy = xp*x1 + yp*y1; + + if (r2 < 1.0e-10) { + /* Use small angle formula. */ + z = r2/2.0; + *theta = 90.0 - R2D*sqrt(r2/(1.0 + sxy)); + + } else { + t = x1*x1 + y1*y1; + a = t + 1.0; + b = sxy - t; + c = r2 - sxy - sxy + t - 1.0; + d = b*b - a*c; + + /* Check for a solution. */ + if (d < 0.0) { + return 2; + } + d = sqrt(d); + + /* Choose solution closest to pole. */ + sth1 = (-b + d)/a; + sth2 = (-b - d)/a; + sthe = (sth1 > sth2) ? sth1 : sth2; + if (sthe > 1.0) { + if (sthe-1.0 < tol) { + sthe = 1.0; + } else { + sthe = (sth1 < sth2) ? sth1 : sth2; + } + } + + if (sthe < -1.0) { + if (sthe+1.0 > -tol) { + sthe = -1.0; + } + } + + if (sthe > 1.0 || sthe < -1.0) { + return 2; + } + + *theta = asindeg (sthe); + + z = 1.0 - sthe; + } + + *phi = atan2deg (xp - x1*z, -(yp - y1*z)); + + return 0; +} + +/*============================================================================ +* TAN: gnomonic projection. +* +* Given and/or returned: +* prj->flag TAN, or -TAN if prj->flag is given < 0. +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "TAN" +* prj->phi0 0.0 +* prj->theta0 90.0 +* prj->prjfwd Pointer to tanfwd(). +* prj->prjrev Pointer to tanrev(). +*===========================================================================*/ + +int tanset(prj) + +struct prjprm *prj; + +{ + int k; + + strcpy(prj->code, "TAN"); + prj->flag = copysgni (TAN, prj->flag); + prj->phi0 = 0.0; + prj->theta0 = 90.0; + + if (prj->r0 == 0.0) prj->r0 = R2D; + + prj->prjfwd = tanfwd; + prj->prjrev = tanrev; + + for (k = (MAXPV-1); k >= 0 && prj->ppv[k] == 0.0 && prj->ppv[k+MAXPV] == 0.0; k--); + if (k < 0) + k = 0; + prj->npv = k; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int tanfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double r, s; + double xp[2]; + + if (abs(prj->flag) != TAN) { + if(tanset(prj)) return 1; + } + + s = sindeg (theta); + if (s <= 0.0) { + return 2; + } + + r = prj->r0*cosdeg (theta)/s; + xp[0] = r*sindeg (phi); + xp[1] = -r*cosdeg (phi); + *x = prj->inv_x? poly_func(prj->inv_x, xp) : xp[0]; + *y = prj->inv_y? poly_func(prj->inv_y, xp) : xp[1]; + + if (prj->flag > 0 && s < 0.0) { + return 2; + } + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int tanrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double r; + double xp; + double yp; + + if (abs(prj->flag) != TAN) { + if (tanset(prj)) return 1; + } + + if (prj->npv) { + raw_to_pv(prj, x,y, &xp, &yp); + } else { + xp = x; + yp = y; + } + + r = sqrt(xp*xp + yp*yp); + if (r == 0.0) { + *phi = 0.0; + } else { + *phi = atan2deg (xp, -yp); + } + + *theta = atan2deg (prj->r0, r); + + return 0; +} + +/*============================================================================ +* STG: stereographic projection. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "STG" +* prj->flag STG +* prj->phi0 0.0 +* prj->theta0 90.0 +* prj->w[0] 2*r0 +* prj->w[1] 1/(2*r0) +* prj->prjfwd Pointer to stgfwd(). +* prj->prjrev Pointer to stgrev(). +*===========================================================================*/ + +int stgset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "STG"); + prj->flag = STG; + prj->phi0 = 0.0; + prj->theta0 = 90.0; + + if (prj->r0 == 0.0) { + prj->r0 = R2D; + prj->w[0] = 360.0/PI; + prj->w[1] = PI/360.0; + } else { + prj->w[0] = 2.0*prj->r0; + prj->w[1] = 1.0/prj->w[0]; + } + + prj->prjfwd = stgfwd; + prj->prjrev = stgrev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int stgfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double r, s; + + if (prj->flag != STG) { + if (stgset(prj)) return 1; + } + + s = 1.0 + sindeg (theta); + if (s == 0.0) { + return 2; + } + + r = prj->w[0]*cosdeg (theta)/s; + *x = r*sindeg (phi); + *y = -r*cosdeg (phi); + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int stgrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double r; + + if (prj->flag != STG) { + if (stgset(prj)) return 1; + } + + r = sqrt(x*x + y*y); + if (r == 0.0) { + *phi = 0.0; + } else { + *phi = atan2deg (x, -y); + } + *theta = 90.0 - 2.0*atandeg (r*prj->w[1]); + + return 0; +} + +/*============================================================================ +* SIN: orthographic/synthesis projection. +* +* Given: +* prj->p[1:2] Obliqueness parameters, xi and eta. +* +* Given and/or returned: +* prj->flag SIN, or -SIN if prj->flag is given < 0. +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "SIN" +* prj->phi0 0.0 +* prj->theta0 90.0 +* prj->w[0] 1/r0 +* prj->w[1] xi**2 + eta**2 +* prj->w[2] xi**2 + eta**2 + 1 +* prj->w[3] xi**2 + eta**2 - 1 +* prj->prjfwd Pointer to sinfwd(). +* prj->prjrev Pointer to sinrev(). +*===========================================================================*/ + +int sinset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "SIN"); + prj->flag = copysgni (SIN, prj->flag); + prj->phi0 = 0.0; + prj->theta0 = 90.0; + + if (prj->r0 == 0.0) prj->r0 = R2D; + + prj->w[0] = 1.0/prj->r0; + prj->w[1] = prj->p[1]*prj->p[1] + prj->p[2]*prj->p[2]; + prj->w[2] = prj->w[1] + 1.0; + prj->w[3] = prj->w[1] - 1.0; + + prj->prjfwd = sinfwd; + prj->prjrev = sinrev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int sinfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double cphi, cthe, sphi, t, z; + + if (abs(prj->flag) != SIN) { + if (sinset(prj)) return 1; + } + + t = (90.0 - fabs(theta))*D2R; + if (t < 1.0e-5) { + if (theta > 0.0) { + z = t*t/2.0; + } else { + z = 2.0 - t*t/2.0; + } + cthe = t; + } else { + z = 1.0 - sindeg (theta); + cthe = cosdeg (theta); + } + + cphi = cosdeg (phi); + sphi = sindeg (phi); + *x = prj->r0*(cthe*sphi + prj->p[1]*z); + *y = -prj->r0*(cthe*cphi - prj->p[2]*z); + + /* Validate this solution. */ + if (prj->flag > 0) { + if (prj->w[1] == 0.0) { + /* Orthographic projection. */ + if (theta < 0.0) { + return 2; + } + } else { + /* "Synthesis" projection. */ + t = -atandeg (prj->p[1]*sphi - prj->p[2]*cphi); + if (theta < t) { + return 2; + } + } + } + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int sinrev (x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + const double tol = 1.0e-13; + double a, b, c, d, r2, sth1, sth2, sthe, sxy, x0, x1, xp, y0, y1, yp, z; + + if (abs(prj->flag) != SIN) { + if (sinset(prj)) return 1; + } + + /* Compute intermediaries. */ + x0 = x*prj->w[0]; + y0 = y*prj->w[0]; + r2 = x0*x0 + y0*y0; + + if (prj->w[1] == 0.0) { + /* Orthographic projection. */ + if (r2 != 0.0) { + *phi = atan2deg (x0, -y0); + } else { + *phi = 0.0; + } + + if (r2 < 0.5) { + *theta = acosdeg (sqrt(r2)); + } else if (r2 <= 1.0) { + *theta = asindeg (sqrt(1.0 - r2)); + } else { + return 2; + } + + } else { + /* "Synthesis" projection. */ + x1 = prj->p[1]; + y1 = prj->p[2]; + sxy = x0*x1 + y0*y1; + + if (r2 < 1.0e-10) { + /* Use small angle formula. */ + z = r2/2.0; + *theta = 90.0 - R2D*sqrt(r2/(1.0 + sxy)); + + } else { + a = prj->w[2]; + b = sxy - prj->w[1]; + c = r2 - sxy - sxy + prj->w[3]; + d = b*b - a*c; + + /* Check for a solution. */ + if (d < 0.0) { + return 2; + } + d = sqrt(d); + + /* Choose solution closest to pole. */ + sth1 = (-b + d)/a; + sth2 = (-b - d)/a; + sthe = (sth1 > sth2) ? sth1 : sth2; + if (sthe > 1.0) { + if (sthe-1.0 < tol) { + sthe = 1.0; + } else { + sthe = (sth1 < sth2) ? sth1 : sth2; + } + } + + if (sthe < -1.0) { + if (sthe+1.0 > -tol) { + sthe = -1.0; + } + } + + if (sthe > 1.0 || sthe < -1.0) { + return 2; + } + + *theta = asindeg (sthe); + z = 1.0 - sthe; + } + + xp = -y0 + prj->p[2]*z; + yp = x0 - prj->p[1]*z; + if (xp == 0.0 && yp == 0.0) { + *phi = 0.0; + } else { + *phi = atan2deg (yp,xp); + } + } + + return 0; +} + +/*============================================================================ +* ARC: zenithal/azimuthal equidistant projection. