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gmt_proj.c
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gmt_proj.c
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/*--------------------------------------------------------------------
*
* Copyright (c) 1991-2021 by the GMT Team (https://www.generic-mapping-tools.org/team.html)
* See LICENSE.TXT file for copying and redistribution conditions.
*
* This program 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; version 3 or any later version.
*
* This program 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.
*
* Contact info: www.generic-mapping-tools.org
*--------------------------------------------------------------------*/
/*
* gmt_proj.c contains the specific projection functions that convert
* longitude and latitude to x, y. These are used via function pointers
* set in gmt_map.c
*
* Map_projections include functions that will set up the transformation
* between xy and latlon for several map projections.
*
* A few of the core coordinate transformation functions are based on similar
* FORTRAN routines written by Pat Manley, Doug Shearer, and Bill Haxby, and
* have been rewritten in C and subsequently streamlined. The Lambert conformal
* was originally coded up by Bernie Coakley. The rest is coded by Wessel/Smith
* based on P. Snyder, "Map Projections - a working manual", USGS Prof paper 1395.
*
* Transformations supported (both forward and inverse):
*
* Non-geographic projections:
*
* Linear x/y[/z] scaling
* Polar (theta, r) scaling
*
* Map projections:
*
* Cylindrical:
* Mercator
* Cassini Cylindrical
* Cylindrical Stereographic (e.g., Gall, B.S.A.M)
* Miller Cylindrical
* Oblique Mercator
* TM Transverse Mercator (Ellipsoidal and Spherical)
* UTM Universal Transverse Mercator
* Cylindrical Equal-area (e.g., Gall, Behrmann)
* Cylindrical Equidistant (e.g., Plate Carree)
* Conic:
* Albers Equal-Area Conic
* Lambert Conformal Conic
* Equidistant Conic
* Azimuthal:
* Stereographic Conformal
* Lambert Azimuthal Equal-Area
* Orthographic
* Azimuthal Equidistant
* Gnomonic
* Thematic:
* Mollweide Equal-Area
* Hammer-Aitoff Equal-Area
* Sinusoidal Equal-Area
* Winkel Tripel
* Robinson
* Eckert IV
* Eckert IV
* Van der Grinten
*
* Author: Paul Wessel
* Date: 1-JAN-2010
* Version: 5.x
*/
#include "gmt_dev.h"
#include "gmt_internals.h"
#define GMT_PROJ_MAX_ITERATIONS 200
#define GMT_PROJ_CONV_LIMIT 1e-9
#define GMT_PROJ_IS_ZERO(x) (fabs (x) < GMT_PROJ_CONV_LIMIT)
GMT_LOCAL double gmtproj_robinson_spline (struct GMT_CTRL *GMT, double xp, double *x, double *y, double *c) {
/* Returns the interpolated value y(xp) from the Robinson coefficients */
int j = 0, j1;
double yp, a, b, h, ih, dx;
if (xp < x[0] || xp > x[GMT_N_ROBINSON-1]) /* Desired point outside data range */
return (GMT->session.d_NaN);
while (j < GMT_N_ROBINSON && x[j] <= xp) j++;
if (j == GMT_N_ROBINSON) j--;
if (j > 0) j--;
dx = xp - x[j];
switch (GMT->current.setting.interpolant) { /* gmtproj_vrobinson would not allow case 0 so only GMT_SPLINE_AKIMA | GMT_SPLINE_CUBIC is possible */
case GMT_SPLINE_AKIMA:
yp = ((c[3*j+2]*dx + c[3*j+1])*dx + c[3*j])*dx + y[j];
break;
case GMT_SPLINE_CUBIC:
j1 = j + 1;
h = x[j1] - x[j];
ih = 1.0 / h;
a = (x[j1] - xp) * ih;
b = dx * ih;
yp = a * y[j] + b * y[j1] + ((a*a*a - a) * c[j] + (b*b*b - b) * c[j1]) * (h*h) / 6.0;
break;
default:
yp = 0;
}
return (yp);
}
GMT_LOCAL void gmtproj_check_R_J (struct GMT_CTRL *GMT, double *clon) /* Make sure -R and -J agree for global plots; J given priority */ {
double lon0 = 0.5 * (GMT->common.R.wesn[XLO] + GMT->common.R.wesn[XHI]);
if (GMT->current.map.is_world && lon0 != *clon) {
GMT->common.R.wesn[XLO] = *clon - 180.0;
GMT->common.R.wesn[XHI] = *clon + 180.0;
GMT_Report (GMT->parent, GMT_MSG_INFORMATION, "Central meridian set with -J (%g) implies -R%g/%g/%g/%g\n",
*clon, GMT->common.R.wesn[XLO], GMT->common.R.wesn[XHI], GMT->common.R.wesn[YLO], GMT->common.R.wesn[YHI]);
}
else if (!GMT->current.map.is_world) {
lon0 = *clon - 360.0;
while (lon0 < GMT->common.R.wesn[XLO]) lon0 += 360.0;
if (lon0 > GMT->common.R.wesn[XHI]) GMT_Report (GMT->parent, GMT_MSG_INFORMATION, "Central meridian outside region\n");
}
}
GMT_LOCAL void gmtproj_iwinkel_sub (struct GMT_CTRL *GMT, double y, double *phi) {
/* Valid only along meridian 180 degree from central meridian. Used in left/right_winkel only */
