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healpix_utils.c
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healpix_utils.c
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/*
hacked apart healpix base2 and healpix_base functions
converted int64 to long to work in C on 64 bit machines
-Matthew R Becker, Univ. of Chicago 2009
*/
/*
* This file is part of Healpix_cxx.
*
* Healpix_cxx is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* Healpix_cxx 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 General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Healpix_cxx; if not, write to the Free Software
* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*
* For more information about HEALPix, see http://healpix.jpl.nasa.gov
*/
/*
* Healpix_cxx is being developed at the Max-Planck-Institut fuer Astrophysik
* and financially supported by the Deutsches Zentrum fuer Luft- und Raumfahrt
* (DLR).
*/
/*! \file healpix_base2.h
* Copyright (C) 2003, 2004, 2005, 2006 Max-Planck-Society
* \author Martin Reinecke
*/
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <assert.h>
#include <gsl/gsl_math.h>
#include "healpix_utils.h"
static long ctab[0x100];
static long utab[0x100];
static const long jrll[] = { 2,2,2,2,3,3,3,3,4,4,4,4 };
static const long jpll[] = { 1,3,5,7,0,2,4,6,1,3,5,7 };
static int HEALPIX_TOOLS_INIT = 1;
long isqrt(long i)
{
return sqrt(((double) (i)) + 0.5);
}
long ilog2(long arg)
{
unsigned long res=0;
while(arg > 0x0000FFFF)
{
res += 16;
arg >>= 16;
}
if(arg > 0x000000FF)
{
res |= 8;
arg >>= 8;
}
if(arg > 0x0000000F)
{
res |= 4;
arg >>= 4;
}
if(arg > 0x00000003)
{
res |= 2;
arg >>= 2;
}
if(arg > 0x00000001)
{
res |= 1;
}
return res;
}
long imodulo(long v1, long v2)
{
return (v1>=0) ? ((v1<v2) ? v1 : (v1%v2)) : ((v1%v2)+v2);
}
void ang2radec(double theta, double phi, double *ra, double *dec)
{
*ra = phi/M_PI*180.0;
*dec = (M_PI/2.0 - theta)/M_PI*180.0;
}
void radec2ang(double *theta, double *phi, double ra, double dec)
{
*phi = ra/180.0*M_PI;
*theta = M_PI/2.0 - dec/180.0*M_PI;
}
void vec2radec(double vec[3], double *ra, double *dec)
{
/*double rad;
rad = sqrt(vec[0]*vec[0] + vec[1]*vec[1] + vec[2]*vec[2]);
if(vec[0] == 0.0 && vec[1] == 0.0)
*ra = 0.0;
else
*ra = (float) ((vec[1] < 0.0) ? 360.0 + atan2(vec[1],vec[0])*180.0/M_PI : atan2(vec[1],vec[0])*180.0/M_PI);
*dec = (float) (90.0-acos(vec[2]/rad)*180.0/M_PI);
*/
double theta,phi;
vec2ang(vec,&theta,&phi);
ang2radec(theta,phi,ra,dec);
}
void vec2ang(double vec[3], double *theta, double *phi)
{
double norm = sqrt(vec[0]*vec[0] + vec[1]*vec[1] + vec[2]*vec[2]);
if(vec[0] == 0.0 && vec[1] == 0.0)
*phi = 0.0;
else
*phi = atan2(vec[1],vec[0]);
if(*phi < 0.0)
*phi = *phi + 2.0*M_PI;
*theta = acos(vec[2]/norm);