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "ARC" +* prj->flag ARC +* prj->phi0 0.0 +* prj->theta0 90.0 +* prj->w[0] r0*(pi/180) +* prj->w[1] (180/pi)/r0 +* prj->prjfwd Pointer to arcfwd(). +* prj->prjrev Pointer to arcrev(). +*===========================================================================*/ + +int arcset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "ARC"); + prj->flag = ARC; + prj->phi0 = 0.0; + prj->theta0 = 90.0; + + if (prj->r0 == 0.0) { + prj->r0 = R2D; + prj->w[0] = 1.0; + prj->w[1] = 1.0; + } else { + prj->w[0] = prj->r0*D2R; + prj->w[1] = 1.0/prj->w[0]; + } + + prj->prjfwd = arcfwd; + prj->prjrev = arcrev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int arcfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double r; + + if (prj->flag != ARC) { + if (arcset(prj)) return 1; + } + + r = prj->w[0]*(90.0 - theta); + *x = r*sindeg (phi); + *y = -r*cosdeg (phi); + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int arcrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double r; + + if (prj->flag != ARC) { + if (arcset(prj)) return 1; + } + + r = sqrt(x*x + y*y); + if (r == 0.0) { + *phi = 0.0; + } else { + *phi = atan2deg (x, -y); + } + *theta = 90.0 - r*prj->w[1]; + + return 0; +} + +/*============================================================================ +* ZPN: zenithal/azimuthal polynomial projection. +* +* Given: +* prj->p[0:9] Polynomial coefficients. +* +* Given and/or returned: +* prj->flag ZPN, or -ZPN if prj->flag is given < 0. +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "ZPN" +* prj->phi0 0.0 +* prj->theta0 90.0 +* prj->n Degree of the polynomial, N. +* prj->w[0] Co-latitude of the first point of inflection (N > 2). +* prj->w[1] Radius of the first point of inflection (N > 2). +* prj->prjfwd Pointer to zpnfwd(). +* prj->prjrev Pointer to zpnrev(). +*===========================================================================*/ + +int zpnset(prj) + +struct prjprm *prj; + +{ + int i, j, k; + double d, d1, d2, r, zd, zd1, zd2; + const double tol = 1.0e-13; + + strcpy(prj->code, "ZPN"); + prj->flag = copysgni (ZPN, prj->flag); + prj->phi0 = 0.0; + prj->theta0 = 90.0; + + if (prj->r0 == 0.0) prj->r0 = R2D; + + /* Find the highest non-zero coefficient. */ + for (k = 9; k >= 0 && prj->p[k] == 0.0; k--){ + i = 0; } + /* if (k < 0) return 1; */ + + /* if (k < 0 switch to ARC projection */ + if (k < 0) { + return (arcset (prj)); + } + + prj->n = k; + + /* No negative derivative -> no point of inflection. */ + zd = PI; + + /* Processing subroutines */ + prj->prjfwd = zpnfwd; + prj->prjrev = zpnrev; + + if (k >= 3) { + /* Find the point of inflection closest to the pole. */ + zd1 = 0.0; + d1 = prj->p[1]; + if (d1 <= 0.0) { + return 1; + } + + /* Find the point where the derivative first goes negative. */ + for (i = 0; i < 180; i++) { + zd2 = i*D2R; + d2 = 0.0; + for (j = k; j > 0; j--) { + d2 = d2*zd2 + j*prj->p[j]; + } + + if (d2 <= 0.0) break; + zd1 = zd2; + d1 = d2; + } + + if (i == 180) { + /* No negative derivative -> no point of inflection. */ + zd = PI; + } else { + /* Find where the derivative is zero. */ + for (i = 1; i <= 10; i++) { + zd = zd1 - d1*(zd2-zd1)/(d2-d1); + + d = 0.0; + for (j = k; j > 0; j--) { + d = d*zd + j*prj->p[j]; + } + + if (fabs(d) < tol) break; + + if (d < 0.0) { + zd2 = zd; + d2 = d; + } else { + zd1 = zd; + d1 = d; + } + } + } + + r = 0.0; + for (j = k; j >= 0; j--) { + r = r*zd + prj->p[j]; + } + prj->w[0] = zd; + prj->w[1] = r; + } + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int zpnfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + int j; + double r, s; + + if (abs(prj->flag) != ZPN) { + if (zpnset(prj)) return 1; + } + + s = (90.0 - theta)*D2R; + + r = 0.0; + for (j = 9; j >= 0; j--) { + r = r*s + prj->p[j]; + } + r = prj->r0*r; + + *x = r*sindeg (phi); + *y = -r*cosdeg (phi); + + if (prj->flag > 0 && s > prj->w[0]) { + return 2; + } + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int zpnrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + int i, j, k; + double a, b, c, d, lambda, r, r1, r2, rt, zd, zd1, zd2; + const double tol = 1.0e-13; + + if (abs(prj->flag) != ZPN) { + if (zpnset(prj)) return 1; + } + + k = prj->n; + + r = sqrt(x*x + y*y)/prj->r0; + + if (k < 1) { + /* Constant - no solution. */ + return 1; + } else if (k == 1) { + /* Linear. */ + zd = (r - prj->p[0])/prj->p[1]; + } else if (k == 2) { + /* Quadratic. */ + a = prj->p[2]; + b = prj->p[1]; + c = prj->p[0] - r; + + d = b*b - 4.0*a*c; + if (d < 0.0) { + return 2; + } + d = sqrt(d); + + /* Choose solution closest to pole. */ + zd1 = (-b + d)/(2.0*a); + zd2 = (-b - d)/(2.0*a); + zd = (zd1<zd2) ? zd1 : zd2; + if (zd < -tol) zd = (zd1>zd2) ? zd1 : zd2; + if (zd < 0.0) { + if (zd < -tol) { + return 2; + } + zd = 0.0; + } else if (zd > PI) { + if (zd > PI+tol) { + return 2; + } + zd = PI; + } + } else { + /* Higher order - solve iteratively. */ + zd1 = 0.0; + r1 = prj->p[0]; + zd2 = prj->w[0]; + r2 = prj->w[1]; + + if (r < r1) { + if (r < r1-tol) { + return 2; + } + zd = zd1; + } else if (r > r2) { + if (r > r2+tol) { + return 2; + } + zd = zd2; + } else { + /* Disect the interval. */ + for (j = 0; j < 100; j++) { + lambda = (r2 - r)/(r2 - r1); + if (lambda < 0.1) { + lambda = 0.1; + } else if (lambda > 0.9) { + lambda = 0.9; + } + + zd = zd2 - lambda*(zd2 - zd1); + + rt = 0.0; + for (i = k; i >= 0; i--) { + rt = (rt * zd) + prj->p[i]; + } + + if (rt < r) { + if (r-rt < tol) break; + r1 = rt; + zd1 = zd; + } else { + if (rt-r < tol) break; + r2 = rt; + zd2 = zd; + } + + if (fabs(zd2-zd1) < tol) break; + } + } + } + + if (r == 0.0) { + *phi = 0.0; + } else { + *phi = atan2deg (x, -y); + } + *theta = 90.0 - zd*R2D; + + return 0; +} + +/*============================================================================ +* ZEA: zenithal/azimuthal equal area projection. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "ZEA" +* prj->flag ZEA +* prj->phi0 0.0 +* prj->theta0 90.0 +* prj->w[0] 2*r0 +* prj->w[1] 1/(2*r0) +* prj->prjfwd Pointer to zeafwd(). +* prj->prjrev Pointer to zearev(). +*===========================================================================*/ + +int zeaset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "ZEA"); + prj->flag = ZEA; + prj->phi0 = 0.0; + prj->theta0 = 90.0; + + if (prj->r0 == 0.0) { + prj->r0 = R2D; + prj->w[0] = 360.0/PI; + prj->w[1] = PI/360.0; + } else { + prj->w[0] = 2.0*prj->r0; + prj->w[1] = 1.0/prj->w[0]; + } + + prj->prjfwd = zeafwd; + prj->prjrev = zearev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int zeafwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double r; + + if (prj->flag != ZEA) { + if (zeaset(prj)) return 1; + } + + r = prj->w[0]*sindeg ((90.0 - theta)/2.0); + *x = r*sindeg (phi); + *y = -r*cosdeg (phi); + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int zearev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double r, s; + const double tol = 1.0e-12; + + if (prj->flag != ZEA) { + if (zeaset(prj)) return 1; + } + + r = sqrt(x*x + y*y); + if (r == 0.0) { + *phi = 0.0; + } else { + *phi = atan2deg (x, -y); + } + + s = r*prj->w[1]; + if (fabs(s) > 1.0) { + if (fabs(r - prj->w[0]) < tol) { + *theta = -90.0; + } else { + return 2; + } + } else { + *theta = 90.0 - 2.0*asindeg (s); + } + + return 0; +} + +/*============================================================================ +* AIR: Airy's projection. +* +* Given: +* prj->p[1] Latitude theta_b within which the error is minimized, in +* degrees. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "AIR" +* prj->flag AIR +* prj->phi0 0.0 +* prj->theta0 90.0 +* prj->w[0] 2*r0 +* prj->w[1] ln(cos(xi_b))/tan(xi_b)**2, where xi_b = (90-theta_b)/2 +* prj->w[2] 1/2 - prj->w[1] +* prj->w[3] 2*r0*prj->w[2] +* prj->w[4] tol, cutoff for using small angle approximation, in +* radians. +* prj->w[5] prj->w[2]*tol +* prj->w[6] (180/pi)/prj->w[2] +* prj->prjfwd Pointer to airfwd(). +* prj->prjrev Pointer to airrev(). +*===========================================================================*/ + +int airset(prj) + +struct prjprm *prj; + +{ + const double tol = 1.0e-4; + double cxi; + + strcpy(prj->code, "AIR"); + prj->flag = AIR; + prj->phi0 = 0.0; + prj->theta0 = 90.0; + + if (prj->r0 == 0.0) prj->r0 = R2D; + + prj->w[0] = 2.0*prj->r0; + if (prj->p[1] == 90.0) { + prj->w[1] = -0.5; + prj->w[2] = 1.0; + } else if (prj->p[1] > -90.0) { + cxi = cosdeg ((90.0 - prj->p[1])/2.0); + prj->w[1] = log(cxi)*(cxi*cxi)/(1.0-cxi*cxi); + prj->w[2] = 0.5 - prj->w[1]; + } else { + return 1; + } + + prj->w[3] = prj->w[0] * prj->w[2]; + prj->w[4] = tol; + prj->w[5] = prj->w[2]*tol; + prj->w[6] = R2D/prj->w[2]; + + prj->prjfwd = airfwd; + prj->prjrev = airrev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int airfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double cxi, r, txi, xi; + + if (prj->flag != AIR) { + if (airset(prj)) return 1; + } + + if (theta == 90.0) { + r = 0.0; + } else if (theta > -90.0) { + xi = D2R*(90.0 - theta)/2.0; + if (xi < prj->w[4]) { + r = xi*prj->w[3]; + } else { + cxi = cosdeg ((90.0 - theta)/2.0); + txi = sqrt(1.0-cxi*cxi)/cxi; + r = -prj->w[0]*(log(cxi)/txi + prj->w[1]*txi); + } + } else { + return 2; + } + + *x = r*sindeg (phi); + *y = -r*cosdeg (phi); + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int airrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + int j; + double cxi, lambda, r, r1, r2, rt, txi, x1, x2, xi; + const double tol = 1.0e-12; + + if (prj->flag != AIR) { + if (airset(prj)) return 1; + } + + r = sqrt(x*x + y*y)/prj->w[0]; + + if (r == 0.0) { + xi = 0.0; + } else if (r < prj->w[5]) { + xi = r*prj->w[6]; + } else { + /* Find a solution interval. */ + x1 = 1.0; + r1 = 0.0; + for (j = 0; j < 30; j++) { + x2 = x1/2.0; + txi = sqrt(1.0-x2*x2)/x2; + r2 = -(log(x2)/txi + prj->w[1]*txi); + + if (r2 >= r) break; + x1 = x2; + r1 = r2; + } + if (j == 30) return 2; + + for (j = 0; j < 100; j++) { + /* Weighted division of the interval. */ + lambda = (r2-r)/(r2-r1); + if (lambda < 0.1) { + lambda = 0.1; + } else if (lambda > 0.9) { + lambda = 0.9; + } + cxi = x2 - lambda*(x2-x1); + + txi = sqrt(1.0-cxi*cxi)/cxi; + rt = -(log(cxi)/txi + prj->w[1]*txi); + + if (rt < r) { + if (r-rt < tol) break; + r1 = rt; + x1 = cxi; + } else { + if (rt-r < tol) break; + r2 = rt; + x2 = cxi; + } + } + if (j == 100) return 2; + + xi = acosdeg (cxi); + } + + if (r == 0.0) { + *phi = 0.0; + } else { + *phi = atan2deg (x, -y); + } + *theta = 90.0 - 2.0*xi; + + return 0; +} + +/*============================================================================ +* CYP: cylindrical perspective projection. +* +* Given: +* prj->p[1] Distance of point of projection from the centre of the +* generating sphere, mu, in units of r0. +* prj->p[2] Radius of the cylinder of projection, lambda, in units of +* r0. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "CYP" +* prj->flag CYP +* prj->phi0 0.0 +* prj->theta0 0.0 +* prj->w[0] r0*lambda*(pi/180) +* prj->w[1] (180/pi)/(r0*lambda) +* prj->w[2] r0*(mu + lambda) +* prj->w[3] 1/(r0*(mu + lambda)) +* prj->prjfwd Pointer to cypfwd(). +* prj->prjrev Pointer to cyprev(). +*===========================================================================*/ + +int cypset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "CYP"); + prj->flag = CYP; + prj->phi0 = 0.0; + prj->theta0 = 0.0; + + if (prj->r0 == 0.0) { + prj->r0 = R2D; + + prj->w[0] = prj->p[2]; + if (prj->w[0] == 0.0) { + return 1; + } + + prj->w[1] = 1.0/prj->w[0]; + + prj->w[2] = R2D*(prj->p[1] + prj->p[2]); + if (prj->w[2] == 0.0) { + return 1; + } + + prj->w[3] = 1.0/prj->w[2]; + } else { + prj->w[0] = prj->r0*prj->p[2]*D2R; + if (prj->w[0] == 0.0) { + return 1; + } + + prj->w[1] = 1.0/prj->w[0]; + + prj->w[2] = prj->r0*(prj->p[1] + prj->p[2]); + if (prj->w[2] == 0.0) { + return 1; + } + + prj->w[3] = 1.0/prj->w[2]; + } + + prj->prjfwd = cypfwd; + prj->prjrev = cyprev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int cypfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double s; + + if (prj->flag != CYP) { + if (cypset(prj)) return 1; + } + + s = prj->p[1] + cosdeg (theta); + if (s == 0.0) { + return 2; + } + + *x = prj->w[0]*phi; + *y = prj->w[2]*sindeg (theta)/s; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int cyprev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double eta; + + if (prj->flag != CYP) { + if (cypset(prj)) return 1; + } + + *phi = x*prj->w[1]; + eta = y*prj->w[3]; + *theta = atan2deg (eta,1.0) + asindeg (eta*prj->p[1]/sqrt(eta*eta+1.0)); + + return 0; +} + +/*============================================================================ +* CEA: cylindrical equal area projection. +* +* Given: +* prj->p[1] Square of the cosine of the latitude at which the +* projection is conformal, lambda. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "CEA" +* prj->flag CEA +* prj->phi0 0.0 +* prj->theta0 0.0 +* prj->w[0] r0*(pi/180) +* prj->w[1] (180/pi)/r0 +* prj->w[2] r0/lambda +* prj->w[3] lambda/r0 +* prj->prjfwd Pointer to ceafwd(). +* prj->prjrev Pointer to cearev(). +*===========================================================================*/ + +int ceaset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "CEA"); + prj->flag = CEA; + prj->phi0 = 0.0; + prj->theta0 = 0.0; + + if (prj->r0 == 0.0) { + prj->r0 = R2D; + prj->w[0] = 1.0; + prj->w[1] = 1.0; + if (prj->p[1] <= 0.0 || prj->p[1] > 1.0) { + return 1; + } + prj->w[2] = prj->r0/prj->p[1]; + prj->w[3] = prj->p[1]/prj->r0; + } else { + prj->w[0] = prj->r0*D2R; + prj->w[1] = R2D/prj->r0; + if (prj->p[1] <= 0.0 || prj->p[1] > 1.0) { + return 1; + } + prj->w[2] = prj->r0/prj->p[1]; + prj->w[3] = prj->p[1]/prj->r0; + } + + prj->prjfwd = ceafwd; + prj->prjrev = cearev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int ceafwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + if (prj->flag != CEA) { + if (ceaset(prj)) return 1; + } + + *x = prj->w[0]*phi; + *y = prj->w[2]*sindeg (theta); + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int cearev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double s; + const double tol = 1.0e-13; + + if (prj->flag != CEA) { + if (ceaset(prj)) return 1; + } + + s = y*prj->w[3]; + if (fabs(s) > 1.0) { + if (fabs(s) > 1.0+tol) { + return 2; + } + s = copysgn (1.0,s); + } + + *phi = x*prj->w[1]; + *theta = asindeg (s); + + return 0; +} + +/*============================================================================ +* CAR: Cartesian projection. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "CAR" +* prj->flag CAR +* prj->phi0 0.0 +* prj->theta0 0.0 +* prj->w[0] r0*(pi/180) +* prj->w[1] (180/pi)/r0 +* prj->prjfwd Pointer to carfwd(). +* prj->prjrev Pointer to carrev(). +*===========================================================================*/ + +int carset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "CAR"); + prj->flag = CAR; + prj->phi0 = 0.0; + prj->theta0 = 0.0; + + if (prj->r0 == 0.0) { + prj->r0 = R2D; + prj->w[0] = 1.0; + prj->w[1] = 1.0; + } else { + prj->w[0] = prj->r0*D2R; + prj->w[1] = 1.0/prj->w[0]; + } + + prj->prjfwd = carfwd; + prj->prjrev = carrev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int carfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + if (prj->flag != CAR) { + if (carset(prj)) return 1; + } + + *x = prj->w[0]*phi; + *y = prj->w[0]*theta; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int carrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + if (prj->flag != CAR) { + if (carset(prj)) return 1; + } + + *phi = prj->w[1]*x; + *theta = prj->w[1]*y; + + return 0; +} + +/*============================================================================ +* MER: Mercator's projection. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "MER" +* prj->flag MER +* prj->phi0 0.0 +* prj->theta0 0.0 +* prj->w[0] r0*(pi/180) +* prj->w[1] (180/pi)/r0 +* prj->prjfwd Pointer to merfwd(). +* prj->prjrev Pointer to merrev(). +*===========================================================================*/ + +int merset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "MER"); + prj->flag = MER; + prj->phi0 = 0.0; + prj->theta0 = 0.0; + + if (prj->r0 == 0.0) { + prj->r0 = R2D; + prj->w[0] = 1.0; + prj->w[1] = 1.0; + } else { + prj->w[0] = prj->r0*D2R; + prj->w[1] = 1.0/prj->w[0]; + } + + prj->prjfwd = merfwd; + prj->prjrev = merrev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int merfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + if (prj->flag != MER) { + if (merset(prj)) return 1; + } + + if (theta <= -90.0 || theta >= 90.0) { + return 2; + } + + *x = prj->w[0]*phi; + *y = prj->r0*log(tandeg ((90.0+theta)/2.0)); + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int merrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + if (prj->flag != MER) { + if (merset(prj)) return 1; + } + + *phi = x*prj->w[1]; + *theta = 2.0*atandeg (exp(y/prj->r0)) - 90.0; + + return 0; +} + +/*============================================================================ +* SFL: Sanson-Flamsteed ("global sinusoid") projection. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "SFL" +* prj->flag SFL +* prj->phi0 0.0 +* prj->theta0 0.0 +* prj->w[0] r0*(pi/180) +* prj->w[1] (180/pi)/r0 +* prj->prjfwd Pointer to sflfwd(). +* prj->prjrev Pointer to sflrev(). +*===========================================================================*/ + +int sflset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "SFL"); + prj->flag = SFL; + prj->phi0 = 0.0; + prj->theta0 = 0.0; + + if (prj->r0 == 0.0) { + prj->r0 = R2D; + prj->w[0] = 1.0; + prj->w[1] = 1.0; + } else { + prj->w[0] = prj->r0*D2R; + prj->w[1] = 1.0/prj->w[0]; + } + + prj->prjfwd = sflfwd; + prj->prjrev = sflrev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int sflfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + if (prj->flag != SFL) { + if (sflset(prj)) return 1; + } + + *x = prj->w[0]*phi*cosdeg (theta); + *y = prj->w[0]*theta; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int sflrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double w; + + if (prj->flag != SFL) { + if (sflset(prj)) return 1; + } + + w = cos(y/prj->r0); + if (w == 0.0) { + *phi = 0.0; + } else { + *phi = x*prj->w[1]/cos(y/prj->r0); + } + *theta = y*prj->w[1]; + + return 0; +} + +/*============================================================================ +* PAR: parabolic projection. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "PAR" +* prj->flag PAR +* prj->phi0 0.0 +* prj->theta0 0.0 +* prj->w[0] r0*(pi/180) +* prj->w[1] (180/pi)/r0 +* prj->w[2] pi*r0 +* prj->w[3] 1/(pi*r0) +* prj->prjfwd Pointer to parfwd(). +* prj->prjrev Pointer to parrev(). +*===========================================================================*/ + +int parset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "PAR"); + prj->flag = PAR; + prj->phi0 = 0.0; + prj->theta0 = 0.0; + + if (prj->r0 == 0.0) { + prj->r0 = R2D; + prj->w[0] = 1.0; + prj->w[1] = 1.0; + prj->w[2] = 180.0; + prj->w[3] = 1.0/prj->w[2]; + } else { + prj->w[0] = prj->r0*D2R; + prj->w[1] = 1.0/prj->w[0]; + prj->w[2] = PI*prj->r0; + prj->w[3] = 1.0/prj->w[2]; + } + + prj->prjfwd = parfwd; + prj->prjrev = parrev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int parfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double s; + + if (prj->flag != PAR) { + if (parset(prj)) return 1; + } + + s = sindeg (theta/3.0); + *x = prj->w[0]*phi*(1.0 - 4.0*s*s); + *y = prj->w[2]*s; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int parrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double s, t; + + if (prj->flag != PAR) { + if (parset(prj)) return 1; + } + + s = y*prj->w[3]; + if (s > 1.0 || s < -1.0) { + return 2; + } + + t = 1.0 - 4.0*s*s; + if (t == 0.0) { + if (x == 0.0) { + *phi = 0.0; + } else { + return 2; + } + } else { + *phi = prj->w[1]*x/t; + } + + *theta = 3.0*asindeg (s); + + return 0; +} + +/*============================================================================ +* MOL: Mollweide's projection. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "MOL" +* prj->flag MOL +* prj->phi0 0.0 +* prj->theta0 0.0 +* prj->w[0] sqrt(2)*r0 +* prj->w[1] sqrt(2)*r0/90 +* prj->w[2] 1/(sqrt(2)*r0) +* prj->w[3] 90/r0 +* prj->prjfwd Pointer to molfwd(). +* prj->prjrev Pointer to molrev(). +*===========================================================================*/ + +int molset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "MOL"); + prj->flag = MOL; + prj->phi0 = 0.0; + prj->theta0 = 0.0; + + if (prj->r0 == 0.0) prj->r0 = R2D; + + prj->w[0] = SQRT2*prj->r0; + prj->w[1] = prj->w[0]/90.0; + prj->w[2] = 1.0/prj->w[0]; + prj->w[3] = 90.0/prj->r0; + prj->w[4] = 2.0/PI; + + prj->prjfwd = molfwd; + prj->prjrev = molrev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int molfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + int j; + double gamma, resid, u, v, v0, v1; + const double tol = 1.0e-13; + + if (prj->flag != MOL) { + if (molset(prj)) return 1; + } + + if (fabs(theta) == 90.0) { + *x = 0.0; + *y = copysgn (prj->w[0],theta); + } else if (theta == 0.0) { + *x = prj->w[1]*phi; + *y = 0.0; + } else { + u = PI*sindeg (theta); + v0 = -PI; + v1 = PI; + v = u; + for (j = 0; j < 100; j++) { + resid = (v - u) + sin(v); + if (resid < 0.0) { + if (resid > -tol) break; + v0 = v; + } else { + if (resid < tol) break; + v1 = v; + } + v = (v0 + v1)/2.0; + } + + gamma = v/2.0; + *x = prj->w[1]*phi*cos(gamma); + *y = prj->w[0]*sin(gamma); + } + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int molrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double s, y0, z; + const double tol = 1.0e-12; + + if (prj->flag != MOL) { + if (molset(prj)) return 1; + } + + y0 = y/prj->r0; + s = 2.0 - y0*y0; + if (s <= tol) { + if (s < -tol) { + return 2; + } + s = 0.0; + + if (fabs(x) > tol) { + return 2; + } + *phi = 0.0; + } else { + s = sqrt(s); + *phi = prj->w[3]*x/s; + } + + z = y*prj->w[2]; + if (fabs(z) > 1.0) { + if (fabs(z) > 1.0+tol) { + return 2; + } + z = copysgn (1.0,z) + y0*s/PI; + } else { + z = asin(z)*prj->w[4] + y0*s/PI; + } + + if (fabs(z) > 1.0) { + if (fabs(z) > 1.0+tol) { + return 2; + } + z = copysgn (1.0,z); + } + + *theta = asindeg (z); + + return 0; +} + +/*============================================================================ +* AIT: Hammer-Aitoff projection. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "AIT" +* prj->flag AIT +* prj->phi0 0.0 +* prj->theta0 0.0 +* prj->w[0] 2*r0**2 +* prj->w[1] 1/(2*r0)**2 +* prj->w[2] 1/(4*r0)**2 +* prj->w[3] 1/(2*r0) +* prj->prjfwd Pointer to aitfwd(). +* prj->prjrev Pointer to aitrev(). +*===========================================================================*/ + +int aitset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "AIT"); + prj->flag = AIT; + prj->phi0 = 0.0; + prj->theta0 = 0.0; + + if (prj->r0 == 0.0) prj->r0 = R2D; + + prj->w[0] = 2.0*prj->r0*prj->r0; + prj->w[1] = 1.0/(2.0*prj->w[0]); + prj->w[2] = prj->w[1]/4.0; + prj->w[3] = 1.0/(2.0*prj->r0); + + prj->prjfwd = aitfwd; + prj->prjrev = aitrev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int aitfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double cthe, w; + + if (prj->flag != AIT) { + if (aitset(prj)) return 1; + } + + cthe = cosdeg (theta); + w = sqrt(prj->w[0]/(1.0 + cthe*cosdeg (phi/2.0))); + *x = 2.0*w*cthe*sindeg (phi/2.0); + *y = w*sindeg (theta); + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int aitrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double s, u, xp, yp, z; + const double tol = 1.0e-13; + + if (prj->flag != AIT) { + if (aitset(prj)) return 1; + } + + u = 1.0 - x*x*prj->w[2] - y*y*prj->w[1]; + if (u < 0.0) { + if (u < -tol) { + return 2; + } + + u = 0.0; + } + + z = sqrt(u); + s = z*y/prj->r0; + if (fabs(s) > 1.0) { + if (fabs(s) > 1.0+tol) { + return 2; + } + s = copysgn (1.0,s); + } + + xp = 2.0*z*z - 1.0; + yp = z*x*prj->w[3]; + if (xp == 0.0 && yp == 0.0) { + *phi = 0.0; + } else { + *phi = 2.0*atan2deg (yp, xp); + } + *theta = asindeg (s); + + return 0; +} + +/*============================================================================ +* COP: conic perspective projection. +* +* Given: +* prj->p[1] sigma = (theta2+theta1)/2 +* prj->p[2] delta = (theta2-theta1)/2, where theta1 and theta2 are the +* latitudes of the standard parallels, in degrees. +* +* Given and/or returned: +* prj->flag COP, or -COP if prj->flag is given < 0. +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "COP" +* prj->phi0 0.0 +* prj->theta0 sigma +* prj->w[0] C = sin(sigma) +* prj->w[1] 1/C +* prj->w[2] Y0 = r0*cos(delta)*cot(sigma) +* prj->w[3] r0*cos(delta) +* prj->w[4] 1/(r0*cos(delta) +* prj->w[5] cot(sigma) +* prj->prjfwd Pointer to copfwd(). +* prj->prjrev Pointer to coprev(). +*===========================================================================*/ + +int copset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "COP"); + prj->flag = copysgni (COP, prj->flag); + prj->phi0 = 0.0; + prj->theta0 = prj->p[1]; + + if (prj->r0 == 0.0) prj->r0 = R2D; + + prj->w[0] = sindeg (prj->p[1]); + if (prj->w[0] == 0.0) { + return 1; + } + + prj->w[1] = 1.0/prj->w[0]; + + prj->w[3] = prj->r0*cosdeg (prj->p[2]); + if (prj->w[3] == 0.0) { + return 1; + } + + prj->w[4] = 1.0/prj->w[3]; + prj->w[5] = 1.0/tandeg (prj->p[1]); + + prj->w[2] = prj->w[3]*prj->w[5]; + + prj->prjfwd = copfwd; + prj->prjrev = coprev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int copfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double a, r, s, t; + + if (abs(prj->flag) != COP) { + if (copset(prj)) return 1; + } + + t = theta - prj->p[1]; + s = cosdeg (t); + if (s == 0.0) { + return 2; + } + + a = prj->w[0]*phi; + r = prj->w[2] - prj->w[3]*sindeg (t)/s; + + *x = r*sindeg (a); + *y = prj->w[2] - r*cosdeg (a); + + if (prj->flag > 0 && r*prj->w[0] < 0.0) { + return 2; + } + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int coprev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double a, dy, r; + + if (abs(prj->flag) != COP) { + if (copset(prj)) return 1; + } + + dy = prj->w[2] - y; + r = sqrt(x*x + dy*dy); + if (prj->p[1] < 0.0) r = -r; + + if (r == 0.0) { + a = 0.0; + } else { + a = atan2deg (x/r, dy/r); + } + + *phi = a*prj->w[1]; + *theta = prj->p[1] + atandeg (prj->w[5] - r*prj->w[4]); + + return 0; +} + +/*============================================================================ +* COE: conic equal area projection. +* +* Given: +* prj->p[1] sigma = (theta2+theta1)/2 +* prj->p[2] delta = (theta2-theta1)/2, where theta1 and theta2 are the +* latitudes of the standard parallels, in degrees. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "COE" +* prj->flag COE +* prj->phi0 0.0 +* prj->theta0 sigma +* prj->w[0] C = (sin(theta1) + sin(theta2))/2 +* prj->w[1] 1/C +* prj->w[2] Y0 = chi*sqrt(psi - 2C*sindeg (sigma)) +* prj->w[3] chi = r0/C +* prj->w[4] psi = 1 + sin(theta1)*sin(theta2) +* prj->w[5] 2C +* prj->w[6] (1 + sin(theta1)*sin(theta2))*(r0/C)**2 +* prj->w[7] C/(2*r0**2) +* prj->w[8] chi*sqrt(psi + 2C) +* prj->prjfwd Pointer to coefwd(). +* prj->prjrev Pointer to coerev(). +*===========================================================================*/ + +int coeset(prj) + +struct prjprm *prj; + +{ + double theta1, theta2; + + strcpy(prj->code, "COE"); + prj->flag = COE; + prj->phi0 = 0.0; + prj->theta0 = prj->p[1]; + + if (prj->r0 == 0.0) prj->r0 = R2D; + + theta1 = prj->p[1] - prj->p[2]; + theta2 = prj->p[1] + prj->p[2]; + + prj->w[0] = (sindeg (theta1) + sindeg (theta2))/2.0; + if (prj->w[0] == 0.0) { + return 1; + } + + prj->w[1] = 1.0/prj->w[0]; + + prj->w[3] = prj->r0/prj->w[0]; + prj->w[4] = 1.0 + sindeg (theta1)*sindeg (theta2); + prj->w[5] = 2.0*prj->w[0]; + prj->w[6] = prj->w[3]*prj->w[3]*prj->w[4]; + prj->w[7] = 1.0/(2.0*prj->r0*prj->w[3]); + prj->w[8] = prj->w[3]*sqrt(prj->w[4] + prj->w[5]); + + prj->w[2] = prj->w[3]*sqrt(prj->w[4] - prj->w[5]*sindeg (prj->p[1])); + + prj->prjfwd = coefwd; + prj->prjrev = coerev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int coefwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double a, r; + + if (prj->flag != COE) { + if (coeset(prj)) return 1; + } + + a = phi*prj->w[0]; + if (theta == -90.0) { + r = prj->w[8]; + } else { + r = prj->w[3]*sqrt(prj->w[4] - prj->w[5]*sindeg (theta)); + } + + *x = r*sindeg (a); + *y = prj->w[2] - r*cosdeg (a); + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int coerev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double a, dy, r, w; + const double tol = 1.0e-12; + + if (prj->flag != COE) { + if (coeset(prj)) return 1; + } + + dy = prj->w[2] - y; + r = sqrt(x*x + dy*dy); + if (prj->p[1] < 0.0) r = -r; + + if (r == 0.0) { + a = 0.0; + } else { + a = atan2deg (x/r, dy/r); + } + + *phi = a*prj->w[1]; + if (fabs(r - prj->w[8]) < tol) { + *theta = -90.0; + } else { + w = (prj->w[6] - r*r)*prj->w[7]; + if (fabs(w) > 1.0) { + if (fabs(w-1.0) < tol) { + *theta = 90.0; + } else if (fabs(w+1.0) < tol) { + *theta = -90.0; + } else { + return 2; + } + } else { + *theta = asindeg (w); + } + } + + return 0; +} + +/*============================================================================ +* COD: conic equidistant projection. +* +* Given: +* prj->p[1] sigma = (theta2+theta1)/2 +* prj->p[2] delta = (theta2-theta1)/2, where theta1 and theta2 are the +* latitudes of the standard parallels, in degrees. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "COD" +* prj->flag COD +* prj->phi0 0.0 +* prj->theta0 sigma +* prj->w[0] C = r0*sin(sigma)*sin(delta)/delta +* prj->w[1] 1/C +* prj->w[2] Y0 = delta*cot(delta)*cot(sigma) +* prj->w[3] Y0 + sigma +* prj->prjfwd Pointer to codfwd(). +* prj->prjrev Pointer to codrev(). +*===========================================================================*/ + +int codset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "COD"); + prj->flag = COD; + prj->phi0 = 0.0; + prj->theta0 = prj->p[1]; + + if (prj->r0 == 0.0) prj->r0 = R2D; + + if (prj->p[2] == 0.0) { + prj->w[0] = prj->r0*sindeg (prj->p[1])*D2R; + } else { + prj->w[0] = prj->r0*sindeg (prj->p[1])*sindeg (prj->p[2])/prj->p[2]; + } + + if (prj->w[0] == 0.0) { + return 1; + } + + prj->w[1] = 1.0/prj->w[0]; + prj->w[2] = prj->r0*cosdeg (prj->p[2])*cosdeg (prj->p[1])/prj->w[0]; + prj->w[3] = prj->w[2] + prj->p[1]; + + prj->prjfwd = codfwd; + prj->prjrev = codrev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int codfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double a, r; + + if (prj->flag != COD) { + if (codset(prj)) return 1; + } + + a = prj->w[0]*phi; + r = prj->w[3] - theta; + + *x = r*sindeg (a); + *y = prj->w[2] - r*cosdeg (a); + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int codrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double a, dy, r; + + if (prj->flag != COD) { + if (codset(prj)) return 1; + } + + dy = prj->w[2] - y; + r = sqrt(x*x + dy*dy); + if (prj->p[1] < 0.0) r = -r; + + if (r == 0.0) { + a = 0.0; + } else { + a = atan2deg (x/r, dy/r); + } + + *phi = a*prj->w[1]; + *theta = prj->w[3] - r; + + return 0; +} + +/*============================================================================ +* COO: conic orthomorphic projection. +* +* Given: +* prj->p[1] sigma = (theta2+theta1)/2 +* prj->p[2] delta = (theta2-theta1)/2, where theta1 and theta2 are the +* latitudes of the standard parallels, in degrees. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "COO" +* prj->flag COO +* prj->phi0 0.0 +* prj->theta0 sigma +* prj->w[0] C = ln(cos(theta2)/cos(theta1))/ln(tan(tau2)/tan(tau1)) +* where tau1 = (90 - theta1)/2 +* tau2 = (90 - theta2)/2 +* prj->w[1] 1/C +* prj->w[2] Y0 = psi*tan((90-sigma)/2)**C +* prj->w[3] psi = (r0*cos(theta1)/C)/tan(tau1)**C +* prj->w[4] 1/psi +* prj->prjfwd Pointer to coofwd(). +* prj->prjrev Pointer to coorev(). +*===========================================================================*/ + +int cooset(prj) + +struct prjprm *prj; + +{ + double cos1, cos2, tan1, tan2, theta1, theta2; + + strcpy(prj->code, "COO"); + prj->flag = COO; + prj->phi0 = 0.0; + prj->theta0 = prj->p[1]; + + if (prj->r0 == 0.0) prj->r0 = R2D; + + theta1 = prj->p[1] - prj->p[2]; + theta2 = prj->p[1] + prj->p[2]; + + tan1 = tandeg ((90.0 - theta1)/2.0); + cos1 = cosdeg (theta1); + + if (theta1 == theta2) { + prj->w[0] = sindeg (theta1); + } else { + tan2 = tandeg ((90.0 - theta2)/2.0); + cos2 = cosdeg (theta2); + prj->w[0] = log(cos2/cos1)/log(tan2/tan1); + } + if (prj->w[0] == 0.0) { + return 1; + } + + prj->w[1] = 1.0/prj->w[0]; + + prj->w[3] = prj->r0*(cos1/prj->w[0])/pow(tan1,prj->w[0]); + if (prj->w[3] == 0.0) { + return 1; + } + prj->w[2] = prj->w[3]*pow(tandeg ((90.0 - prj->p[1])/2.0),prj->w[0]); + prj->w[4] = 1.0/prj->w[3]; + + prj->prjfwd = coofwd; + prj->prjrev = coorev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int coofwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double a, r; + + if (prj->flag != COO) { + if (cooset(prj)) return 1; + } + + a = prj->w[0]*phi; + if (theta == -90.0) { + if (prj->w[0] < 0.0) { + r = 0.0; + } else { + return 2; + } + } else { + r = prj->w[3]*pow(tandeg ((90.0 - theta)/2.0),prj->w[0]); + } + + *x = r*sindeg (a); + *y = prj->w[2] - r*cosdeg (a); + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int coorev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double a, dy, r; + + if (prj->flag != COO) { + if (cooset(prj)) return 1; + } + + dy = prj->w[2] - y; + r = sqrt(x*x + dy*dy); + if (prj->p[1] < 0.0) r = -r; + + if (r == 0.0) { + a = 0.0; + } else { + a = atan2deg (x/r, dy/r); + } + + *phi = a*prj->w[1]; + if (r == 0.0) { + if (prj->w[0] < 0.0) { + *theta = -90.0; + } else { + return 2; + } + } else { + *theta = 90.0 - 2.0*atandeg (pow(r*prj->w[4],prj->w[1])); + } + + return 0; +} + +/*============================================================================ +* BON: Bonne's projection. +* +* Given: +* prj->p[1] Bonne conformal latitude, theta1, in degrees. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "BON" +* prj->flag BON +* prj->phi0 0.0 +* prj->theta0 0.0 +* prj->w[1] r0*pi/180 +* prj->w[2] Y0 = r0*(cot(theta1) + theta1*pi/180) +* prj->prjfwd Pointer to bonfwd(). +* prj->prjrev Pointer to bonrev(). +*===========================================================================*/ + +int bonset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "BON"); + prj->flag = BON; + prj->phi0 = 0.0; + prj->theta0 = 0.0; + + if (prj->r0 == 0.0) { + prj->r0 = R2D; + prj->w[1] = 1.0; + prj->w[2] = prj->r0*cosdeg (prj->p[1])/sindeg (prj->p[1]) + prj->p[1]; + } else { + prj->w[1] = prj->r0*D2R; + prj->w[2] = prj->r0*(cosdeg (prj->p[1])/sindeg (prj->p[1]) + prj->p[1]*D2R); + } + + prj->prjfwd = bonfwd; + prj->prjrev = bonrev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int bonfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double a, r; + + if (prj->p[1] == 0.0) { + /* Sanson-Flamsteed. */ + return sflfwd(phi, theta, prj, x, y); + } + + if (prj->flag != BON) { + if (bonset(prj)) return 1; + } + + r = prj->w[2] - theta*prj->w[1]; + a = prj->r0*phi*cosdeg (theta)/r; + + *x = r*sindeg (a); + *y = prj->w[2] - r*cosdeg (a); + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int bonrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double a, cthe, dy, r; + + if (prj->p[1] == 0.0) { + /* Sanson-Flamsteed. */ + return sflrev(x, y, prj, phi, theta); + } + + if (prj->flag != BON) { + if (bonset(prj)) return 1; + } + + dy = prj->w[2] - y; + r = sqrt(x*x + dy*dy); + if (prj->p[1] < 0.0) r = -r; + + if (r == 0.0) { + a = 0.0; + } else { + a = atan2deg (x/r, dy/r); + } + + *theta = (prj->w[2] - r)/prj->w[1]; + cthe = cosdeg (*theta); + if (cthe == 0.0) { + *phi = 0.0; + } else { + *phi = a*(r/prj->r0)/cthe; + } + + return 0; +} + +/*============================================================================ +* PCO: polyconic projection. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "PCO" +* prj->flag PCO +* prj->phi0 0.0 +* prj->theta0 0.0 +* prj->w[0] r0*(pi/180) +* prj->w[1] 1/r0 +* prj->w[2] 2*r0 +* prj->prjfwd Pointer to pcofwd(). +* prj->prjrev Pointer to pcorev(). +*===========================================================================*/ + +int pcoset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "PCO"); + prj->flag = PCO; + prj->phi0 = 0.0; + prj->theta0 = 0.0; + + if (prj->r0 == 0.0) { + prj->r0 = R2D; + prj->w[0] = 1.0; + prj->w[1] = 1.0; + prj->w[2] = 360.0/PI; + } else { + prj->w[0] = prj->r0*D2R; + prj->w[1] = 1.0/prj->w[0]; + prj->w[2] = 2.0*prj->r0; + } + + prj->prjfwd = pcofwd; + prj->prjrev = pcorev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int pcofwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + double a, cthe, cotthe, sthe; + + if (prj->flag != PCO) { + if (pcoset(prj)) return 1; + } + + cthe = cosdeg (theta); + sthe = sindeg (theta); + a = phi*sthe; + + if (sthe == 0.0) { + *x = prj->w[0]*phi; + *y = 0.0; + } else { + cotthe = cthe/sthe; + *x = prj->r0*cotthe*sindeg (a); + *y = prj->r0*(cotthe*(1.0 - cosdeg (a)) + theta*D2R); + } + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int pcorev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + int j; + double f, fneg, fpos, lambda, tanthe, theneg, thepos, w, xp, xx, ymthe, yp; + const double tol = 1.0e-12; + + if (prj->flag != PCO) { + if (pcoset(prj)) return 1; + } + + w = fabs(y*prj->w[1]); + if (w < tol) { + *phi = x*prj->w[1]; + *theta = 0.0; + } else if (fabs(w-90.0) < tol) { + *phi = 0.0; + *theta = copysgn (90.0,y); + } else { + /* Iterative solution using weighted division of the interval. */ + if (y > 0.0) { + thepos = 90.0; + } else { + thepos = -90.0; + } + theneg = 0.0; + + xx = x*x; + ymthe = y - prj->w[0]*thepos; + fpos = xx + ymthe*ymthe; + fneg = -999.0; + + for (j = 0; j < 64; j++) { + if (fneg < -100.0) { + /* Equal division of the interval. */ + *theta = (thepos+theneg)/2.0; + } else { + /* Weighted division of the interval. */ + lambda = fpos/(fpos-fneg); + if (lambda < 0.1) { + lambda = 0.1; + } else if (lambda > 0.9) { + lambda = 0.9; + } + *theta = thepos - lambda*(thepos-theneg); + } + + /* Compute the residue. */ + ymthe = y - prj->w[0]*(*theta); + tanthe = tandeg (*theta); + f = xx + ymthe*(ymthe - prj->w[2]/tanthe); + + /* Check for convergence. */ + if (fabs(f) < tol) break; + if (fabs(thepos-theneg) < tol) break; + + /* Redefine the interval. */ + if (f > 0.0) { + thepos = *theta; + fpos = f; + } else { + theneg = *theta; + fneg = f; + } + } + + xp = prj->r0 - ymthe*tanthe; + yp = x*tanthe; + if (xp == 0.0 && yp == 0.0) { + *phi = 0.0; + } else { + *phi = atan2deg (yp, xp)/sindeg (*theta); + } + } + + return 0; +} + +/*============================================================================ +* TSC: tangential spherical cube projection. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "TSC" +* prj->flag TSC +* prj->phi0 0.0 +* prj->theta0 0.0 +* prj->w[0] r0*(pi/4) +* prj->w[1] (4/pi)/r0 +* prj->prjfwd Pointer to tscfwd(). +* prj->prjrev Pointer to tscrev(). +*===========================================================================*/ + +int tscset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "TSC"); + prj->flag = TSC; + prj->phi0 = 0.0; + prj->theta0 = 0.0; + + if (prj->r0 == 0.0) { + prj->r0 = R2D; + prj->w[0] = 45.0; + prj->w[1] = 1.0/45.0; + } else { + prj->w[0] = prj->r0*PI/4.0; + prj->w[1] = 1.0/prj->w[0]; + } + + prj->prjfwd = tscfwd; + prj->prjrev = tscrev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int tscfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + int face; + double cthe, l, m, n, rho; + double x0 = 0.0; + double y0 = 0.0; + double xf = 0.0; + double yf = 0.0; + const double tol = 1.0e-12; + + if (prj->flag != TSC) { + if (tscset(prj)) return 1; + } + + cthe = cosdeg (theta); + l = cthe*cosdeg (phi); + m = cthe*sindeg (phi); + n = sindeg (theta); + + face = 0; + rho = n; + if (l > rho) { + face = 1; + rho = l; + } + if (m > rho) { + face = 2; + rho = m; + } + if (-l > rho) { + face = 3; + rho = -l; + } + if (-m > rho) { + face = 4; + rho = -m; + } + if (-n > rho) { + face = 5; + rho = -n; + } + + if (face == 0) { + xf = m/rho; + yf = -l/rho; + x0 = 0.0; + y0 = 2.0; + } else if (face == 1) { + xf = m/rho; + yf = n/rho; + x0 = 0.0; + y0 = 0.0; + } else if (face == 2) { + xf = -l/rho; + yf = n/rho; + x0 = 2.0; + y0 = 0.0; + } else if (face == 3) { + xf = -m/rho; + yf = n/rho; + x0 = 4.0; + y0 = 0.0; + } else if (face == 4) { + xf = l/rho; + yf = n/rho; + x0 = 6.0; + y0 = 0.0; + } else if (face == 5) { + xf = m/rho; + yf = l/rho; + x0 = 0.0; + y0 = -2.0; + } + + if (fabs(xf) > 1.0) { + if (fabs(xf) > 1.0+tol) { + return 2; + } + xf = copysgn (1.0,xf); + } + if (fabs(yf) > 1.0) { + if (fabs(yf) > 1.0+tol) { + return 2; + } + yf = copysgn (1.0,yf); + } + + *x = prj->w[0]*(xf + x0); + *y = prj->w[0]*(yf + y0); + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int tscrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + double l, m, n, xf, yf; + + if (prj->flag != TSC) { + if (tscset(prj)) return 1; + } + + xf = x*prj->w[1]; + yf = y*prj->w[1]; + + /* Check bounds. */ + if (fabs(xf) <= 1.0) { + if (fabs(yf) > 3.0) return 2; + } else { + if (fabs(xf) > 7.0) return 2; + if (fabs(yf) > 1.0) return 2; + } + + /* Map negative faces to the other side. */ + if (xf < -1.0) xf += 8.0; + + /* Determine the face. */ + if (xf > 5.0) { + /* face = 4 */ + xf = xf - 6.0; + m = -1.0/sqrt(1.0 + xf*xf + yf*yf); + l = -m*xf; + n = -m*yf; + } else if (xf > 3.0) { + /* face = 3 */ + xf = xf - 4.0; + l = -1.0/sqrt(1.0 + xf*xf + yf*yf); + m = l*xf; + n = -l*yf; + } else if (xf > 1.0) { + /* face = 2 */ + xf = xf - 2.0; + m = 1.0/sqrt(1.0 + xf*xf + yf*yf); + l = -m*xf; + n = m*yf; + } else if (yf > 1.0) { + /* face = 0 */ + yf = yf - 2.0; + n = 1.0/sqrt(1.0 + xf*xf + yf*yf); + l = -n*yf; + m = n*xf; + } else if (yf < -1.0) { + /* face = 5 */ + yf = yf + 2.0; + n = -1.0/sqrt(1.0 + xf*xf + yf*yf); + l = -n*yf; + m = -n*xf; + } else { + /* face = 1 */ + l = 1.0/sqrt(1.0 + xf*xf + yf*yf); + m = l*xf; + n = l*yf; + } + + if (l == 0.0 && m == 0.0) { + *phi = 0.0; + } else { + *phi = atan2deg (m, l); + } + *theta = asindeg (n); + + return 0; +} + +/*============================================================================ +* CSC: COBE quadrilateralized spherical cube projection. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "CSC" +* prj->flag CSC +* prj->phi0 0.0 +* prj->theta0 0.0 +* prj->w[0] r0*(pi/4) +* prj->w[1] (4/pi)/r0 +* prj->prjfwd Pointer to cscfwd(). +* prj->prjrev Pointer to cscrev(). +*===========================================================================*/ + +int cscset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "CSC"); + prj->flag = CSC; + prj->phi0 = 0.0; + prj->theta0 = 0.0; + + if (prj->r0 == 0.0) { + prj->r0 = R2D; + prj->w[0] = 45.0; + prj->w[1] = 1.0/45.0; + } else { + prj->w[0] = prj->r0*PI/4.0; + prj->w[1] = 1.0/prj->w[0]; + } + + prj->prjfwd = cscfwd; + prj->prjrev = cscrev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int cscfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + int face; + double cthe, eta=0.0, l, m, n, rho, xi=0.0; + const float tol = 1.0e-7; + + float a, a2, a2b2, a4, ab, b, b2, b4, ca2, cb2; + float x0 = 0.0; + float y0 = 0.0; + float xf = 0.0; + float yf = 0.0; + const float gstar = 1.37484847732; + const float mm = 0.004869491981; + const float gamma = -0.13161671474; + const float omega1 = -0.159596235474; + const float d0 = 0.0759196200467; + const float d1 = -0.0217762490699; + const float c00 = 0.141189631152; + const float c10 = 0.0809701286525; + const float c01 = -0.281528535557; + const float c11 = 0.15384112876; + const float c20 = -0.178251207466; + const float c02 = 0.106959469314; + + if (prj->flag != CSC) { + if (cscset(prj)) return 1; + } + + cthe = cosdeg (theta); + l = cthe*cosdeg (phi); + m = cthe*sindeg (phi); + n = sindeg (theta); + + face = 0; + rho = n; + if (l > rho) { + face = 1; + rho = l; + } + if (m > rho) { + face = 2; + rho = m; + } + if (-l > rho) { + face = 3; + rho = -l; + } + if (-m > rho) { + face = 4; + rho = -m; + } + if (-n > rho) { + face = 5; + rho = -n; + } + + if (face == 0) { + xi = m; + eta = -l; + x0 = 0.0; + y0 = 2.0; + } else if (face == 1) { + xi = m; + eta = n; + x0 = 0.0; + y0 = 0.0; + } else if (face == 2) { + xi = -l; + eta = n; + x0 = 2.0; + y0 = 0.0; + } else if (face == 3) { + xi = -m; + eta = n; + x0 = 4.0; + y0 = 0.0; + } else if (face == 4) { + xi = l; + eta = n; + x0 = 6.0; + y0 = 0.0; + } else if (face == 5) { + xi = m; + eta = l; + x0 = 0.0; + y0 = -2.0; + } + + a = xi/rho; + b = eta/rho; + + a2 = a*a; + b2 = b*b; + ca2 = 1.0 - a2; + cb2 = 1.0 - b2; + + /* Avoid floating underflows. */ + ab = fabs(a*b); + a4 = (a2 > 1.0e-16) ? a2*a2 : 0.0; + b4 = (b2 > 1.0e-16) ? b2*b2 : 0.0; + a2b2 = (ab > 1.0e-16) ? a2*b2 : 0.0; + + xf = a*(a2 + ca2*(gstar + b2*(gamma*ca2 + mm*a2 + + cb2*(c00 + c10*a2 + c01*b2 + c11*a2b2 + c20*a4 + c02*b4)) + + a2*(omega1 - ca2*(d0 + d1*a2)))); + yf = b*(b2 + cb2*(gstar + a2*(gamma*cb2 + mm*b2 + + ca2*(c00 + c10*b2 + c01*a2 + c11*a2b2 + c20*b4 + c02*a4)) + + b2*(omega1 - cb2*(d0 + d1*b2)))); + + if (fabs(xf) > 1.0) { + if (fabs(xf) > 1.0+tol) { + return 2; + } + xf = copysgn (1.0,xf); + } + if (fabs(yf) > 1.0) { + if (fabs(yf) > 1.0+tol) { + return 2; + } + yf = copysgn (1.0,yf); + } + + *x = prj->w[0]*(x0 + xf); + *y = prj->w[0]*(y0 + yf); + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int cscrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + int face; + double l = 0.0; + double m = 0.0; + double n = 0.0; + + float a, b, xf, xx, yf, yy, z0, z1, z2, z3, z4, z5, z6; + const float p00 = -0.27292696; + const float p10 = -0.07629969; + const float p20 = -0.22797056; + const float p30 = 0.54852384; + const float p40 = -0.62930065; + const float p50 = 0.25795794; + const float p60 = 0.02584375; + const float p01 = -0.02819452; + const float p11 = -0.01471565; + const float p21 = 0.48051509; + const float p31 = -1.74114454; + const float p41 = 1.71547508; + const float p51 = -0.53022337; + const float p02 = 0.27058160; + const float p12 = -0.56800938; + const float p22 = 0.30803317; + const float p32 = 0.98938102; + const float p42 = -0.83180469; + const float p03 = -0.60441560; + const float p13 = 1.50880086; + const float p23 = -0.93678576; + const float p33 = 0.08693841; + const float p04 = 0.93412077; + const float p14 = -1.41601920; + const float p24 = 0.33887446; + const float p05 = -0.63915306; + const float p15 = 0.52032238; + const float p06 = 0.14381585; + + if (prj->flag != CSC) { + if (cscset(prj)) return 1; + } + + xf = x*prj->w[1]; + yf = y*prj->w[1]; + + /* Check bounds. */ + if (fabs(xf) <= 1.0) { + if (fabs(yf) > 3.0) return 2; + } else { + if (fabs(xf) > 7.0) return 2; + if (fabs(yf) > 1.0) return 2; + } + + /* Map negative faces to the other side. */ + if (xf < -1.0) xf += 8.0; + + /* Determine the face. */ + if (xf > 5.0) { + face = 4; + xf = xf - 6.0; + } else if (xf > 3.0) { + face = 3; + xf = xf - 4.0; + } else if (xf > 1.0) { + face = 2; + xf = xf - 2.0; + } else if (yf > 1.0) { + face = 0; + yf = yf - 2.0; + } else if (yf < -1.0) { + face = 5; + yf = yf + 2.0; + } else { + face = 1; + } + + xx = xf*xf; + yy = yf*yf; + + z0 = p00 + xx*(p10 + xx*(p20 + xx*(p30 + xx*(p40 + xx*(p50 + xx*(p60)))))); + z1 = p01 + xx*(p11 + xx*(p21 + xx*(p31 + xx*(p41 + xx*(p51))))); + z2 = p02 + xx*(p12 + xx*(p22 + xx*(p32 + xx*(p42)))); + z3 = p03 + xx*(p13 + xx*(p23 + xx*(p33))); + z4 = p04 + xx*(p14 + xx*(p24)); + z5 = p05 + xx*(p15); + z6 = p06; + + a = z0 + yy*(z1 + yy*(z2 + yy*(z3 + yy*(z4 + yy*(z5 + yy*z6))))); + a = xf + xf*(1.0 - xx)*a; + + z0 = p00 + yy*(p10 + yy*(p20 + yy*(p30 + yy*(p40 + yy*(p50 + yy*(p60)))))); + z1 = p01 + yy*(p11 + yy*(p21 + yy*(p31 + yy*(p41 + yy*(p51))))); + z2 = p02 + yy*(p12 + yy*(p22 + yy*(p32 + yy*(p42)))); + z3 = p03 + yy*(p13 + yy*(p23 + yy*(p33))); + z4 = p04 + yy*(p14 + yy*(p24)); + z5 = p05 + yy*(p15); + z6 = p06; + + b = z0 + xx*(z1 + xx*(z2 + xx*(z3 + xx*(z4 + xx*(z5 + xx*z6))))); + b = yf + yf*(1.0 - yy)*b; + + if (face == 0) { + n = 1.0/sqrt(a*a + b*b + 1.0); + l = -b*n; + m = a*n; + } else if (face == 1) { + l = 1.0/sqrt(a*a + b*b + 1.0); + m = a*l; + n = b*l; + } else if (face == 2) { + m = 1.0/sqrt(a*a + b*b + 1.0); + l = -a*m; + n = b*m; + } else if (face == 3) { + l = -1.0/sqrt(a*a + b*b + 1.0); + m = a*l; + n = -b*l; + } else if (face == 4) { + m = -1.0/sqrt(a*a + b*b + 1.0); + l = -a*m; + n = -b*m; + } else if (face == 5) { + n = -1.0/sqrt(a*a + b*b + 1.0); + l = -b*n; + m = -a*n; + } + + if (l == 0.0 && m == 0.0) { + *phi = 0.0; + } else { + *phi = atan2deg (m, l); + } + *theta = asindeg (n); + + return 0; +} + +/*============================================================================ +* QSC: quadrilaterilized spherical cube projection. +* +* Given and/or returned: +* prj->r0 r0; reset to 180/pi if 0. +* +* Returned: +* prj->code "QSC" +* prj->flag QSC +* prj->phi0 0.0 +* prj->theta0 0.0 +* prj->w[0] r0*(pi/4) +* prj->w[1] (4/pi)/r0 +* prj->prjfwd Pointer to qscfwd(). +* prj->prjrev Pointer to qscrev(). +*===========================================================================*/ + +int qscset(prj) + +struct prjprm *prj; + +{ + strcpy(prj->code, "QSC"); + prj->flag = QSC; + prj->phi0 = 0.0; + prj->theta0 = 0.0; + + if (prj->r0 == 0.0) { + prj->r0 = R2D; + prj->w[0] = 45.0; + prj->w[1] = 1.0/45.0; + } else { + prj->w[0] = prj->r0*PI/4.0; + prj->w[1] = 1.0/prj->w[0]; + } + + prj->prjfwd = qscfwd; + prj->prjrev = qscrev; + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int qscfwd(phi, theta, prj, x, y) + +const double phi, theta; +struct prjprm *prj; +double *x, *y; + +{ + int face; + double cthe, l, m, n, omega, p, rho, rhu, t, tau; + double xi = 0.0; + double eta = 0.0; + double x0 = 0.0; + double y0 = 0.0; + double xf = 0.0; + double yf = 0.0; + const double tol = 1.0e-12; + + if (prj->flag != QSC) { + if (qscset(prj)) return 1; + } + + if (fabs(theta) == 90.0) { + *x = 0.0; + *y = copysgn (2.0*prj->w[0],theta); + return 0; + } + + cthe = cosdeg (theta); + l = cthe*cosdeg (phi); + m = cthe*sindeg (phi); + n = sindeg (theta); + + face = 0; + rho = n; + if (l > rho) { + face = 1; + rho = l; + } + if (m > rho) { + face = 2; + rho = m; + } + if (-l > rho) { + face = 3; + rho = -l; + } + if (-m > rho) { + face = 4; + rho = -m; + } + if (-n > rho) { + face = 5; + rho = -n; + } + + rhu = 1.0 - rho; + + if (face == 0) { + xi = m; + eta = -l; + if (rhu < 1.0e-8) { + /* Small angle formula. */ + t = (90.0 - theta)*D2R; + rhu = t*t/2.0; + } + x0 = 0.0; + y0 = 2.0; + } else if (face == 1) { + xi = m; + eta = n; + if (rhu < 1.0e-8) { + /* Small angle formula. */ + t = theta*D2R; + p = fmod(phi,360.0); + if (p < -180.0) p += 360.0; + if (p > 180.0) p -= 360.0; + p *= D2R; + rhu = (p*p + t*t)/2.0; + } + x0 = 0.0; + y0 = 0.0; + } else if (face == 2) { + xi = -l; + eta = n; + if (rhu < 1.0e-8) { + /* Small angle formula. */ + t = theta*D2R; + p = fmod(phi,360.0); + if (p < -180.0) p += 360.0; + p = (90.0 - p)*D2R; + rhu = (p*p + t*t)/2.0; + } + x0 = 2.0; + y0 = 0.0; + } else if (face == 3) { + xi = -m; + eta = n; + if (rhu < 1.0e-8) { + /* Small angle formula. */ + t = theta*D2R; + p = fmod(phi,360.0); + if (p < 0.0) p += 360.0; + p = (180.0 - p)*D2R; + rhu = (p*p + t*t)/2.0; + } + x0 = 4.0; + y0 = 0.0; + } else if (face == 4) { + xi = l; + eta = n; + if (rhu < 1.0e-8) { + /* Small angle formula. */ + t = theta*D2R; + p = fmod(phi,360.0); + if (p > 180.0) p -= 360.0; + p *= (90.0 + p)*D2R; + rhu = (p*p + t*t)/2.0; + } + x0 = 6; + y0 = 0.0; + } else if (face == 5) { + xi = m; + eta = l; + if (rhu < 1.0e-8) { + /* Small angle formula. */ + t = (90.0 + theta)*D2R; + rhu = t*t/2.0; + } + x0 = 0.0; + y0 = -2; + } + + if (xi == 0.0 && eta == 0.0) { + xf = 0.0; + yf = 0.0; + } else if (-xi >= fabs(eta)) { + omega = eta/xi; + tau = 1.0 + omega*omega; + xf = -sqrt(rhu/(1.0-1.0/sqrt(1.0+tau))); + yf = (xf/15.0)*(atandeg (omega) - asindeg (omega/sqrt(tau+tau))); + } else if (xi >= fabs(eta)) { + omega = eta/xi; + tau = 1.0 + omega*omega; + xf = sqrt(rhu/(1.0-1.0/sqrt(1.0+tau))); + yf = (xf/15.0)*(atandeg (omega) - asindeg (omega/sqrt(tau+tau))); + } else if (-eta > fabs(xi)) { + omega = xi/eta; + tau = 1.0 + omega*omega; + yf = -sqrt(rhu/(1.0-1.0/sqrt(1.0+tau))); + xf = (yf/15.0)*(atandeg (omega) - asindeg (omega/sqrt(tau+tau))); + } else if (eta > fabs(xi)) { + omega = xi/eta; + tau = 1.0 + omega*omega; + yf = sqrt(rhu/(1.0-1.0/sqrt(1.0+tau))); + xf = (yf/15.0)*(atandeg (omega) - asindeg (omega/sqrt(tau+tau))); + } + + if (fabs(xf) > 1.0) { + if (fabs(xf) > 1.0+tol) { + return 2; + } + xf = copysgn (1.0,xf); + } + if (fabs(yf) > 1.0) { + if (fabs(yf) > 1.0+tol) { + return 2; + } + yf = copysgn (1.0,yf); + } + + *x = prj->w[0]*(xf + x0); + *y = prj->w[0]*(yf + y0); + + + return 0; +} + +/*--------------------------------------------------------------------------*/ + +int qscrev(x, y, prj, phi, theta) + +const double x, y; +struct prjprm *prj; +double *phi, *theta; + +{ + int direct, face; + double omega, rho, rhu, tau, xf, yf, w; + double l = 0.0; + double m = 0.0; + double n = 0.0; + const double tol = 1.0e-12; + + if (prj->flag != QSC) { + if (qscset(prj)) return 1; + } + + xf = x*prj->w[1]; + yf = y*prj->w[1]; + + /* Check bounds. */ + if (fabs(xf) <= 1.0) { + if (fabs(yf) > 3.0) return 2; + } else { + if (fabs(xf) > 7.0) return 2; + if (fabs(yf) > 1.0) return 2; + } + + /* Map negative faces to the other side. */ + if (xf < -1.0) xf += 8.0; + + /* Determine the face. */ + if (xf > 5.0) { + face = 4; + xf = xf - 6.0; + } else if (xf > 3.0) { + face = 3; + xf = xf - 4.0; + } else if (xf > 1.0) { + face = 2; + xf = xf - 2.0; + } else if (yf > 1.0) { + face = 0; + yf = yf - 2.0; + } else if (yf < -1.0) { + face = 5; + yf = yf + 2.0; + } else { + face = 1; + } + + direct = (fabs(xf) > fabs(yf)); + if (direct) { + if (xf == 0.0) { + omega = 0.0; + tau = 1.0; + rho = 1.0; + rhu = 0.0; + } else { + w = 15.0*yf/xf; + omega = sindeg (w)/(cosdeg (w) - SQRT2INV); + tau = 1.0 + omega*omega; + rhu = xf*xf*(1.0 - 1.0/sqrt(1.0 + tau)); + rho = 1.0 - rhu; + } + } else { + if (yf == 0.0) { + omega = 0.0; + tau = 1.0; + rho = 1.0; + rhu = 0.0; + } else { + w = 15.0*xf/yf; + omega = sindeg (w)/(cosdeg (w) - SQRT2INV); + tau = 1.0 + omega*omega; + rhu = yf*yf*(1.0 - 1.0/sqrt(1.0 + tau)); + rho = 1.0 - rhu; + } + } + + if (rho < -1.0) { + if (rho < -1.0-tol) { + return 2; + } + + rho = -1.0; + rhu = 2.0; + w = 0.0; + } else { + w = sqrt(rhu*(2.0-rhu)/tau); + } + + if (face == 0) { + n = rho; + if (direct) { + m = w; + if (xf < 0.0) m = -m; + l = -m*omega; + } else { + l = w; + if (yf > 0.0) l = -l; + m = -l*omega; + } + } else if (face == 1) { + l = rho; + if (direct) { + m = w; + if (xf < 0.0) m = -m; + n = m*omega; + } else { + n = w; + if (yf < 0.0) n = -n; + m = n*omega; + } + } else if (face == 2) { + m = rho; + if (direct) { + l = w; + if (xf > 0.0) l = -l; + n = -l*omega; + } else { + n = w; + if (yf < 0.0) n = -n; + l = -n*omega; + } + } else if (face == 3) { + l = -rho; + if (direct) { + m = w; + if (xf > 0.0) m = -m; + n = -m*omega; + } else { + n = w; + if (yf < 0.0) n = -n; + m = -n*omega; + } + } else if (face == 4) { + m = -rho; + if (direct) { + l = w; + if (xf < 0.0) l = -l; + n = l*omega; + } else { + n = w; + if (yf < 0.0) n = -n; + l = n*omega; + } + } else if (face == 5) { + n = -rho; + if (direct) { + m = w; + if (xf < 0.0) m = -m; + l = m*omega; + } else { + l = w; + if (yf < 0.0) l = -l; + m = l*omega; + } + } + + if (l == 0.0 && m == 0.0) { + *phi = 0.0; + } else { + *phi = atan2deg (m, l); + } + *theta = asindeg (n); + + return 0; +} + +/* This routine comes from E. Bertin sextractor-2.8.6 */ + +int +raw_to_pv(struct prjprm *prj, double x, double y, double *xo, double *yo) + +{ + int k; + double *a,*b, + r,r3,r5,r7,xy,x2,x3,x4,x5,x6,x7,y2,y3,y4,y5,y6,y7,xp,yp; + + + k=prj->npv; + a = prj->ppv+MAXPV; /* Latitude comes first for compatibility */ + b = prj->ppv; /* Longitude */ + xp = *(a++); + xp += *(a++)*x; + yp = *(b++); + yp += *(b++)*y; + if (!--k) goto poly_end; + xp += *(a++)*y; + yp += *(b++)*x; + if (!--k) goto poly_end; + r = sqrt(x*x + y*y); + xp += *(a++)*r; + yp += *(b++)*r; + if (!--k) goto poly_end; + xp += *(a++)*(x2=x*x); + yp += *(b++)*(y2=y*y); + if (!--k) goto poly_end; + xp += *(a++)*(xy=x*y); + yp += *(b++)*xy; + if (!--k) goto poly_end; + xp += *(a++)*y2; + yp += *(b++)*x2; + if (!--k) goto poly_end; + xp += *(a++)*(x3=x*x2); + yp += *(b++)*(y3=y*y2); + if (!--k) goto poly_end; + xp += *(a++)*x2*y; + yp += *(b++)*y2*x; + if (!--k) goto poly_end; + xp += *(a++)*x*y2; + yp += *(b++)*y*x2; + if (!--k) goto poly_end; + xp += *(a++)*y3; + yp += *(b++)*x3; + if (!--k) goto poly_end; + xp += *(a++)*(r3=r*r*r); + yp += *(b++)*r3; + if (!--k) goto poly_end; + xp += *(a++)*(x4=x2*x2); + yp += *(b++)*(y4=y2*y2); + if (!--k) goto poly_end; + xp += *(a++)*x3*y; + yp += *(b++)*y3*x; + if (!--k) goto poly_end; + xp += *(a++)*x2*y2; + yp += *(b++)*x2*y2; + if (!--k) goto poly_end; + xp += *(a++)*x*y3; + yp += *(b++)*y*x3; + if (!--k) goto poly_end; + xp += *(a++)*y4; + yp += *(b++)*x4; + if (!--k) goto poly_end; + xp += *(a++)*(x5=x4*x); + yp += *(b++)*(y5=y4*y); + if (!--k) goto poly_end; + xp += *(a++)*x4*y; + yp += *(b++)*y4*x; + if (!--k) goto poly_end; + xp += *(a++)*x3*y2; + yp += *(b++)*y3*x2; + if (!--k) goto poly_end; + xp += *(a++)*x2*y3; + yp += *(b++)*y2*x3; + if (!--k) goto poly_end; + xp += *(a++)*x*y4; + yp += *(b++)*y*x4; + if (!--k) goto poly_end; + xp += *(a++)*y5; + yp += *(b++)*x5; + if (!--k) goto poly_end; + xp += *(a++)*(r5=r3*r*r); + yp += *(b++)*r5; + if (!--k) goto poly_end; + xp += *(a++)*(x6=x5*x); + yp += *(b++)*(y6=y5*y); + if (!--k) goto poly_end; + xp += *(a++)*x5*y; + yp += *(b++)*y5*x; + if (!--k) goto poly_end; + xp += *(a++)*x4*y2; + yp += *(b++)*y4*x2; + if (!--k) goto poly_end; + xp += *(a++)*x3*y3; + yp += *(b++)*y3*x3; + if (!--k) goto poly_end; + xp += *(a++)*x2*y4; + yp += *(b++)*y2*x4; + if (!--k) goto poly_end; + xp += *(a++)*x*y5; + yp += *(b++)*y*x5; + if (!--k) goto poly_end; + xp += *(a++)*y6; + yp += *(b++)*x6; + if (!--k) goto poly_end; + xp += *(a++)*(x7=x6*x); + yp += *(b++)*(y7=y6*y); + if (!--k) goto poly_end; + xp += *(a++)*x6*y; + yp += *(b++)*y6*x; + if (!--k) goto poly_end; + xp += *(a++)*x5*y2; + yp += *(b++)*y5*x2; + if (!--k) goto poly_end; + xp += *(a++)*x4*y3; + yp += *(b++)*y4*x3; + if (!--k) goto poly_end; + xp += *(a++)*x3*y4; + yp += *(b++)*y3*x4; + if (!--k) goto poly_end; + xp += *(a++)*x2*y5; + yp += *(b++)*y2*x5; + if (!--k) goto poly_end; + xp += *(a++)*x*y6; + yp += *(b++)*y*x6; + if (!--k) goto poly_end; + xp += *(a++)*y7; + yp += *(b++)*x7; + if (!--k) goto poly_end; + xp += *a*(r7=r5*r*r); + yp += *b*r7; + +poly_end: + + *xo = xp; + *yo = yp; + + return 0; +} + +/* Dec 20 1999 Doug Mink - Change cosd() and sind() to cosdeg() and sindeg() + * Dec 20 1999 Doug Mink - Include wcslib.h, which includes proj.h, wcsmath.h + * Dec 20 1999 Doug Mink - Define copysign only if it is not defined + * Dec 20 1999 Doug Mink - tanfwd() returns error if s<=0.0, not only if s==0.0 + * + * Jun 2 2000 Doug Mink - include stdlib.h to get abs() + * + * Feb 15 2001 Doug Mink - update zearev() for WCSLIB 2.6 + * Sep 19 2001 Doug Mink - Make above changes for WCSLIB 2.7 + * + * Mar 15 2002 Doug Mink - Make above changes for WCSLIB 2.8.2 + * + * Feb 3 2003 Doug Mink - Use locally defined copysgn() and copysgni(), + * not copysign() + * Apr 1 2003 Doug Mink - include string.h for strcpy() and strcmp() + * + * Mar 14 2011 Doug Mink - If no coefficients in ZPN, make ARC + * Mar 14 2011 Doug Mink - Add Emmanuel Bertin's TAN polynomial from Ed Los + */ |