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+/******************************************************************************
+ * Project: PROJ.4
+ * Purpose: Implementation of the HEALPix and rHEALPix projections.
+ * For background see <http://code.scenzgrid.org/index.php/p/scenzgrid-py/source/tree/master/docs/rhealpix_dggs.pdf>.
+ * Authors: Alex Raichev (raichev@cs.auckland.ac.nz)
+ * Michael Speth (spethm@landcareresearch.co.nz)
+ * Notes: Raichev implemented these projections in Python and
+ * Speth translated them into C here.
+ ******************************************************************************
+ * Copyright (c) 2001, Thomas Flemming, tf@ttqv.com
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included
+ * in all copies or substcounteral portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *****************************************************************************/
+#define PJ_LIB__
+
+#include <errno.h>
+#include <math.h>
+
+#include "proj_internal.h"
+#include "proj.h"
+#include "projects.h"
+
+PROJ_HEAD(healpix, "HEALPix") "\n\tSph&Ell";
+PROJ_HEAD(rhealpix, "rHEALPix") "\n\tSph&Ell\n\tnorth_square= south_square=";
+
+/* Matrix for counterclockwise rotation by pi/2: */
+# define R1 {{ 0,-1},{ 1, 0}}
+/* Matrix for counterclockwise rotation by pi: */
+# define R2 {{-1, 0},{ 0,-1}}
+/* Matrix for counterclockwise rotation by 3*pi/2: */
+# define R3 {{ 0, 1},{-1, 0}}
+/* Identity matrix */
+# define IDENT {{1, 0},{0, 1}}
+/* IDENT, R1, R2, R3, R1 inverse, R2 inverse, R3 inverse:*/
+# define ROT {IDENT, R1, R2, R3, R3, R2, R1}
+/* Fuzz to handle rounding errors: */
+# define EPS 1e-15
+
+struct pj_opaque {
+ int north_square;
+ int south_square;
+ double qp;
+ double *apa;
+};
+
+typedef struct {
+ int cn; /* An integer 0--3 indicating the position of the polar cap. */
+ double x, y; /* Coordinates of the pole point (point of most extreme latitude on the polar caps). */
+ enum Region {north, south, equatorial} region;
+} CapMap;
+
+static const double rot[7][2][2] = ROT;
+
+/**
+ * Returns the sign of the double.
+ * @param v the parameter whose sign is returned.
+ * @return 1 for positive number, -1 for negative, and 0 for zero.
+ **/
+static double sign (double v) {
+ return v > 0 ? 1 : (v < 0 ? -1 : 0);
+}
+
+
+/**
+ * Return the index of the matrix in ROT.
+ * @param index ranges from -3 to 3.
+ */
+static int get_rotate_index(int index) {
+ switch(index) {
+ case 0:
+ return 0;
+ case 1:
+ return 1;
+ case 2:
+ return 2;
+ case 3:
+ return 3;
+ case -1:
+ return 4;
+ case -2:
+ return 5;
+ case -3:
+ return 6;
+ }
+ return 0;
+}
+
+
+/**
+ * Return 1 if point (testx, testy) lies in the interior of the polygon
+ * determined by the vertices in vert, and return 0 otherwise.
+ * See http://paulbourke.net/geometry/polygonmesh/ for more details.
+ * @param nvert the number of vertices in the polygon.
+ * @param vert the (x, y)-coordinates of the polygon's vertices
+ **/
+static int pnpoly(int nvert, double vert[][2], double testx, double testy) {
+ int i;
+ int counter = 0;
+ double xinters;
+ XY p1, p2;
+
+ /* Check for boundrary cases */
+ for (i = 0; i < nvert; i++) {
+ if (testx == vert[i][0] && testy == vert[i][1]) {
+ return 1;
+ }
+ }
+
+ p1.x = vert[0][0];
+ p1.y = vert[0][1];
+
+ for (i = 1; i < nvert; i++) {
+ p2.x = vert[i % nvert][0];
+ p2.y = vert[i % nvert][1];
+ if (testy > MIN(p1.y, p2.y) &&
+ testy <= MAX(p1.y, p2.y) &&
+ testx <= MAX(p1.x, p2.x) &&
+ p1.y != p2.y)
+ {
+ xinters = (testy-p1.y)*(p2.x-p1.x)/(p2.y-p1.y)+p1.x;
+ if (p1.x == p2.x || testx <= xinters)
+ counter++;
+ }
+ p1 = p2;
+ }
+
+ if (counter % 2 == 0) {
+ return 0;
+ } else {
+ return 1;
+ }
+}
+
+
+/**
+ * Return 1 if (x, y) lies in (the interior or boundary of) the image of the
+ * HEALPix projection (in case proj=0) or in the image the rHEALPix projection
+ * (in case proj=1), and return 0 otherwise.