int n_iter = 0;
double c, phi0, delta, sp, cp;
c = 2.0 * y * GMT->current.proj.i_EQ_RAD;
*phi = y * GMT->current.proj.i_EQ_RAD;
do {
phi0 = *phi;
sincos (phi0, &sp, &cp);
*phi = phi0 - (phi0 + M_PI_2 * sp - c) / (1.0 + M_PI_2 * cp);
delta = fabs (*phi - phi0);
n_iter++;
}
while (delta > GMT_PROJ_CONV_LIMIT && n_iter < GMT_PROJ_MAX_ITERATIONS);
*phi *= R2D;
}
GMT_LOCAL void gmtproj_ipolyconic_sub (struct GMT_CTRL *GMT, double y, double lon, double *x) {
/* Used in left/right_polyconic only */
double E, sp, cp, phi0, phi, delta;
int n_iter = 0;
*x = lon;
gmt_M_wind_lon (GMT, *x);
y *= GMT->current.proj.i_EQ_RAD;
y += GMT->current.proj.pole * D2R;
if (GMT_PROJ_IS_ZERO (y))
*x *= GMT->current.proj.EQ_RAD * D2R;
else {
phi = y;
do {
phi0 = phi;
sincos (phi, &sp, &cp);
E = (*x) * sp;
cp /= sp; /* = cot(phi) */
phi = y - cp * (1.0 - cosd(E));
delta = fabs (phi - phi0);
n_iter++;
}
while (delta > GMT_PROJ_CONV_LIMIT && n_iter < GMT_PROJ_MAX_ITERATIONS);
*x = GMT->current.proj.EQ_RAD * cp * sin(E);
}
}
/* conversion from geodetic latitude to geocentric latitude */
GMT_LOCAL double gmtproj_genper_getgeocentric (struct GMT_CTRL *GMT, double phi, double h) {
double phig, sphi, cphi, N1;
sincosd (phi, &sphi, &cphi);
N1 = GMT->current.proj.EQ_RAD/sqrt(1.0 - (GMT->current.proj.ECC2*sphi*sphi));
phig = phi - asind(N1*GMT->current.proj.ECC2*sphi*cphi/((h/GMT->current.proj.EQ_RAD+1.0)*GMT->current.proj.EQ_RAD));
return (phig);
}
GMT_LOCAL void gmtproj_genper_toxy (struct GMT_CTRL *P, double lat, double lon, double h, double *x, double *y) {
double angle;
double xp, yp, rp;
double N, C, S, K;
double sphi, cphi;
double sdphi, cdphi;
double sphi1, cphi1;
double sdlon, cdlon;
cdphi = P->current.proj.g_cdphi;
sdphi = P->current.proj.g_sdphi;
cphi1 = P->current.proj.g_cphi1;
sphi1 = P->current.proj.g_sphi1;
h *= 1e3;
sincosd (lat, &sphi, &cphi);
N = P->current.proj.g_R/sqrt(1.0 - (P->current.proj.ECC2*sphi*sphi));
C = ((N+h)/P->current.proj.g_R)*cphi;
S = ((N*P->current.proj.one_m_ECC2 + h)/P->current.proj.g_R)*sphi;
sincosd (lon - P->current.proj.g_lon0, &sdlon, &cdlon);
K = P->current.proj.g_H / (P->current.proj.g_P*cdphi - S*sphi1 - C*cphi1*cdlon);
xp = K*C*sdlon;
yp = K*(P->current.proj.g_P*sdphi + S*cphi1 - C*sphi1*cdlon);
rp = sqrt(xp*xp + yp*yp);
if (rp > P->current.proj.g_rmax) {
angle = atan2(xp, yp);
sincos (angle, &xp, &yp);
xp *= P->current.proj.g_rmax;
yp *= P->current.proj.g_rmax;
}
*x = xp;
*y = yp;
if (P->current.proj.g_debug > 1) {
GMT_Report (P->parent, GMT_MSG_DEBUG, "\n");
GMT_Report (P->parent, GMT_MSG_DEBUG, "lat %12.3f\n", lat);
GMT_Report (P->parent, GMT_MSG_DEBUG, "lon %12.3f\n", lon);
GMT_Report (P->parent, GMT_MSG_DEBUG, "h %12.3f\n", h);
GMT_Report (P->parent, GMT_MSG_DEBUG, "N %12.1f\n", N);
GMT_Report (P->parent, GMT_MSG_DEBUG, "C %12.7f\n", C);
GMT_Report (P->parent, GMT_MSG_DEBUG, "S %12.7f\n", S);
GMT_Report (P->parent, GMT_MSG_DEBUG, "K %12.1f\n", K);
GMT_Report (P->parent, GMT_MSG_DEBUG, "x %12.1f\n", *x);
GMT_Report (P->parent, GMT_MSG_DEBUG, "y %12.1f\n", *y);
}
}
GMT_LOCAL void gmtproj_genper_to_xtyt (struct GMT_CTRL *GMT, double angle, double x, double y, double offset, double *xt, double *yt) {
double A, theta, xp, yp;
theta = GMT->current.proj.g_azimuth - angle;
A = (y * GMT->current.proj.g_cos_azimuth + x * GMT->current.proj.g_sin_azimuth) * GMT->current.proj.g_sin_tilt / GMT->current.proj.g_H + GMT->current.proj.g_cos_tilt;
if (A > 0.0) {
xp = (x * GMT->current.proj.g_cos_azimuth - y * GMT->current.proj.g_sin_azimuth) * GMT->current.proj.g_cos_tilt / A;
yp = (y * GMT->current.proj.g_cos_azimuth + x * GMT->current.proj.g_sin_azimuth) / A;
if (fabs(yp) > fabs(GMT->current.proj.g_max_yt)) {
yp = -GMT->current.proj.g_max_yt;
xp = -yp * tand(theta);
}
}
else {
yp = -GMT->current.proj.g_max_yt;
xp = -yp * tand(theta);
}
yp -= offset;
*xt = xp * GMT->current.proj.g_cos_twist - yp * GMT->current.proj.g_sin_twist;
*yt = yp * GMT->current.proj.g_cos_twist + xp * GMT->current.proj.g_sin_twist;
return;
}
GMT_LOCAL int gmtproj_genper_tolatlong (struct GMT_CTRL *GMT, double x, double y, double h, double *lat, double *lon) {
double P, H, B, D;
double u, v, t, Kp, X, Y;
double E, S;
double phi_last;
double Kp2;
double phi, sphi;
double cphig;
double e2, R, one_m_e2;
double cphi1, sphi1;
int niter;
int set_exit = 0;
h *= 1e3;
H = GMT->current.proj.g_H;
P = GMT->current.proj.g_P;
