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vide_public/external/healpix/Healpix_cxx/healpix_base2.cc
Guilhem Lavaux 4bfb62f177 Imported healpix tree
2012-10-30 13:56:48 -04:00

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/*
* 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).
*/
/*
* Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008, 2009 Max-Planck-Society
* Author: Martin Reinecke
*/
#include "healpix_base2.h"
#include "cxxutils.h"
#include "pointing.h"
#include "arr.h"
#include "geom_utils.h"
#include "lsconstants.h"
using namespace std;
short Healpix_Base2::ctab[];
short Healpix_Base2::utab[];
Healpix_Base2::Tablefiller::Tablefiller()
{
for (int m=0; m<0x100; ++m)
{
ctab[m] = short(
(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] = short(
(m&0x1 ) | ((m&0x2 ) << 1) | ((m&0x4 ) << 2) | ((m&0x8 ) << 3)
| ((m&0x10) << 4) | ((m&0x20) << 5) | ((m&0x40) << 6) | ((m&0x80) << 7));
}
}
Healpix_Base2::Tablefiller Healpix_Base2::Filler;
const int Healpix_Base2::jrll[] = { 2,2,2,2,3,3,3,3,4,4,4,4 };
const int Healpix_Base2::jpll[] = { 1,3,5,7,0,2,4,6,1,3,5,7 };
int64 Healpix_Base2::npix2nside (int64 npix)
{
int64 res=isqrt(npix/12);
planck_assert (npix==res*res*12, "npix2nside: invalid argument");
return res;
}
int64 Healpix_Base2::ring_above (double z) const
{
double az=abs(z);
if (az>twothird) // polar caps
{
int64 iring = int64(nside_*sqrt(3*(1-az)));
return (z>0) ? iring : 4*nside_-iring-1;
}
else // ----- equatorial region ---------
return int64(nside_*(2-1.5*z));
}
void Healpix_Base2::nest2xyf (int64 pix, int &ix, int &iy, int &face_num)
const
{
face_num = int(pix>>(2*order_));
pix &= (npface_-1);
int32 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);
}
int64 Healpix_Base2::xyf2nest (int ix, int iy, int face_num) const
{
return (int64(face_num)<<(2*order_)) +
( (int64(utab[ ix &0xff]))
| (int64(utab[(ix>> 8)&0xff])<<16)
| (int64(utab[(ix>>16)&0xff])<<32)
| (int64(utab[(ix>>24)&0xff])<<48)
| (int64(utab[ iy &0xff])<<1)
| (int64(utab[(iy>> 8)&0xff])<<17)
| (int64(utab[(iy>>16)&0xff])<<33)
| (int64(utab[(iy>>24)&0xff])<<49) );
}
void Healpix_Base2::ring2xyf (int64 pix, int &ix, int &iy, int &face_num)
const
{
int64 iring, iphi, kshift, nr;
int64 nl2 = 2*nside_;
if (pix<ncap_) // North Polar cap
{
iring = int64(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;
int64 tmp = iphi-1;
if (tmp>=(2*iring))
{
face_num=2;
tmp-=2*iring;
}
if (tmp>=iring) ++face_num;
}
else if (pix<(npix_-ncap_)) // Equatorial region
{
int64 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_;
int64 ire = iring-nside_+1;
int64 irm = nl2+2-ire;
int64 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
{
int64 ip = npix_ - pix;
iring = int64(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;
int64 tmp = iphi-1;
if (tmp>=(2*nr))
{
face_num=10;
tmp-=2*nr;
}
if (tmp>=nr) ++face_num;
}
int64 irt = iring - (jrll[face_num]*nside_) + 1;
int64 ipt = 2*iphi- jpll[face_num]*nr - kshift -1;
if (ipt>=nl2) ipt-=8*nside_;
ix = (ipt-irt) >>1;
iy =(-(ipt+irt))>>1;
}
int64 Healpix_Base2::xyf2ring (int ix, int iy, int face_num) const
{
int64 nl4 = 4*nside_;
int64 jr = (jrll[face_num]*nside_) - ix - iy - 1;
int64 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;