+ * @param north_square the position of the north polar square (rHEALPix only)
+ * @param south_square the position of the south polar square (rHEALPix only)
+ **/
+static int in_image(double x, double y, int proj, int north_square,
+ int south_square) {
+ if (proj == 0) {
+ double healpixVertsJit[][2] = {
+ {-M_PI - EPS, M_FORTPI},
+ {-3*M_FORTPI, M_HALFPI + EPS},
+ {-M_HALFPI, M_FORTPI + EPS},
+ {-M_FORTPI, M_HALFPI + EPS},
+ {0.0, M_FORTPI + EPS},
+ {M_FORTPI, M_HALFPI + EPS},
+ {M_HALFPI, M_FORTPI + EPS},
+ {3*M_FORTPI, M_HALFPI + EPS},
+ {M_PI + EPS, M_FORTPI},
+ {M_PI + EPS, -M_FORTPI},
+ {3*M_FORTPI, -M_HALFPI - EPS},
+ {M_HALFPI, -M_FORTPI - EPS},
+ {M_FORTPI, -M_HALFPI - EPS},
+ {0.0, -M_FORTPI - EPS},
+ {-M_FORTPI, -M_HALFPI - EPS},
+ {-M_HALFPI, -M_FORTPI - EPS},
+ {-3*M_FORTPI, -M_HALFPI - EPS},
+ {-M_PI - EPS, -M_FORTPI}
+ };
+ return pnpoly((int)sizeof(healpixVertsJit)/
+ sizeof(healpixVertsJit[0]), healpixVertsJit, x, y);
+ } else {
+ /**
+ * Assigning each element by index to avoid warnings such as
+ * 'initializer element is not computable at load time'.
+ * Before C99 this was not allowed and to keep as portable as
+ * possible we do it the C89 way here.
+ * We need to assign the array this way because the input is
+ * dynamic (north_square and south_square vars are unknown at
+ * compile time).
+ **/
+ double rhealpixVertsJit[12][2];
+ rhealpixVertsJit[0][0] = -M_PI - EPS;
+ rhealpixVertsJit[0][1] = M_FORTPI + EPS;
+ rhealpixVertsJit[1][0] = -M_PI + north_square*M_HALFPI- EPS;
+ rhealpixVertsJit[1][1] = M_FORTPI + EPS;
+ rhealpixVertsJit[2][0] = -M_PI + north_square*M_HALFPI- EPS;
+ rhealpixVertsJit[2][1] = 3*M_FORTPI + EPS;
+ rhealpixVertsJit[3][0] = -M_PI + (north_square + 1.0)*M_HALFPI + EPS;
+ rhealpixVertsJit[3][1] = 3*M_FORTPI + EPS;
+ rhealpixVertsJit[4][0] = -M_PI + (north_square + 1.0)*M_HALFPI + EPS;
+ rhealpixVertsJit[4][1] = M_FORTPI + EPS;
+ rhealpixVertsJit[5][0] = M_PI + EPS;
+ rhealpixVertsJit[5][1] = M_FORTPI + EPS;
+ rhealpixVertsJit[6][0] = M_PI + EPS;
+ rhealpixVertsJit[6][1] = -M_FORTPI - EPS;
+ rhealpixVertsJit[7][0] = -M_PI + (south_square + 1.0)*M_HALFPI + EPS;
+ rhealpixVertsJit[7][1] = -M_FORTPI - EPS;
+ rhealpixVertsJit[8][0] = -M_PI + (south_square + 1.0)*M_HALFPI + EPS;
+ rhealpixVertsJit[8][1] = -3*M_FORTPI - EPS;
+ rhealpixVertsJit[9][0] = -M_PI + south_square*M_HALFPI - EPS;
+ rhealpixVertsJit[9][1] = -3*M_FORTPI - EPS;
+ rhealpixVertsJit[10][0] = -M_PI + south_square*M_HALFPI - EPS;
+ rhealpixVertsJit[10][1] = -M_FORTPI - EPS;
+ rhealpixVertsJit[11][0] = -M_PI - EPS;
+ rhealpixVertsJit[11][1] = -M_FORTPI - EPS;
+
+ return pnpoly((int)sizeof(rhealpixVertsJit)/
+ sizeof(rhealpixVertsJit[0]), rhealpixVertsJit, x, y);
+ }
+}
+
+
+/**
+ * Return the authalic latitude of latitude alpha (if inverse=0) or
+ * return the approximate latitude of authalic latitude alpha (if inverse=1).