R = GMT->current.proj.g_R;
one_m_e2 = GMT->current.proj.one_m_ECC2;
e2 = GMT->current.proj.ECC2;
cphig = GMT->current.proj.g_cphig;
cphi1 = GMT->current.proj.g_cphi1;
sphi1 = GMT->current.proj.g_sphi1;
B = GMT->current.proj.g_B;
D = GMT->current.proj.g_D;
u = GMT->current.proj.g_BLH - GMT->current.proj.g_DG*y + GMT->current.proj.g_BJ*y + GMT->current.proj.g_DHJ;
v = GMT->current.proj.g_LH2 + GMT->current.proj.g_G*y*y - GMT->current.proj.g_HJ*y + one_m_e2*x*x;
if (GMT->current.proj.g_debug > 1) {
gmt_message (GMT, "\n");
gmt_message (GMT, "gmtproj_genper_tolatlong - 1 \n");
gmt_message (GMT, "x %12.1f\n", x);
gmt_message (GMT, "y %12.1f\n", y);
gmt_message (GMT, "\n");
gmt_message (GMT, "P %12.7f\n", P);
gmt_message (GMT, "phig %12.7f\n", GMT->current.proj.g_phig);
gmt_message (GMT, "\n");
gmt_message (GMT, "B %12.7f\n", B);
gmt_message (GMT, "D %12.7f\n", D);
gmt_message (GMT, "u %12.1f\n", u);
gmt_message (GMT, "v %12.6e\n", v);
}
E = 1;
t = P*P*(1.0 - e2*cphig*cphig) - E*one_m_e2;
Kp2 = (1.0 - 4.0*(t/u)*(v/u));
if (Kp2 < 0.0)
Kp = -u/(2.0*t);
else
Kp = (-u + sqrt(u*u-4.0*t*v))/(2.0*t);
X = R*((B-H/Kp)*cphi1 - (y/Kp - D)*sphi1);
Y = R*x/Kp;
S = (y/Kp-D)*cphi1 + (B-H/Kp)*sphi1;
if (gmt_M_is_dnan(Kp) || gmt_M_is_dnan(X) || gmt_M_is_dnan(Y) || gmt_M_is_dnan(S)) set_exit++;
if (set_exit == 1) {
gmt_message (GMT, "\n");
gmt_message (GMT, "gmtproj_genper_tolatlong - 2\n");
gmt_message (GMT, "x %12.1f\n", x);
gmt_message (GMT, "y %12.1f\n", y);
gmt_message (GMT, "\n");
gmt_message (GMT, "P %12.7f\n", P);
gmt_message (GMT, "phig %12.7f\n", GMT->current.proj.g_phig);
gmt_message (GMT, "\n");
gmt_message (GMT, "B %12.7f\n", B);
gmt_message (GMT, "D %12.7f\n", D);
gmt_message (GMT, "u %12.1f\n", u);
gmt_message (GMT, "v %12.6e\n", v);
}
if (set_exit || GMT->current.proj.g_debug > 1) {
gmt_message (GMT, "t %12.7f\n", t);
gmt_message (GMT, "Kp %12.1f\n", Kp);
gmt_message (GMT, "Kp2 %12.1f\n", Kp2);
gmt_message (GMT, "X %12.1f\n", X);
gmt_message (GMT, "Y %12.1f\n", Y);
gmt_message (GMT, "S %12.7f\n", S);
}
if (h == 0) {
phi = atan(S/sqrt(one_m_e2*(1.0 - e2 - S*S)));
/* if (gmt_M_is_dnan(phi)) set_exit++; */
}
else {
double t1, t2;
niter = 0;
t2 = h*h/(R*R*one_m_e2);
sphi = S/(one_m_e2/sqrt(1.0 - e2*S*S) + h/R);
phi = asin(sphi);
t1 = (1.0/sqrt(1.0 - e2*sphi*sphi) + h/R);
E = t1 * t1 - e2*sphi*sphi*(1.0/(1.0 - e2*sphi*sphi) - t2);
if (gmt_M_is_dnan(E)) set_exit++;
if (set_exit == 1) gmt_message (GMT, "gmtproj_genper_tolatlong - 3\n");
if (GMT->current.proj.g_debug > 1 || set_exit) {
gmt_message (GMT, "asinS %12.7f\n", asind(S));
gmt_message (GMT, "phi %12.7f\n", R2D*phi);
gmt_message (GMT, "E %12.7f\n", E);
}
do {
niter++;
phi_last = phi;
t = P*P*(1.0 - e2*cphig*cphig) - E*one_m_e2;
Kp2 = (1.0 - 4.0*(t/u)*(v/u));
if (Kp2 < 0.0)
Kp = -u/(2.0*t);
else
Kp = (-u + sqrt(u*u-4.0*t*v))/(2.0*t);
X = R*((B-H/Kp)*cphi1 - (y/Kp - D)*sphi1);
Y = R*x/Kp;
S = (y/Kp-D)*cphi1 + (B-H/Kp)*sphi1;
sphi = S/(one_m_e2/sqrt(1.0 - e2*sphi*sphi) + h/R);
phi = asin(sphi);
t1 = (1.0/sqrt(1.0 - e2*sphi*sphi) + h/R);
E = t1 * t1 - e2*sphi*sphi*(1.0/(1.0 - e2*sphi*sphi) - t2);
if (gmt_M_is_dnan(Kp) || gmt_M_is_dnan(X) || gmt_M_is_dnan(Y) || gmt_M_is_dnan(S) || gmt_M_is_dnan(phi) || gmt_M_is_dnan(E)) set_exit++;
if (set_exit == 1) gmt_message (GMT, "gmtproj_genper_tolatlong - 4 \n");
if (set_exit || GMT->current.proj.g_debug > 1) {
gmt_message (GMT, "\niter %d\n", niter);
gmt_message (GMT, "t %12.7f\n", t);
gmt_message (GMT, "Kp %12.1f\n", Kp);
gmt_message (GMT, "X %12.1f\n", X);
gmt_message (GMT, "Y %12.1f\n", Y);
gmt_message (GMT, "S %12.7f\n", S);
gmt_message (GMT, "phi %12.7f\n", phi*R2D);
gmt_message (GMT, "E %12.7f\n", E);
}
}
while (fabs(phi - phi_last) > 1e-7);
}
if (set_exit == 1) gmt_message (GMT, "gmtproj_genper_tolatlong - 5\n");
if (set_exit || GMT->current.proj.g_debug > 1) {
gmt_message (GMT, "gmtproj_genper_tolatlong phi %12.7f\n", phi*R2D);
return GMT_PROJECTION_ERROR;
}
*lat = phi * R2D;
*lon = atan2d (Y, X) + GMT->current.proj.g_lon0;
return (GMT_OK);
}
GMT_LOCAL void gmtproj_genper_setup (struct GMT_CTRL *GMT, double h0, double altitude, double lat, double lon0) {
/* if ellipsoid lat0 is geodetic latitude and must convert to geocentric latitude */
double N1, phig_last;
double R, H, P;
double sphi1, cphi1, sphig, cphig;
double a, e2, phig;
int niter;
a = GMT->current.proj.EQ_RAD;
e2 = GMT->current.proj.ECC2;
h0 *= 1e3;