}
void ang2vec(double vec[3], double theta, double phi)
{
double costheta = cos(theta);
double sintheta = sqrt((1.0 + costheta)*(1.0 - costheta));
vec[0] = sintheta*cos(phi);
vec[1] = sintheta*sin(phi);
vec[2] = costheta;
}
void tablefiller(void)
{
assert(CHAR_BIT == 8);
int m;
for (m=0; m<0x100; ++m)
{
ctab[m] =
(m&0x1 ) | ((m&0x2 ) << 7) | ((m&0x4 ) >> 1) | ((m&0x8 ) << 6)
| ((m&0x10) >> 2) | ((m&0x20) << 5) | ((m&0x40) >> 3) | ((m&0x80) << 4);
utab[m] =
(m&0x1 ) | ((m&0x2 ) << 1) | ((m&0x4 ) << 2) | ((m&0x8 ) << 3)
| ((m&0x10) << 4) | ((m&0x20) << 5) | ((m&0x40) << 6) | ((m&0x80) << 7);
}
}
long order2npix(long order_)
{
long npix_ = 1;
npix_ = 12*(npix_ << (2*order_));
return npix_;
}
long order2nside(long order_)
{
long nside_ = 1;
nside_ = nside_ << order_;
return nside_;
}
long npix2nside(long npix)
{
long res=isqrt(npix/12);
assert(npix==res*res*12);
return res;
}
long npix2order(long npix)
{
return nside2order(npix2nside(npix));
}
long nside2npix(long nside)
{
assert(nside>0 && !((nside)&(nside-1)));
return 12*nside*nside;
}
long nside2order(long nside)
{
assert(nside>0 && !((nside)&(nside-1)));
return ilog2(nside);
}
void nest2xyf(long pix, long *ix, long *iy, long *face_num, long order_)
{
if(HEALPIX_TOOLS_INIT)
{
tablefiller();
HEALPIX_TOOLS_INIT = 0;
}
long npix_ = 1;
npix_ = 12*(npix_ << (2*order_));
assert(pix >= 0 && pix < npix_);
long npface_ = 1;
npface_ = npface_ << (2*order_);
*face_num = pix>>(2*order_);
pix &= (npface_-1);
long raw = ((pix&0x555500000000ull)>>16)
| ((pix&0x5555000000000000ull)>>31)
| (pix&0x5555)
| ((pix&0x55550000)>>15);
*ix = ctab[raw&0xff]
| (ctab[(raw>>8)&0xff]<<4)
| (ctab[(raw>>16)&0xff]<<16)
| (ctab[(raw>>24)&0xff]<<20);
pix >>= 1;
raw = ((pix&0x555500000000ull)>>16)
| ((pix&0x5555000000000000ull)>>31)
| (pix&0x5555)
| ((pix&0x55550000)>>15);
*iy = ctab[raw&0xff]
| (ctab[(raw>>8)&0xff]<<4)
| (ctab[(raw>>16)&0xff]<<16)
| (ctab[(raw>>24)&0xff]<<20);
}
long xyf2nest(long ix, long iy, long face_num, long order_)
{
if(HEALPIX_TOOLS_INIT)
{
tablefiller();
HEALPIX_TOOLS_INIT = 0;
}
long pix = ((face_num)<<(2*order_)) +
( ((utab[ ix &0xff]))
| ((utab[(ix>> 8)&0xff])<<16)
| ((utab[(ix>>16)&0xff])<<32)
| ((utab[(ix>>24)&0xff])<<48)
| ((utab[ iy &0xff])<<1)
| ((utab[(iy>> 8)&0xff])<<17)
| ((utab[(iy>>16)&0xff])<<33)
| ((utab[(iy>>24)&0xff])<<49) );
long npix_ = 1;
npix_ = 12*(npix_ << (2*order_));
assert(pix >= 0 && pix < npix_);
return pix;
}
void ring2xyf(long pix, long *ix, long *iy, long *face_num, long order_)
{
long iring, iphi, kshift, nr;
long npix_ = 1;
npix_ = 12*(npix_ << (2*order_));
assert(pix >= 0 && pix < npix_);
long nside_ = 1;
nside_ = nside_ << order_;
long npface_ = 1;
npface_ = npface_ << (2*order_);
long ncap_ = (npface_-nside_)<<1;