+ * P contains the relevant ellipsoid parameters.
+ **/
+static double auth_lat(PJ *P, double alpha, int inverse) {
+ struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
+ if (inverse == 0) {
+ /* Authalic latitude. */
+ double q = pj_qsfn(sin(alpha), P->e, 1.0 - P->es);
+ double qp = Q->qp;
+ double ratio = q/qp;
+
+ if (fabs(ratio) > 1) {
+ /* Rounding error. */
+ ratio = sign(ratio);
+ }
+ return asin(ratio);
+ } else {
+ /* Approximation to inverse authalic latitude. */
+ return pj_authlat(alpha, Q->apa);
+ }
+}
+
+
+/**
+ * Return the HEALPix projection of the longitude-latitude point lp on
+ * the unit sphere.
+**/
+static XY healpix_sphere(LP lp) {
+ double lam = lp.lam;
+ double phi = lp.phi;
+ double phi0 = asin(2.0/3.0);
+ XY xy;
+
+ /* equatorial region */
+ if ( fabs(phi) <= phi0) {
+ xy.x = lam;
+ xy.y = 3*M_PI/8*sin(phi);
+ } else {
+ double lamc;
+ double sigma = sqrt(3*(1 - fabs(sin(phi))));
+ double cn = floor(2*lam / M_PI + 2);
+ if (cn >= 4) {
+ cn = 3;
+ }
+ lamc = -3*M_FORTPI + M_HALFPI*cn;
+ xy.x = lamc + (lam - lamc)*sigma;
+ xy.y = sign(phi)*M_FORTPI*(2 - sigma);
+ }
+ return xy;
+}
+
+
+/**
+ * Return the inverse of healpix_sphere().
+**/
+static LP healpix_sphere_inverse(XY xy) {
+ LP lp;
+ double x = xy.x;
+ double y = xy.y;
+ double y0 = M_FORTPI;
+
+ /* Equatorial region. */
+ if (fabs(y) <= y0) {
+ lp.lam = x;
+ lp.phi = asin(8*y/(3*M_PI));
+ } else if (fabs(y) < M_HALFPI) {
+ double cn = floor(2*x/M_PI + 2);
+ double xc, tau;
+ if (cn >= 4) {
+ cn = 3;
+ }
+ xc = -3*M_FORTPI + M_HALFPI*cn;
+ tau = 2.0 - 4*fabs(y)/M_PI;
+ lp.lam = xc + (x - xc)/tau;
+ lp.phi = sign(y)*asin(1.0 - pow(tau, 2)/3.0);
+ } else {
+ lp.lam = -M_PI;
+ lp.phi = sign(y)*M_HALFPI;
+ }
+ return (lp);
+}
+
+
+/**
+ * Return the vector sum a + b, where a and b are 2-dimensional vectors.
+ * @param ret holds a + b.
+ **/
+static void vector_add(const double a[2], const double b[2], double *ret) {
+ int i;
+ for(i = 0; i < 2; i++) {
+ ret[i] = a[i] + b[i];
+ }
+}
+
+
+/**
+ * Return the vector difference a - b, where a and b are 2-dimensional vectors.
+ * @param ret holds a - b.
+ **/
+static void vector_sub(const double a[2], const double b[2], double*ret) {
+ int i;
+ for(i = 0; i < 2; i++) {
+ ret[i] = a[i] - b[i];
+ }
+}
+
+
+/**
+ * Return the 2 x 1 matrix product a*b, where a is a 2 x 2 matrix and
+ * b is a 2 x 1 matrix.
+ * @param ret holds a*b.