sincosd (lat, &sphi1, &cphi1);
sphig = sphi1; cphig = cphi1;
N1 = a / sqrt (1.0 - (e2*sphi1*sphi1));
niter = 0;
if (GMT->current.proj.g_radius || altitude < -10.0) {
/* use altitude as the radial distance from the center of the earth */
H = fabs (altitude*1e3) - a;
P = H/a + 1.0;
phig = lat;
}
else if (altitude <= 0.0) {
/* setup altitude of geosynchronous viewpoint n */
double temp = 86164.1/TWO_PI;
H = pow (3.98603e14*temp*temp, 0.3333) - a;
P = H/a + 1.0;
phig = lat - asind(N1*e2*sphi1*cphi1/(P*a));
sincosd (phig, &sphig, &cphig);
if (cphi1 != 0.0)
H = P*a*cphig/cphi1 - N1 - h0;
else
H = P*a - N1 - h0;
}
else if (altitude < 10.0) {
P = altitude;
/* need to setup H from P equation */
phig = lat - asind(N1*e2*sphi1*cphi1/(P*a));
sincosd (phig, &sphig, &cphig);
if (cphi1 != 0.0)
H = P*a*cphig/cphi1 - N1 - h0;
else
H = P*a - N1 - h0;
}
else {
/* gmt_message (GMT, "altitude %f\n", altitude); */
H = altitude*1e3;
/* need to setup P from iterating phig */
phig = lat;
do {
niter++;
sincosd (phig, &sphig, &cphig);
P = (cphi1/cphig) * (H + N1 + h0)/a;
phig_last = phig;
phig = lat - asind(N1*e2*sphi1*cphi1/(P*a));
/* gmt_message (GMT, "%2d P %12.7f phig %12.7f\n", niter, P, phig); */
}
while (fabs (phig - phig_last) > 1e-9);
sincosd (phig, &sphig, &cphig);
P = (cphi1/cphig)*(H + N1 + h0)/a;
}
/* R = H/(P-1.0); */
R = a;
/* XXX Which one is it ? */
GMT->current.proj.g_H = H;
GMT->current.proj.g_P = P;
GMT->current.proj.g_R = R;
GMT->current.proj.g_lon0 = lon0;
GMT->current.proj.g_sphi1 = sphi1;
GMT->current.proj.g_cphi1 = cphi1;
GMT->current.proj.g_phig = phig;
GMT->current.proj.g_sphig = sphig;
GMT->current.proj.g_cphig = cphig;
sincosd (lat-phig, &(GMT->current.proj.g_sdphi), &(GMT->current.proj.g_cdphi));
GMT->current.proj.g_L = 1.0 - e2*cphi1*cphi1;
GMT->current.proj.g_G = 1.0 - e2*sphi1*sphi1;
GMT->current.proj.g_J = 2.0*e2*sphi1*cphi1;
GMT->current.proj.g_B = P*GMT->current.proj.g_cdphi;
GMT->current.proj.g_D = P*GMT->current.proj.g_sdphi;
GMT->current.proj.g_BLH = -2.0*GMT->current.proj.g_B*GMT->current.proj.g_L*H;
GMT->current.proj.g_DG = 2.0*GMT->current.proj.g_D*GMT->current.proj.g_G;
GMT->current.proj.g_BJ = GMT->current.proj.g_B*GMT->current.proj.g_J;
GMT->current.proj.g_HJ = H*GMT->current.proj.g_J;
GMT->current.proj.g_DHJ = GMT->current.proj.g_D*GMT->current.proj.g_HJ;
GMT->current.proj.g_LH2 = GMT->current.proj.g_L*H*H;
if (GMT->current.proj.g_debug > 0) {
gmt_message (GMT, "a %12.4f\n", a);
gmt_message (GMT, "R %12.4f\n", R);
gmt_message (GMT, "e^2 %12.7f\n", e2);
gmt_message (GMT, "H %12.4f\n", H);
gmt_message (GMT, "phi1 %12.4f\n", lat);
gmt_message (GMT, "lon0 %12.4f\n", lon0);
gmt_message (GMT, "h0 %12.4f\n", h0);
gmt_message (GMT, "N1 %12.1f\n", N1);
gmt_message (GMT, "P %12.7f\n", P);
gmt_message (GMT, "phig %12.7f\n", phig);
}
return;
}
/* LINEAR TRANSFORMATIONS */
void gmtlib_translin (struct GMT_CTRL *GMT, double forw, double *inv) /* Linear forward */ {
gmt_M_unused(GMT);
*inv = forw;
}
GMT_LOCAL void gmtproj_translind (struct GMT_CTRL *GMT, double forw, double *inv) /* Linear forward, but with degrees*/ {
gmt_M_wind_lon (GMT, forw) /* Make sure forw is in -180/+180 range after removing central meridian */
*inv = forw ;
}
GMT_LOCAL void gmtproj_itranslind (struct GMT_CTRL *GMT, double *forw, double inv) /* Linear inverse, but with degrees*/ {
while (inv < -GMT_180) inv += 360.0;
while (inv > +GMT_180) inv -= 360.0;
*forw = inv + GMT->current.proj.central_meridian;
}
void gmtlib_itranslin (struct GMT_CTRL *GMT, double *forw, double inv) /* Linear inverse */ {
gmt_M_unused(GMT);
*forw = inv;
}
GMT_LOCAL void gmtproj_translog10 (struct GMT_CTRL *GMT, double forw, double *inv) /* Log10 forward */ {
*inv = d_log10 (GMT, forw);
}
GMT_LOCAL void gmtproj_itranslog10 (struct GMT_CTRL *GMT, double *forw, double inv) /* Log10 inverse */ {
gmt_M_unused(GMT);
*forw = pow (10.0, inv);
}
GMT_LOCAL void gmtproj_transpowx (struct GMT_CTRL *GMT, double x, double *x_in) /* pow x forward */ {
*x_in = pow (x, GMT->current.proj.xyz_pow[GMT_X]);
}
GMT_LOCAL void gmtproj_itranspowx (struct GMT_CTRL *GMT, double *x, double x_in) /* pow x inverse */ {
*x = pow (x_in, GMT->current.proj.xyz_ipow[GMT_X]);
}
GMT_LOCAL void gmtproj_transpowy (struct GMT_CTRL *GMT, double y, double *y_in) /* pow y forward */ {
*y_in = pow (y, GMT->current.proj.xyz_pow[GMT_Y]);
}