long nl2 = 2*nside_;
if (pix<ncap_) // North Polar cap
{
iring = (long) (0.5*(1+isqrt(1+2*pix))); //counted from North pole
iphi = (pix+1) - 2*iring*(iring-1);
kshift = 0;
nr = iring;
*face_num=0;
long tmp = iphi-1;
if (tmp>=(2*iring))
{
*face_num=2;
tmp-=2*iring;
}
if (tmp>=iring) (*face_num) = (*face_num) + 1;
}
else if (pix<(npix_-ncap_)) // Equatorial region
{
long ip = pix - ncap_;
if (order_>=0)
{
iring = (ip>>(order_+2)) + nside_; // counted from North pole
iphi = (ip&(4*nside_-1)) + 1;
}
else
{
iring = (ip/(4*nside_)) + nside_; // counted from North pole
iphi = (ip%(4*nside_)) + 1;
}
kshift = (iring+nside_)&1;
nr = nside_;
long ire = iring-nside_+1;
long irm = nl2+2-ire;
long ifm, ifp;
if (order_>=0)
{
ifm = (iphi - ire/2 + nside_ -1) >> order_;
ifp = (iphi - irm/2 + nside_ -1) >> order_;
}
else
{
ifm = (iphi - ire/2 + nside_ -1) / nside_;
ifp = (iphi - irm/2 + nside_ -1) / nside_;
}
if (ifp == ifm) // faces 4 to 7
*face_num = (ifp==4) ? 4 : ifp+4;
else if (ifp<ifm) // (half-)faces 0 to 3
*face_num = ifp;
else // (half-)faces 8 to 11
*face_num = ifm + 8;
}
else // South Polar cap
{
long ip = npix_ - pix;
iring = (long) (0.5*(1+isqrt(2*ip-1))); //counted from South pole
iphi = 4*iring + 1 - (ip - 2*iring*(iring-1));
kshift = 0;
nr = iring;
iring = 2*nl2-iring;
*face_num=8;
long tmp = iphi-1;
if (tmp>=(2*nr))
{
*face_num=10;
tmp-=2*nr;
}
if (tmp>=nr) (*face_num) = (*face_num) + 1;
}
long irt = iring - (jrll[*face_num]*nside_) + 1;
long ipt = 2*iphi- jpll[*face_num]*nr - kshift -1;
if (ipt>=nl2) ipt-=8*nside_;
*ix = (ipt-irt) >>1;
*iy =(-(ipt+irt))>>1;
}
long xyf2ring(long ix, long iy, long face_num, long order_)
{
long npix_ = 1;
npix_ = 12*(npix_ << (2*order_));
long nside_ = 1;
nside_ = nside_ << order_;
long npface_ = 1;
npface_ = npface_ << (2*order_);
long ncap_ = (npface_-nside_)<<1;
long nl4 = 4*nside_;
long jr = (jrll[face_num]*nside_) - ix - iy - 1;
long nr, kshift, n_before;
if (jr<nside_)
{
nr = jr;
n_before = 2*nr*(nr-1);
kshift = 0;
}
else if (jr > 3*nside_)
{
nr = nl4-jr;
n_before = npix_ - 2*(nr+1)*nr;
kshift = 0;
}
else
{
nr = nside_;
n_before = ncap_ + (jr-nside_)*nl4;
kshift = (jr-nside_)&1;
}
long jp = (jpll[face_num]*nr + ix - iy + 1 + kshift) / 2;
if (jp>nl4)
jp-=nl4;
else
if (jp<1) jp+=nl4;
long pix = n_before + jp - 1;
assert(pix >= 0 && pix < npix_);
return pix;
}
long nest2ring(long pix, long order_)
{
long ix, iy, face_num;
nest2xyf(pix,&ix,&iy,&face_num,order_);
return xyf2ring(ix,iy,face_num,order_);
}
long ring2nest(long pix, long order_)
{
long ix, iy, face_num;
ring2xyf(pix,&ix,&iy,&face_num,order_);
return xyf2nest(ix,iy,face_num,order_);
}
long nest2peano(long pix, long order_)
{
static const unsigned long subpix[8][4] = {