+ **/
+static void dot_product(const double a[2][2], const double b[2], double *ret) {
+ int i, j;
+ int length = 2;
+ for(i = 0; i < length; i++) {
+ ret[i] = 0;
+ for(j = 0; j < length; j++) {
+ ret[i] += a[i][j]*b[j];
+ }
+ }
+}
+
+
+/**
+ * Return the number of the polar cap, the pole point coordinates, and
+ * the region that (x, y) lies in.
+ * If inverse=0, then assume (x,y) lies in the image of the HEALPix
+ * projection of the unit sphere.
+ * If inverse=1, then assume (x,y) lies in the image of the
+ * (north_square, south_square)-rHEALPix projection of the unit sphere.
+ **/
+static CapMap get_cap(double x, double y, int north_square, int south_square,
+ int inverse) {
+ CapMap capmap;
+ double c;
+
+ capmap.x = x;
+ capmap.y = y;
+ if (inverse == 0) {
+ if (y > M_FORTPI) {
+ capmap.region = CapMap::north;
+ c = M_HALFPI;
+ } else if (y < -M_FORTPI) {
+ capmap.region = CapMap::south;
+ c = -M_HALFPI;
+ } else {
+ capmap.region = CapMap::equatorial;
+ capmap.cn = 0;
+ return capmap;
+ }
+ /* polar region */
+ if (x < -M_HALFPI) {
+ capmap.cn = 0;
+ capmap.x = (-3*M_FORTPI);
+ capmap.y = c;
+ } else if (x >= -M_HALFPI && x < 0) {
+ capmap.cn = 1;
+ capmap.x = -M_FORTPI;
+ capmap.y = c;
+ } else if (x >= 0 && x < M_HALFPI) {
+ capmap.cn = 2;
+ capmap.x = M_FORTPI;
+ capmap.y = c;
+ } else {
+ capmap.cn = 3;
+ capmap.x = 3*M_FORTPI;
+ capmap.y = c;
+ }
+ } else {
+ if (y > M_FORTPI) {
+ capmap.region = CapMap::north;
+ capmap.x = -3*M_FORTPI + north_square*M_HALFPI;
+ capmap.y = M_HALFPI;
+ x = x - north_square*M_HALFPI;
+ } else if (y < -M_FORTPI) {
+ capmap.region = CapMap::south;
+ capmap.x = -3*M_FORTPI + south_square*M_HALFPI;
+ capmap.y = -M_HALFPI;
+ x = x - south_square*M_HALFPI;
+ } else {
+ capmap.region = CapMap::equatorial;
+ capmap.cn = 0;
+ return capmap;
+ }
+ /* Polar Region, find the HEALPix polar cap number that
+ x, y moves to when rHEALPix polar square is disassembled. */
+ if (capmap.region == CapMap::north) {
+ if (y >= -x - M_FORTPI - EPS && y < x + 5*M_FORTPI - EPS) {
+ capmap.cn = (north_square + 1) % 4;
+ } else if (y > -x -M_FORTPI + EPS && y >= x + 5*M_FORTPI - EPS) {
+ capmap.cn = (north_square + 2) % 4;
+ } else if (y <= -x -M_FORTPI + EPS && y > x + 5*M_FORTPI + EPS) {
+ capmap.cn = (north_square + 3) % 4;
+ } else {
+ capmap.cn = north_square;
+ }
+ } else if (capmap.region == CapMap::south) {
+ if (y <= x + M_FORTPI + EPS && y > -x - 5*M_FORTPI + EPS) {
+ capmap.cn = (south_square + 1) % 4;
+ } else if (y < x + M_FORTPI - EPS && y <= -x - 5*M_FORTPI + EPS) {
+ capmap.cn = (south_square + 2) % 4;
+ } else if (y >= x + M_FORTPI - EPS && y < -x - 5*M_FORTPI - EPS) {
+ capmap.cn = (south_square + 3) % 4;
+ } else {
+ capmap.cn = south_square;
+ }
+ }
+ }
+ return capmap;
+}
+
+
+/**
+ * Rearrange point (x, y) in the HEALPix projection by
+ * combining the polar caps into two polar squares.
+ * Put the north polar square in position north_square and
+ * the south polar square in position south_square.
+ * If inverse=1, then uncombine the polar caps.
+ * @param north_square integer between 0 and 3.
+ * @param south_square integer between 0 and 3.