GMT_LOCAL void gmtproj_itranspowy (struct GMT_CTRL *GMT, double *y, double y_in) /* pow y inverse */ {
*y = pow (y_in, GMT->current.proj.xyz_ipow[GMT_Y]);
}
GMT_LOCAL void gmtproj_transpowz (struct GMT_CTRL *GMT, double z, double *z_in) /* pow z forward */ {
*z_in = pow (z, GMT->current.proj.xyz_pow[GMT_Z]);
}
GMT_LOCAL void gmtproj_itranspowz (struct GMT_CTRL *GMT, double *z, double z_in) /* pow z inverse */ {
*z = pow (z_in, GMT->current.proj.xyz_ipow[GMT_Z]);
}
/* -JP POLAR (r-theta) PROJECTION */
GMT_LOCAL double gmtproj_planet_radius (struct GMT_CTRL *GMT, char *modifier) {
static char *U[2] = {"m", "km"};
unsigned int k = 0;
double r;
/* Set planetary radius in correct units (m or km) depending on y-range */
r = GMT->current.setting.ref_ellipsoid[GMT->current.setting.proj_ellipsoid].eq_radius; /* In meters */
if ((r/ (GMT->common.R.wesn[YHI] - GMT->common.R.wesn[YLO])) >= METERS_IN_A_KM) { /* -R seems given in km */
r /= METERS_IN_A_KM;
k = 1;
}
GMT_Report (GMT->parent, GMT_MSG_INFORMATION, "Planetary radius (%s) automatically set to %g %s\n", modifier, r, U[k]);
return (r);
}
GMT_LOCAL void gmtproj_vpolar (struct GMT_CTRL *GMT, double lon0) {
/* Set up a Polar (theta,r) transformation */
GMT->current.proj.p_base_angle = lon0;
GMT->current.proj.central_meridian = 0.5 * (GMT->common.R.wesn[XHI] + GMT->common.R.wesn[XLO]);
if (GMT->current.proj.flip) { /* Want radial direction inwards */
if (GMT->current.proj.flip_radius < 0.0) /* Flag to just flip z = north - r */
GMT->current.proj.flip_radius = GMT->common.R.wesn[YHI];
else if (GMT->current.proj.flip_radius == 0.0) /* Flag to just flip z = planet_radius - r */
GMT->current.proj.flip_radius = gmtproj_planet_radius (GMT, "+fp");
/* else the radius was set specifically */
}
if (GMT->current.proj.z_down) { /* Annotate a flavor of z = radius - r */
if (GMT->current.proj.z_down == GMT_ZDOWN_ZP) { /* Given z; annotate r = planet_radius - z */
if (GMT->current.proj.flip_radius > 0.0) /* Already obtained above */
GMT->current.proj.z_radius = GMT->current.proj.flip_radius;
else
GMT->current.proj.z_radius = GMT->current.proj.flip_radius = gmtproj_planet_radius (GMT, "+zp");
GMT->current.proj.flip = true;
}
else if (GMT->current.proj.z_down == GMT_ZDOWN_Z) /* z = north - r */
GMT->current.proj.z_radius = GMT->common.R.wesn[YHI];
}
/* Plus pretend that it is kind of a geographic polar projection */
GMT->current.proj.north_pole = GMT->current.proj.got_elevations;
GMT->current.proj.pole = (GMT->current.proj.got_elevations) ? 90.0 : 0.0;
GMT->current.proj.radial_offset /= GMT->current.proj.pars[0]; /* Convert any radial offset in inches to user units so we can use it in gmtproj_polar/ipolar */
}
GMT_LOCAL void gmtproj_polar (struct GMT_CTRL *GMT, double x, double y, double *x_i, double *y_i) {
/* Transform x and y to polar(cylindrical) coordinates */
if (GMT->current.proj.got_azimuths) x = 90.0 - x; /* Azimuths, not directions given as x */
if (GMT->current.proj.flip) y = GMT->current.proj.flip_radius - y; /* Depth down or elevations given as y */
sincosd (x - GMT->current.proj.p_base_angle, y_i, x_i); /* Change base line angle */
(*x_i) *= (y + GMT->current.proj.radial_offset); /* Allow for inner circle radius before we start plotting */
(*y_i) *= (y + GMT->current.proj.radial_offset);
}
GMT_LOCAL void gmtproj_ipolar (struct GMT_CTRL *GMT, double *x, double *y, double x_i, double y_i) {
/* Inversely transform both x and y from polar(cylindrical) coordinates */
*x = d_atan2d (y_i, x_i) + GMT->current.proj.p_base_angle;
if (GMT->current.proj.got_azimuths) *x = 90.0 - (*x); /* Azimuths, not directions for x */
*y = hypot (x_i, y_i) - GMT->current.proj.radial_offset; /* Allow for inner circle radius */
if (GMT->current.proj.flip) *y = GMT->current.proj.flip_radius - (*y); /* Depth down or elevations for y */
}
/* -JM MERCATOR PROJECTION */
GMT_LOCAL void gmtproj_vmerc (struct GMT_CTRL *GMT, double lon0, double lat0) {
/* Set up a Mercator transformation with origin at (lon0, lat0) */
double aux_lat0 = (GMT->current.proj.GMT_convert_latitudes) ? gmt_M_latg_to_latc (GMT, lat0) : lat0;
GMT->current.proj.central_meridian = lon0;
/* Need geodetic latitude in this expression: */
GMT->current.proj.j_x = cosd (lat0) / d_sqrt (1.0 - GMT->current.proj.ECC2 * sind (lat0) * sind (lat0)) * GMT->current.proj.EQ_RAD;
GMT->current.proj.j_ix = 1.0 / GMT->current.proj.j_x;