{ 0, 1, 3, 2 }, { 3, 0, 2, 1 }, { 2, 3, 1, 0 }, { 1, 2, 0, 3 },
{ 0, 3, 1, 2 }, { 1, 0, 2, 3 }, { 2, 1, 3, 0 }, { 3, 2, 0, 1 } };
static const unsigned long subpath[8][4] = {
{ 4, 0, 6, 0 }, { 7, 5, 1, 1 }, { 2, 4, 2, 6 }, { 3, 3, 7, 5 },
{ 0, 2, 4, 4 }, { 5, 1, 5, 3 }, { 6, 6, 0, 2 }, { 1, 7, 3, 7 } };
static const unsigned long face2path[12] = {
2, 5, 2, 5, 3, 6, 3, 6, 2, 3, 2, 3 };
static const unsigned long face2peanoface[12] = {
0, 5, 6, 11, 10, 1, 4, 7, 2, 3, 8, 9 };
long npix_ = 1;
npix_ = 12*(npix_ << (2*order_));
assert(pix >= 0 && pix < npix_);
long face = pix>>(2*order_);
unsigned long path = face2path[face];
long result = 0;
long shift;
for(shift=2*order_-2; shift>=0; shift-=2)
{
unsigned char spix = (pix>>shift) & 0x3;
result <<= 2;
result |= subpix[path][spix];
path=subpath[path][spix];
}
return result + ((face2peanoface[face])<<(2*order_));
}
long peano2nest(long pix, long order_)
{
static const unsigned long subpix[8][4] = {
{ 0, 1, 3, 2 }, { 1, 3, 2, 0 }, { 3, 2, 0, 1 }, { 2, 0, 1, 3 },
{ 0, 2, 3, 1 }, { 1, 0, 2, 3 }, { 3, 1, 0, 2 }, { 2, 3, 1, 0 } };
static const unsigned long subpath[8][4] = {
{ 4, 0, 0, 6 }, { 5, 1, 1, 7 }, { 6, 2, 2, 4 }, { 7, 3, 3, 5 },
{ 0, 4, 4, 2 }, { 1, 5, 5, 3 }, { 2, 6, 6, 0 }, { 3, 7, 7, 1 } };
static const unsigned long face2path[12] = {
2, 6, 2, 3, 3, 5, 2, 6, 2, 3, 3, 5 };
static const unsigned long peanoface2face[12] = {
0, 5, 8, 9, 6, 1, 2, 7, 10, 11, 4, 3 };
long npix_ = 1;
npix_ = 12*(npix_ << (2*order_));
assert(pix >= 0 && pix < npix_);
long face = pix>>(2*order_);
unsigned long path = face2path[face];
long result = 0;
long shift;
for(shift=2*order_-2; shift>=0; shift-=2)
{
unsigned long spix = (pix>>shift) & 0x3;
result <<= 2;
result |= subpix[path][spix];
path=subpath[path][spix];
}
return result + ((peanoface2face[face])<<(2*order_));
}
long ang2ring(double theta, double phi, long order_)
{
long npix_ = 1;
npix_ = 12*(npix_ << (2*order_));
long nside_ = 1;
nside_ = nside_ << order_;
long npface_ = 1;
npface_ = npface_ << (2*order_);
long ncap_ = (npface_-nside_)<<1;
double z = cos(theta);
double za = fabs(z);
double tt = phi;
long tt_long = (floor(tt/2/M_PI));
tt = tt - ((double) (tt_long))*2*M_PI;
tt *= M_2_PI; // in [0,4)
if(za <= 2.0/3.0) // Equatorial region
{
double temp1 = nside_*(0.5+tt);
double temp2 = nside_*z*0.75;
long jp = (long) (temp1-temp2); // index of ascending edge line
long jm = (long) (temp1+temp2); // index of descending edge line
// ring number counted from z=2/3
long ir = nside_ + 1 + jp - jm; // in {1,2n+1}
long kshift = 1-(ir&1); // kshift=1 if ir even, 0 otherwise
long ip = (jp+jm-nside_+kshift+1)/2; // in {0,4n-1}
ip = imodulo(ip,4*nside_);
return ncap_ + (ir-1)*4*nside_ + ip;
}
else // North & South polar caps
{