+ **/
+static XY combine_caps(double x, double y, int north_square, int south_square,
+ int inverse) {
+ XY xy;
+ double v[2];
+ double c[2];
+ double vector[2];
+ double v_min_c[2];
+ double ret_dot[2];
+ const double (*tmpRot)[2];
+ int pole = 0;
+
+ CapMap capmap = get_cap(x, y, north_square, south_square, inverse);
+ if (capmap.region == CapMap::equatorial) {
+ xy.x = capmap.x;
+ xy.y = capmap.y;
+ return xy;
+ }
+
+ v[0] = x; v[1] = y;
+ c[0] = capmap.x; c[1] = capmap.y;
+
+ if (inverse == 0) {
+ /* Rotate (x, y) about its polar cap tip and then translate it to
+ north_square or south_square. */
+
+ if (capmap.region == CapMap::north) {
+ pole = north_square;
+ tmpRot = rot[get_rotate_index(capmap.cn - pole)];
+ } else {
+ pole = south_square;
+ tmpRot = rot[get_rotate_index(-1*(capmap.cn - pole))];
+ }
+ } else {
+ /* Inverse function.
+ Unrotate (x, y) and then translate it back. */
+
+ /* disassemble */
+ if (capmap.region == CapMap::north) {
+ pole = north_square;
+ tmpRot = rot[get_rotate_index(-1*(capmap.cn - pole))];
+ } else {
+ pole = south_square;
+ tmpRot = rot[get_rotate_index(capmap.cn - pole)];
+ }
+ }
+
+ vector_sub(v, c, v_min_c);
+ dot_product(tmpRot, v_min_c, ret_dot);
+ {
+ double a[2];
+ /* Workaround cppcheck git issue */
+ double* pa = a;
+ pa[0] = -3*M_FORTPI + ((inverse == 0) ? pole : capmap.cn) *M_HALFPI;
+ pa[1] = ((capmap.region == CapMap::north) ? 1 : -1) *M_HALFPI;
+ vector_add(ret_dot, a, vector);
+ }
+
+ xy.x = vector[0];
+ xy.y = vector[1];
+ return xy;
+}
+
+
+static XY s_healpix_forward(LP lp, PJ *P) { /* sphere */
+ (void) P;
+ return healpix_sphere(lp);
+}
+
+
+static XY e_healpix_forward(LP lp, PJ *P) { /* ellipsoid */
+ lp.phi = auth_lat(P, lp.phi, 0);
+ return healpix_sphere(lp);
+}
+
+
+static LP s_healpix_inverse(XY xy, PJ *P) { /* sphere */
+ /* Check whether (x, y) lies in the HEALPix image */
+ if (in_image(xy.x, xy.y, 0, 0, 0) == 0) {
+ LP lp;
+ lp.lam = HUGE_VAL;
+ lp.phi = HUGE_VAL;
+ pj_ctx_set_errno(P->ctx, PJD_ERR_INVALID_X_OR_Y);
+ return lp;
+ }
+ return healpix_sphere_inverse(xy);
+}
+
+
+static LP e_healpix_inverse(XY xy, PJ *P) { /* ellipsoid */
+ LP lp = {0.0,0.0};
+
+ /* Check whether (x, y) lies in the HEALPix image. */
+ if (in_image(xy.x, xy.y, 0, 0, 0) == 0) {
+ lp.lam = HUGE_VAL;
+ lp.phi = HUGE_VAL;
+ pj_ctx_set_errno(P->ctx, PJD_ERR_INVALID_X_OR_Y);
+ return lp;
+ }
+ lp = healpix_sphere_inverse(xy);
+ lp.phi = auth_lat(P, lp.phi, 1);
+ return lp;
+}
+
+
+static XY s_rhealpix_forward(LP lp, PJ *P) { /* sphere */
+ struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
+
+ XY xy = healpix_sphere(lp);
+ return combine_caps(xy.x, xy.y, Q->north_square, Q->south_square, 0);
+}
+
+
+static XY e_rhealpix_forward(LP lp, PJ *P) { /* ellipsoid */
+ struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
+ XY xy;
+ lp.phi = auth_lat(P, lp.phi, 0);
+ xy = healpix_sphere(lp);
+ return combine_caps(xy.x, xy.y, Q->north_square, Q->south_square, 0);
+}
+
+
+static LP s_rhealpix_inverse(XY xy, PJ *P) { /* sphere */
+ struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
+
+ /* Check whether (x, y) lies in the rHEALPix image. */
+ if (in_image(xy.x, xy.y, 1, Q->north_square, Q->south_square) == 0) {
+ LP lp;
+ lp.lam = HUGE_VAL;
+ lp.phi = HUGE_VAL;
+ pj_ctx_set_errno(P->ctx, PJD_ERR_INVALID_X_OR_Y);
+ return lp;
+ }
+ xy = combine_caps(xy.x, xy.y, Q->north_square, Q->south_square, 1);
+ return healpix_sphere_inverse(xy);
+}
+
+
+static LP e_rhealpix_inverse(XY xy, PJ *P) { /* ellipsoid */
+ struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
+ LP lp = {0.0,0.0};
+
+ /* Check whether (x, y) lies in the rHEALPix image. */
+ if (in_image(xy.x, xy.y, 1, Q->north_square, Q->south_square) == 0) {
+ lp.lam = HUGE_VAL;
+ lp.phi = HUGE_VAL;
+ pj_ctx_set_errno(P->ctx, PJD_ERR_INVALID_X_OR_Y);
+ return lp;
+ }
+ xy = combine_caps(xy.x, xy.y, Q->north_square, Q->south_square, 1);
+ lp = healpix_sphere_inverse(xy);
+ lp.phi = auth_lat(P, lp.phi, 1);
+ return lp;
+}
+
+
+static PJ *destructor (PJ *P, int errlev) { /* Destructor */
+ if (0==P)
+ return 0;
+
+ if (0==P->opaque)
+ return pj_default_destructor (P, errlev);
+
+ pj_dealloc (static_cast<struct pj_opaque*>(P->opaque)->apa);
+ return pj_default_destructor (P, errlev);
+}
+
+
+PJ *PROJECTION(healpix) {
+ struct pj_opaque *Q = static_cast<struct pj_opaque*>(pj_calloc (1, sizeof (struct pj_opaque)));
+ if (0==Q)
+ return pj_default_destructor (P, ENOMEM);
+ P->opaque = Q;
+ P->destructor = destructor;
+
+ if (P->es != 0.0) {
+ Q->apa = pj_authset(P->es); /* For auth_lat(). */
+ if (0==Q->apa)
+ return destructor(P, ENOMEM);
+ Q->qp = pj_qsfn(1.0, P->e, P->one_es); /* For auth_lat(). */
+ P->a = P->a*sqrt(0.5*Q->qp); /* Set P->a to authalic radius. */
+ pj_calc_ellipsoid_params (P, P->a, P->es); /* Ensure we have a consistent parameter set */
+ P->fwd = e_healpix_forward;
+ P->inv = e_healpix_inverse;
+ } else {
+ P->fwd = s_healpix_forward;
+ P->inv = s_healpix_inverse;
+ }
+
+ return P;
+}
+
+
+PJ *PROJECTION(rhealpix) {
+ struct pj_opaque *Q = static_cast<struct pj_opaque*>(pj_calloc (1, sizeof (struct pj_opaque)));
+ if (0==Q)
+ return pj_default_destructor (P, ENOMEM);
+ P->opaque = Q;
+ P->destructor = destructor;
+
+ Q->north_square = pj_param(P->ctx, P->params,"inorth_square").i;
+ Q->south_square = pj_param(P->ctx, P->params,"isouth_square").i;
+
+ /* Check for valid north_square and south_square inputs. */
+ if (Q->north_square < 0 || Q->north_square > 3)
+ return destructor (P, PJD_ERR_AXIS);
+ if (Q->south_square < 0 || Q->south_square > 3)
+ return destructor (P, PJD_ERR_AXIS);
+ if (P->es != 0.0) {
+ Q->apa = pj_authset(P->es); /* For auth_lat(). */
+ if (0==Q->apa)
+ return destructor(P, ENOMEM);
+ Q->qp = pj_qsfn(1.0, P->e, P->one_es); /* For auth_lat(). */
+ P->a = P->a*sqrt(0.5*Q->qp); /* Set P->a to authalic radius. */
+ P->ra = 1.0/P->a;
+ P->fwd = e_rhealpix_forward;
+ P->inv = e_rhealpix_inverse;
+ } else {
+ P->fwd = s_rhealpix_forward;
+ P->inv = s_rhealpix_inverse;
+ }
+
+ return P;
+}
generated by cgit v1.2.3 (git 2.25.1) at 2025-12-15 21:54:54 +0000