/* Need conformal latitude in this expression (same as in gmtproj_merc_sph) */
GMT->current.proj.j_yc = (fabs (lat0) > 0.0) ? GMT->current.proj.j_x * d_log (GMT, tand (45.0 + 0.5 * aux_lat0)) : 0.0;
}
/* Mercator projection for the sphere */
GMT_LOCAL void gmtproj_merc_sph (struct GMT_CTRL *GMT, double lon, double lat, double *x, double *y) {
/* Convert lon/lat to Mercator x/y (GMT->current.proj.EQ_RAD in GMT->current.proj.j_x) */
gmt_M_wind_lon (GMT, lon) /* Remove central meridian and place lon in -180/+180 range */
if (GMT->current.proj.GMT_convert_latitudes) lat = gmt_M_latg_to_latc (GMT, lat);
*x = GMT->current.proj.j_x * D2R * lon;
*y = (fabs (lat) < 90.0) ? GMT->current.proj.j_x * d_log (GMT, tand (45.0 + 0.5 * lat)) : copysign (DBL_MAX, lat);
}
GMT_LOCAL void gmtproj_imerc_sph (struct GMT_CTRL *GMT, double *lon, double *lat, double x, double y) {
/* Convert Mercator x/y to lon/lat (GMT->current.proj.EQ_RAD in GMT->current.proj.j_ix) */
*lon = x * GMT->current.proj.j_ix * R2D + GMT->current.proj.central_meridian;
*lat = atand (sinh (y * GMT->current.proj.j_ix));
if (GMT->current.proj.GMT_convert_latitudes) *lat = gmt_M_latc_to_latg (GMT, *lat);
}
/* -JY CYLINDRICAL EQUAL-AREA PROJECTION */
GMT_LOCAL void gmtproj_vcyleq (struct GMT_CTRL *GMT, double lon0, double slat) {
/* Set up a Cylindrical equal-area transformation */
gmtproj_check_R_J (GMT, &lon0);
GMT->current.proj.central_meridian = lon0;
GMT->current.proj.j_x = GMT->current.proj.EQ_RAD * D2R * cosd (slat);
GMT->current.proj.j_y = GMT->current.proj.EQ_RAD / cosd (slat);
GMT->current.proj.j_ix = 1.0 / GMT->current.proj.j_x;
GMT->current.proj.j_iy = 1.0 / GMT->current.proj.j_y;
}
GMT_LOCAL void gmtproj_cyleq (struct GMT_CTRL *GMT, double lon, double lat, double *x, double *y) {
/* Convert lon/lat to Cylindrical equal-area x/y */
gmt_M_wind_lon (GMT, lon) /* Remove central meridian and place lon in -180/+180 range */
if (GMT->current.proj.GMT_convert_latitudes) lat = gmt_M_latg_to_lata (GMT, lat);
*x = lon * GMT->current.proj.j_x;
*y = GMT->current.proj.j_y * sind (lat);
if (GMT->current.proj.GMT_convert_latitudes) { /* Gotta fudge abit */
(*x) *= GMT->current.proj.Dx;
(*y) *= GMT->current.proj.Dy;
}
}
GMT_LOCAL void gmtproj_icyleq (struct GMT_CTRL *GMT, double *lon, double *lat, double x, double y) {
/* Convert Cylindrical equal-area x/y to lon/lat */
if (GMT->current.proj.GMT_convert_latitudes) { /* Gotta fudge abit */
x *= GMT->current.proj.iDx;
y *= GMT->current.proj.iDy;
}
*lon = x * GMT->current.proj.j_ix + GMT->current.proj.central_meridian;
*lat = d_asind (y * GMT->current.proj.j_iy);
if (GMT->current.proj.GMT_convert_latitudes) *lat = gmt_M_lata_to_latg (GMT, *lat);
}
/* -JQ CYLINDRICAL EQUIDISTANT PROJECTION */
GMT_LOCAL void gmtproj_vcyleqdist (struct GMT_CTRL *GMT, double lon0, double slat) {
/* Set up a Cylindrical equidistant transformation */
gmtproj_check_R_J (GMT, &lon0);
GMT->current.proj.central_meridian = lon0;
GMT->current.proj.j_x = D2R * GMT->current.proj.EQ_RAD * cosd (slat);
GMT->current.proj.j_y = D2R * GMT->current.proj.EQ_RAD;
GMT->current.proj.j_ix = 1.0 / GMT->current.proj.j_x;
GMT->current.proj.j_iy = 1.0 / GMT->current.proj.j_y;
}
GMT_LOCAL void gmtproj_cyleqdist (struct GMT_CTRL *GMT, double lon, double lat, double *x, double *y) {
/* Convert lon/lat to Cylindrical equidistant x/y */
gmt_M_wind_lon (GMT, lon) /* Remove central meridian and place lon in -180/+180 range */
*x = lon * GMT->current.proj.j_x;
*y = lat * GMT->current.proj.j_y;
}
GMT_LOCAL void gmtproj_icyleqdist (struct GMT_CTRL *GMT, double *lon, double *lat, double x, double y) {
/* Convert Cylindrical equal-area x/y to lon/lat */
*lon = x * GMT->current.proj.j_ix + GMT->current.proj.central_meridian;
*lat = y * GMT->current.proj.j_iy;
}
/* -JJ MILLER CYLINDRICAL PROJECTION */
//#define CHRISTMAS
/* Turning on Christmas makes the Miller projection a triangular projection
* that projects 90 degrees of longitude and latitudes 45-90 into a 45-degree
* triangle. Doing all for quadrants results in a square map with radial
* meridians and lots of distortion along the boundaries. This was used to
* build a 3-D cube of the world with this triangle projection being used to
* map the top (N polar to 34N) and bottom (S pole to 45S) sides, with the
* remaining 4 sides just being -JQ maps. I left it here since I may want
* to mess with this in the future. P. Wessel, Dec. 2016.