double tp = tt- ((long) (tt));
double tmp = nside_*sqrt(3*(1-za));
long jp = (long) (tp*tmp); // increasing edge line index
long jm = (long) ((1.0-tp)*tmp); // decreasing edge line index
long ir = jp+jm+1; // ring number counted from the closest pole
long ip = (long) (tt*ir); // in {0,4*ir-1}
ip = imodulo(ip,4*ir);
if(z>0)
return 2*ir*(ir-1) + ip;
else
return npix_ - 2*ir*(ir+1) + ip;
}
}
long ang2nest(double theta, double phi, long inorder_)
{
//done at highest resolution and then degraded to specified resolution
long order_ = 29;
long nside_ = 1;
nside_ = nside_ << order_;
long innside_ = 1;
innside_ = innside_ << inorder_;
double z = cos(theta);
double za = fabs(z);
double tt = phi;
long tt_long = (floor(tt/2/M_PI));
tt = tt - ((double) (tt_long))*2*M_PI;
tt *= M_2_PI; // in [0,4)
long face_num, ix, iy;
if(za<=2.0/3.0) // Equatorial region
{
double temp1 = nside_*(0.5+tt);
double temp2 = nside_*(z*0.75);
long jp = (long) (temp1-temp2); // index of ascending edge line
long jm = (long) (temp1+temp2); // index of descending edge line
long ifp = jp >> order_; // in {0,4}
long ifm = jm >> order_;
if(ifp == ifm) // faces 4 to 7
face_num = (ifp==4) ? 4: ifp+4;
else if(ifp < ifm) // (half-)faces 0 to 3
face_num = ifp;
else // (half-)faces 8 to 11
face_num = ifm + 8;
ix = jm & (nside_-1);
iy = nside_ - (jp & (nside_-1)) - 1;
}
else // polar region, za > 2/3
{
long ntt = (long) (tt);
if (ntt>=4) ntt=3;
double tp = tt-ntt;
double tmp = nside_*sqrt(3*(1-za));
long jp = (long) (tp*tmp); // increasing edge line index
long jm = (long) ((1.0-tp)*tmp); // decreasing edge line index
if(jp>=nside_) jp = nside_-1; // for points too close to the boundary
if(jm>=nside_) jm = nside_-1;
if(z >= 0)
{
face_num = ntt; // in {0,3}
ix = nside_ - jm - 1;
iy = nside_ - jp - 1;
}
else
{
face_num = ntt + 8; // in {8,11}
ix = jp;
iy = jm;
}
}
long opix = xyf2nest(ix,iy,face_num,order_);
//fprintf(stderr,"opix = %ld\n",opix);
//degrade to inorder_ map resolution
long ip = opix - nside_*nside_*face_num;
//fprintf(stderr,"ip = %ld, nside_ = %ld, innside_ = %ld\n",ip,nside_,innside_);
long difffac = 1;
difffac = difffac << 2*(order_ - inorder_);
ip = ip/difffac;
//fprintf(stderr,"ip = %ld, nside_ = %ld, innside_ = %ld\n",ip,nside_,innside_);
return (ip + face_num*innside_*innside_);
}
long vec2nest(double *vec, long order_)
{
double theta,phi;
vec2ang(vec,&theta,&phi);
return ang2nest(theta,phi,order_);
}
long vec2ring(double *vec, long order_)
{
double theta,phi;
vec2ang(vec,&theta,&phi);
return ang2ring(theta,phi,order_);
}
void ring2ang(long pix, double *theta, double *phi, long order_)
{
long npix_ = 1;
npix_ = 12*(npix_ << (2*order_));
assert(pix >= 0 && pix < npix_);
long nside_ = 1;
nside_ = nside_ << order_;
long npface_ = 1;
npface_ = npface_ << (2*order_);
long ncap_ = (npface_-nside_)<<1;
double z;
double fact2_ = 4./npix_;
double fact1_ = (nside_<<1)*fact2_;
if(pix<ncap_) // North Polar cap
{
long iring = (long) (0.5*(1+isqrt(1+2*pix))); //counted from North pole
long iphi = (pix+1) - 2*iring*(iring-1);
z = 1.0 - (iring*iring)*fact2_;
*theta = acos(z);
*phi = (iphi-0.5) * M_PI_2/iring;
}
else if(pix<(npix_-ncap_)) // Equatorial region
{
long ip = pix - ncap_;
long iring = ip/(4*nside_) + nside_; // counted from North pole
long iphi = ip%(4*nside_) + 1;
// 1 if iring+nside is odd, 1/2 otherwise
double fodd = ((iring+nside_)&1) ? 1 : 0.5;
long nl2 = 2*nside_;
z = (nl2-iring)*fact1_;
*theta = acos(z);
*phi = (iphi-fodd) * M_PI/nl2;
}
else // South Polar cap
{
long ip = npix_ - pix;
long iring = (long) (0.5*(1+isqrt(2*ip-1))); //counted from South pole
long iphi = 4*iring + 1 - (ip - 2*iring*(iring-1));
z = -1.0 + (iring*iring)*fact2_;
*theta = acos(z);
*phi = (iphi-0.5) * M_PI_2/iring;
}
}
void ring2vec(long pix, double *vec, long order_)
{
double theta,phi;
ring2ang(pix,&theta,&phi,order_);
ang2vec(vec,theta,phi);
}
void nest2ang(long pix, double *theta, double *phi, long order_)
{
long npix_ = 1;
npix_ = 12*(npix_ << (2*order_));
assert(pix >= 0 && pix < npix_);
long nside_ = 1;
nside_ = nside_ << order_;
double z;
double fact2_ = 4./npix_;
double fact1_ = (nside_<<1)*fact2_;
long nl4 = nside_*4;
long face_num, ix, iy;
nest2xyf(pix,&ix,&iy,&face_num,order_);
long jr = ((jrll[face_num])<<order_) - ix - iy - 1;
long nr;
long kshift;
if (jr<nside_)
{
nr = jr;
z = 1 - nr*nr*fact2_;
kshift = 0;
}
else if (jr > 3*nside_)
{
nr = nl4-jr;
z = nr*nr*fact2_ - 1;
kshift = 0;
}
else
{
nr = nside_;
z = (2*nside_-jr)*fact1_;
kshift = (jr-nside_)&1;
}
long jp = (jpll[face_num]*nr + ix -iy + 1 + kshift) / 2;
if (jp>nl4) jp-=nl4;
if (jp<1) jp+=nl4;
*phi = (jp-(kshift+1)*0.5)*(M_PI_2/nr);
*theta = acos(z);
}
void nest2vec(long pix, double *vec, long order_)
{
double theta,phi;
nest2ang(pix,&theta,&phi,order_);
ang2vec(vec,theta,phi);
}
void getneighbors_nest(long pix, long *result, long order_)
{
static const long xoffset[] = { -1,-1, 0, 1, 1, 1, 0,-1 };
static const long yoffset[] = { 0, 1, 1, 1, 0,-1,-1,-1 };
static const long facearray[][12] =
{ { 8, 9,10,11,-1,-1,-1,-1,10,11, 8, 9 }, // S
{ 5, 6, 7, 4, 8, 9,10,11, 9,10,11, 8 }, // SE
{ -1,-1,-1,-1, 5, 6, 7, 4,-1,-1,-1,-1 }, // E
{ 4, 5, 6, 7,11, 8, 9,10,11, 8, 9,10 }, // SW
{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11 }, // center
{ 1, 2, 3, 0, 0, 1, 2, 3, 5, 6, 7, 4 }, // NE
{ -1,-1,-1,-1, 7, 4, 5, 6,-1,-1,-1,-1 }, // W
{ 3, 0, 1, 2, 3, 0, 1, 2, 4, 5, 6, 7 }, // NW
{ 2, 3, 0, 1,-1,-1,-1,-1, 0, 1, 2, 3 } }; // N
static const long swaparray[][12] =