*/
#ifdef CHRISTMAS
/* Bypass Miller projection entirely and introduce a triangle projection */
GMT_LOCAL void gmtproj_vmiller (struct GMT_CTRL *GMT, double lon0, double slat) {
/* Set up a Cylindrical equidistant transformation */
GMT->current.proj.north_pole = (slat > 0.0);
gmtproj_check_R_J (GMT, &lon0);
GMT->current.proj.central_meridian = lon0;
GMT->current.proj.j_x = 0.25 * D2R * GMT->current.proj.EQ_RAD;
GMT->current.proj.j_y = 0.25 * D2R * GMT->current.proj.EQ_RAD;
GMT->current.proj.j_ix = 1.0 / GMT->current.proj.j_x;
GMT->current.proj.j_iy = 1.0 / GMT->current.proj.j_y;
}
GMT_LOCAL void gmtproj_miller (struct GMT_CTRL *GMT, double lon, double lat, double *x, double *y) {
/* Convert lon/lat to Cylindrical equidistant x/y */
gmt_M_wind_lon (GMT, lon) /* Remove central meridian and place lon in -180/+180 range */
if (lat > 0.0) {
*x = (0.5 + lon * (90.0 - lat) / 4050.0) * GMT->current.proj.j_x;
*y = ((lat-45.0) / 90.0) * GMT->current.proj.j_y;
}
else {
*x = (0.5 - lon * (90.0 + lat) / 4050.0) * GMT->current.proj.j_x;
*y = -((lat+45) / 90.0) * GMT->current.proj.j_y;
}
}
GMT_LOCAL void gmtproj_imiller (struct GMT_CTRL *GMT, double *lon, double *lat, double x, double y) {
/* Convert Cylindrical equal-area x/y to lon/lat */
if (GMT->current.proj.north_pole) {
*lat = 45.0 + 90.0 * y * GMT->current.proj.j_iy;
*lon = (4050.0 * (x * GMT->current.proj.j_ix - 0.5)) / (90.0 - *lat) + GMT->current.proj.central_meridian;
}
else {
*lat = -(45.0 + 90.0 * y * GMT->current.proj.j_iy);
*lon = -(4050.0 * (x * GMT->current.proj.j_ix - 0.5)) / (90.0 + *lat) + GMT->current.proj.central_meridian;
}
}
#else
GMT_LOCAL void gmtproj_vmiller (struct GMT_CTRL *GMT, double lon0) {
/* Set up a Miller Cylindrical transformation */
gmtproj_check_R_J (GMT, &lon0);
GMT->current.proj.central_meridian = lon0;
GMT->current.proj.j_x = D2R * GMT->current.proj.EQ_RAD;
GMT->current.proj.j_y = 1.25 * GMT->current.proj.EQ_RAD;
GMT->current.proj.j_ix = 1.0 / GMT->current.proj.j_x;
GMT->current.proj.j_iy = 1.0 / GMT->current.proj.j_y;
}
GMT_LOCAL void gmtproj_miller (struct GMT_CTRL *GMT, double lon, double lat, double *x, double *y) {
/* Convert lon/lat to Miller Cylindrical x/y */
gmt_M_wind_lon (GMT, lon) /* Remove central meridian and place lon in -180/+180 range */
*x = lon * GMT->current.proj.j_x;
*y = GMT->current.proj.j_y * d_log (GMT, tand (45.0 + 0.4 * lat));
}
GMT_LOCAL void gmtproj_imiller (struct GMT_CTRL *GMT, double *lon, double *lat, double x, double y) {
/* Convert Miller Cylindrical x/y to lon/lat */
*lon = x * GMT->current.proj.j_ix + GMT->current.proj.central_meridian;
*lat = 2.5 * atand (exp (y * GMT->current.proj.j_iy)) - 112.5;
}
#endif
/* -JCyl_stere CYLINDRICAL STEREOGRAPHIC PROJECTION */
GMT_LOCAL void gmtproj_vcylstereo (struct GMT_CTRL *GMT, double lon0, double slat) {
/* Set up a Cylindrical Stereographic transformation */
gmtproj_check_R_J (GMT, &lon0);
GMT->current.proj.central_meridian = lon0;
GMT->current.proj.j_x = GMT->current.proj.EQ_RAD * D2R * cosd (slat);
GMT->current.proj.j_y = GMT->current.proj.EQ_RAD * (1.0 + cosd (slat));
GMT->current.proj.j_ix = 1.0 / GMT->current.proj.j_x;
GMT->current.proj.j_iy = 1.0 / GMT->current.proj.j_y;
}
GMT_LOCAL void gmtproj_cylstereo (struct GMT_CTRL *GMT, double lon, double lat, double *x, double *y) {
/* Convert lon/lat to Cylindrical Stereographic x/y */
gmt_M_wind_lon (GMT, lon) /* Remove central meridian and place lon in -180/+180 range */
*x = lon * GMT->current.proj.j_x;
*y = GMT->current.proj.j_y * tand (0.5 * lat);
}
GMT_LOCAL void gmtproj_icylstereo (struct GMT_CTRL *GMT, double *lon, double *lat, double x, double y) {
/* Convert Cylindrical Stereographic x/y to lon/lat */
*lon = x * GMT->current.proj.j_ix + GMT->current.proj.central_meridian;
*lat = 2.0 * atand (y * GMT->current.proj.j_iy);
}
/* -JS POLAR STEREOGRAPHIC PROJECTION */
GMT_LOCAL void gmtproj_vstereo (struct GMT_CTRL *GMT, double lon0, double lat0, double horizon) {
/* Set up a Stereographic transformation */
double clat;
if (GMT->current.proj.GMT_convert_latitudes) { /* Set Conformal radius and pole latitude */
gmtlib_scale_eqrad (GMT);
clat = gmt_M_latg_to_latc (GMT, lat0);
}
else
clat = lat0;
GMT->current.proj.central_meridian = lon0;
GMT->current.proj.pole = lat0; /* This is always geodetic */