{ { 0,0,0,0,0,0,0,0,3,3,3,3 }, // S
{ 0,0,0,0,0,0,0,0,6,6,6,6 }, // SE
{ 0,0,0,0,0,0,0,0,0,0,0,0 }, // E
{ 0,0,0,0,0,0,0,0,5,5,5,5 }, // SW
{ 0,0,0,0,0,0,0,0,0,0,0,0 }, // center
{ 5,5,5,5,0,0,0,0,0,0,0,0 }, // NE
{ 0,0,0,0,0,0,0,0,0,0,0,0 }, // W
{ 6,6,6,6,0,0,0,0,0,0,0,0 }, // NW
{ 3,3,3,3,0,0,0,0,0,0,0,0 } }; // N
long ix, iy, face_num;
nest2xyf(pix,&ix,&iy,&face_num,order_);
long nside_ = 1;
nside_ = nside_ << order_;
long nsm1 = nside_-1;
if((ix>0)&&(ix<nsm1)&&(iy>0)&&(iy<nsm1))
{
int m;
for(m=0; m<8; ++m)
result[m] = xyf2nest(ix+xoffset[m],iy+yoffset[m],face_num,order_);
}
else
{
long i;
for(i=0; i<8; ++i)
{
long x=ix+xoffset[i];
long y=iy+yoffset[i];
long nbnum=4;
if (x<0)
{ x+=nside_; nbnum-=1; }
else if (x>=nside_)
{ x-=nside_; nbnum+=1; }
if (y<0)
{ y+=nside_; nbnum-=3; }
else if (y>=nside_)
{ y-=nside_; nbnum+=3; }
long f = facearray[nbnum][face_num];
if(f>=0)
{
if (swaparray[nbnum][face_num]&1) x=nside_-x-1;
if (swaparray[nbnum][face_num]&2) y=nside_-y-1;
if (swaparray[nbnum][face_num]&4)
{
long temp = x;
x = y;
y = temp;
//swap(x,y);
}
result[i] = xyf2nest(x,y,f,order_);
}
else
result[i] = -1;
}
}
}
void getneighbors_ring(long pix, long *result, long order_)
{
static const long xoffset[] = { -1,-1, 0, 1, 1, 1, 0,-1 };
static const long yoffset[] = { 0, 1, 1, 1, 0,-1,-1,-1 };
static const long facearray[][12] =
{ { 8, 9,10,11,-1,-1,-1,-1,10,11, 8, 9 }, // S
{ 5, 6, 7, 4, 8, 9,10,11, 9,10,11, 8 }, // SE
{ -1,-1,-1,-1, 5, 6, 7, 4,-1,-1,-1,-1 }, // E
{ 4, 5, 6, 7,11, 8, 9,10,11, 8, 9,10 }, // SW
{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11 }, // center
{ 1, 2, 3, 0, 0, 1, 2, 3, 5, 6, 7, 4 }, // NE
{ -1,-1,-1,-1, 7, 4, 5, 6,-1,-1,-1,-1 }, // W
{ 3, 0, 1, 2, 3, 0, 1, 2, 4, 5, 6, 7 }, // NW
{ 2, 3, 0, 1,-1,-1,-1,-1, 0, 1, 2, 3 } }; // N
static const long swaparray[][12] =
{ { 0,0,0,0,0,0,0,0,3,3,3,3 }, // S
{ 0,0,0,0,0,0,0,0,6,6,6,6 }, // SE
{ 0,0,0,0,0,0,0,0,0,0,0,0 }, // E
{ 0,0,0,0,0,0,0,0,5,5,5,5 }, // SW
{ 0,0,0,0,0,0,0,0,0,0,0,0 }, // center
{ 5,5,5,5,0,0,0,0,0,0,0,0 }, // NE
{ 0,0,0,0,0,0,0,0,0,0,0,0 }, // W
{ 6,6,6,6,0,0,0,0,0,0,0,0 }, // NW
{ 3,3,3,3,0,0,0,0,0,0,0,0 } }; // N
long ix, iy, face_num;
ring2xyf(pix,&ix,&iy,&face_num,order_);
long nside_ = 1;
nside_ = nside_ << order_;
long nsm1 = nside_-1;
if((ix>0)&&(ix<nsm1)&&(iy>0)&&(iy<nsm1))
{
long m;
for(m=0; m<8; ++m)
result[m] = xyf2ring(ix+xoffset[m],iy+yoffset[m],face_num,order_);
}
else
{
long i;
for(i=0; i<8; ++i)
{
long x=ix+xoffset[i];
long y=iy+yoffset[i];
long nbnum=4;
if (x<0)
{ x+=nside_; nbnum-=1; }
else if (x>=nside_)
{ x-=nside_; nbnum+=1; }
if (y<0)
{ y+=nside_; nbnum-=3; }
else if (y>=nside_)
{ y-=nside_; nbnum+=3; }
long f = facearray[nbnum][face_num];
if (f>=0)
{
if (swaparray[nbnum][face_num]&1) x=nside_-x-1;
if (swaparray[nbnum][face_num]&2) y=nside_-y-1;
if (swaparray[nbnum][face_num]&4)
{
long temp = x;
x = y;
y = temp;
//swap(x,y);
}
result[i] = xyf2ring(x,y,f,order_);
}
else
result[i] = -1;
}
}
}
void get_ring_info2(long ring, long *startpix, long *ringpix, double *costheta, double *sintheta, long *shifted, long order_)
{
long npix_ = 1;
npix_ = 12*(npix_ << (2*order_));
long nside_ = 1;
nside_ = nside_ << order_;
long npface_ = 1;
npface_ = npface_ << (2*order_);
long ncap_ = (npface_-nside_)<<1;
double fact2_ = 4./npix_;
double fact1_ = (nside_<<1)*fact2_;
long northring = (ring>2*nside_) ? 4*nside_-ring : ring;
if(northring < nside_)
{
double tmp = northring*northring*fact2_;
*costheta = 1 - tmp;
*sintheta = sqrt(tmp*(2-tmp));
//double theta = atan2(*sintheta,*costheta);
*ringpix = 4*northring;
*shifted = 1;
*startpix = 2*northring*(northring-1);
}
else
{
*costheta = (2*nside_-northring)*fact1_;
*sintheta = sqrt((1.0 - *costheta)*(1.0 + *costheta));
//*theta = acos(*costheta);
*ringpix = 4*nside_;
if(((northring-nside_) & 1) == 0)
*shifted = 1;
else
*shifted = 0;
*startpix = ncap_ + (northring-nside_)*(*ringpix);
}
if(northring != ring) // southern hemisphere
{
//*theta = M_PI-(*theta);
*costheta = -1.0*(*costheta);
*startpix = npix_ - (*startpix) - (*ringpix);
}
}
long ring_above(double z, long order_)
{
long nside_ = 1;
nside_ = nside_ << order_;
double az=fabs(z);
if (az > 2.0/3.0) // polar caps
{
long iring = (long) (nside_*sqrt(3*(1-az)));
return (z>0) ? iring : 4*nside_-iring-1;
}
else // ----- equatorial region ---------
return (long) (nside_*(2-1.5*z));
}
/* returns ring indexed pixels and weights for interpolation */
void get_interpol(double theta, double phi, long pix[4], double wgt[4], long order_)
{
long npix_ = 1;
npix_ = 12*(npix_ << (2*order_));
long nside_ = 1;
nside_ = nside_ << order_;
double z = cos(theta);
long ir1 = ring_above(z,order_);
long ir2 = ir1+1;
double theta1=0.0, theta2=0.0, w1, tmp, dphi;
double cth1,cth2,sth1,sth2;
long sp,nr;
long shift;
long i1,i2;
if (ir1>0)
{
get_ring_info2(ir1,&sp,&nr,&cth1,&sth1,&shift,order_);
theta1 = atan2(sth1,cth1);
//get_ring_info2 (ir1, sp, nr, theta1, shift);
dphi = 2.0*M_PI/nr;
tmp = (phi/dphi - .5*shift);
i1 = (tmp<0) ? ((long) (tmp))-1 : (long) (tmp);
w1 = (phi-(i1+.5*shift)*dphi)/dphi;
i2 = i1+1;
if (i1<0) i1 +=nr;
if (i2>=nr) i2 -=nr;
pix[0] = sp+i1; pix[1] = sp+i2;
wgt[0] = 1-w1; wgt[1] = w1;
}
if (ir2<(4*nside_))
{
get_ring_info2(ir2,&sp,&nr,&cth2,&sth2,&shift,order_);
theta2 = atan2(sth2,cth2);
//get_ring_info2 (ir2, sp, nr, theta2, shift);
dphi = 2.0*M_PI/nr;
tmp = (phi/dphi - .5*shift);
i1 = (tmp<0) ? ((long) (tmp))-1 : (long) (tmp);
w1 = (phi-(i1+.5*shift)*dphi)/dphi;
i2 = i1+1;