sincosd (clat, &(GMT->current.proj.sinp), &(GMT->current.proj.cosp)); /* These may be conformal */
GMT->current.proj.north_pole = (lat0 > 0.0);
GMT->current.proj.s_c = 2.0 * GMT->current.proj.EQ_RAD * GMT->current.setting.proj_scale_factor;
GMT->current.proj.s_ic = 1.0 / GMT->current.proj.s_c;
GMT->current.proj.f_horizon = horizon;
GMT->current.proj.rho_max = tand (0.5 * horizon) * GMT->current.proj.s_c;
}
GMT_LOCAL void gmtproj_plrs_sph (struct GMT_CTRL *GMT, double lon, double lat, double *x, double *y) {
/* Convert lon/lat to x/y using Spherical polar projection */
double rho, slon, clon;
if (GMT->current.proj.GMT_convert_latitudes) lat = gmt_M_latg_to_latc (GMT, lat);
gmt_M_wind_lon (GMT, lon) /* Remove central meridian and place lon in -180/+180 range */
sincosd (lon, &slon, &clon);
if (GMT->current.proj.north_pole) {
rho = GMT->current.proj.s_c * tand (45.0 - 0.5 * lat);
*y = -rho * clon;
*x = rho * slon;
}
else {
rho = GMT->current.proj.s_c * tand (45.0 + 0.5 * lat);
*y = rho * clon;
*x = rho * slon;
}
if (GMT->current.proj.GMT_convert_latitudes) { /* Gotta fudge abit */
(*x) *= GMT->current.proj.Dx;
(*y) *= GMT->current.proj.Dy;
}
}
GMT_LOCAL void gmtproj_iplrs_sph (struct GMT_CTRL *GMT, double *lon, double *lat, double x, double y) {
/* Convert Spherical polar x/y to lon/lat */
double c;
if (x == 0.0 && y == 0.0) {
*lon = GMT->current.proj.central_meridian;
*lat = GMT->current.proj.pole;
return;
}
if (GMT->current.proj.GMT_convert_latitudes) { /* Undo effect of fudge factors */
x *= GMT->current.proj.iDx;
y *= GMT->current.proj.iDy;
}
c = 2.0 * atan (hypot (x, y) * GMT->current.proj.s_ic);
if (GMT->current.proj.north_pole) {
*lon = GMT->current.proj.central_meridian + d_atan2d (x, -y);
*lat = d_asind (cos (c));
}
else {
*lon = GMT->current.proj.central_meridian + d_atan2d (x, y);
*lat = d_asind (-cos (c));
}
if (GMT->current.proj.GMT_convert_latitudes) *lat = gmt_M_latc_to_latg (GMT, *lat);
}
GMT_LOCAL void gmtproj_stereo1_sph (struct GMT_CTRL *GMT, double lon, double lat, double *x, double *y) {
/* Convert lon/lat to x/y using Spherical stereographic projection, oblique view */
double sin_dlon, cos_dlon, s, c, cc, A;
if (GMT->current.proj.GMT_convert_latitudes) lat = gmt_M_latg_to_latc (GMT, lat);
sincosd (lon - GMT->current.proj.central_meridian, &sin_dlon, &cos_dlon);
sincosd (lat, &s, &c);
cc = c * cos_dlon;
A = GMT->current.proj.s_c / (1.0 + GMT->current.proj.sinp * s + GMT->current.proj.cosp * cc);
*x = A * c * sin_dlon;
*y = A * (GMT->current.proj.cosp * s - GMT->current.proj.sinp * cc);
if (GMT->current.proj.GMT_convert_latitudes) { /* Gotta fudge abit */
(*x) *= GMT->current.proj.Dx;
(*y) *= GMT->current.proj.Dy;
}
}
GMT_LOCAL void gmtproj_istereo_sph (struct GMT_CTRL *GMT, double *lon, double *lat, double x, double y) {
double rho, c, sin_c, cos_c;
if (GMT->current.proj.GMT_convert_latitudes) { /* Undo effect of fudge factors */
x *= GMT->current.proj.iDx;
y *= GMT->current.proj.iDy;
}
rho = hypot (x, y);
if (rho > GMT->current.proj.rho_max) {
*lat = *lon = GMT->session.d_NaN;
return;
}
c = 2.0 * atan (rho * GMT->current.proj.s_ic);
sincos (c, &sin_c, &cos_c);
if (rho != 0.0) sin_c /= rho;
*lat = asind (cos_c * GMT->current.proj.sinp + y * sin_c * GMT->current.proj.cosp);
*lon = d_atan2d (x * sin_c, cos_c * GMT->current.proj.cosp - y * sin_c * GMT->current.proj.sinp) + GMT->current.proj.central_meridian;
if (GMT->current.proj.GMT_convert_latitudes) *lat = gmt_M_latc_to_latg (GMT, *lat);
}
/* Spherical equatorial view */
GMT_LOCAL void gmtproj_stereo2_sph (struct GMT_CTRL *GMT, double lon, double lat, double *x, double *y) {
/* Convert lon/lat to x/y using stereographic projection, equatorial view */
double dlon, s, c, clon, slon, A;
dlon = lon - GMT->current.proj.central_meridian;
if (doubleAlmostEqual (dlon, 180.0)) {
*x = *y = 0.0;
}
else {
if (GMT->current.proj.GMT_convert_latitudes) lat = gmt_M_latg_to_latc (GMT, lat);
sincosd (lat, &s, &c);
sincosd (dlon, &slon, &clon);
A = GMT->current.proj.s_c / (1.0 + c * clon);
*x = A * c * slon;
*y = A * s;
if (GMT->current.proj.GMT_convert_latitudes) { /* Gotta fudge abit */
(*x) *= GMT->current.proj.Dx;
(*y) *= GMT->current.proj.Dy;
}
}
}
/* -JL LAMBERT CONFORMAL CONIC PROJECTION */