}
int64 jp = (jpll[face_num]*nr + ix - iy + 1 + kshift) / 2;
if (jp>nl4)
jp-=nl4;
else
if (jp<1) jp+=nl4;
return n_before + jp - 1;
}
double Healpix_Base2::ring2z (int64 ring) const
{
if (ring<nside_)
return 1 - ring*ring*fact2_;
if (ring <=3*nside_)
return (2*nside_-ring)*fact1_;
ring=4*nside_ - ring;
return ring*ring*fact2_ - 1;
}
int64 Healpix_Base2::pix2ring (int64 pix) const
{
if (scheme_==RING)
{
if (pix<ncap_) // North Polar cap
return int64(0.5*(1+isqrt(1+2*pix))); //counted from North pole
else if (pix<(npix_-ncap_)) // Equatorial region
{
int64 ip = pix - ncap_;
return ip/(4*nside_) + nside_; // counted from North pole
}
else // South Polar cap
{
int64 ip = npix_ - pix;
return 4*nside_ - int64(0.5*(1+isqrt(2*ip-1))); //counted from South pole
}
}
else
{
int face_num, ix, iy;
nest2xyf(pix,ix,iy,face_num);
return (int64(jrll[face_num])<<order_) - ix - iy - 1;
}
}
int64 Healpix_Base2::nest2ring (int64 pix) const
{
planck_assert(order_>=0, "nest2ring: need hierarchical map");
int ix, iy, face_num;
nest2xyf (pix, ix, iy, face_num);
return xyf2ring (ix, iy, face_num);
}
int64 Healpix_Base2::ring2nest (int64 pix) const
{
planck_assert(order_>=0, "ring2nest: need hierarchical map");
int ix, iy, face_num;
ring2xyf (pix, ix, iy, face_num);
return xyf2nest (ix, iy, face_num);
}
int64 Healpix_Base2::nest2peano (int64 pix) const
{
static const uint8 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 uint8 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 uint8 face2path[12] = {
2, 5, 2, 5, 3, 6, 3, 6, 2, 3, 2, 3 };
static const uint8 face2peanoface[12] = {
0, 5, 6, 11, 10, 1, 4, 7, 2, 3, 8, 9 };
int face = pix>>(2*order_);
uint8 path = face2path[face];
int64 result = 0;
for (int shift=2*order_-2; shift>=0; shift-=2)
{
uint8 spix = uint8((pix>>shift) & 0x3);
result <<= 2;
result |= subpix[path][spix];
path=subpath[path][spix];
}
return result + (int64(face2peanoface[face])<<(2*order_));
}
int64 Healpix_Base2::peano2nest (int64 pix) const
{
static const uint8 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 uint8 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 uint8 face2path[12] = {
2, 6, 2, 3, 3, 5, 2, 6, 2, 3, 3, 5 };
static const uint8 peanoface2face[12] = {
0, 5, 8, 9, 6, 1, 2, 7, 10, 11, 4, 3 };
int face = pix>>(2*order_);
uint8 path = face2path[face];
int64 result = 0;
for (int shift=2*order_-2; shift>=0; shift-=2)
{
uint8 spix = uint8((pix>>shift) & 0x3);
result <<= 2;
result |= subpix[path][spix];
path=subpath[path][spix];
}
return result + (int64(peanoface2face[face])<<(2*order_));
}
int64 Healpix_Base2::ang2pix_z_phi (double z, double phi) const
{
double za = abs(z);
double tt = fmodulo(phi,twopi) * inv_halfpi; // in [0,4)
if (scheme_==RING)
{
if (za<=twothird) // Equatorial region
{
double temp1 = nside_*(0.5+tt);
double temp2 = nside_*z*0.75;
int64 jp = int64(temp1-temp2); // index of ascending edge line
int64 jm = int64(temp1+temp2); // index of descending edge line
// ring number counted from z=2/3
int64 ir = nside_ + 1 + jp - jm; // in {1,2n+1}
int kshift = 1-(ir&1); // kshift=1 if ir even, 0 otherwise
int64 ip = (jp+jm-nside_+kshift+1)/2; // in {0,4n-1}
ip = imodulo<int64>(ip,4*nside_);
return ncap_ + (ir-1)*4*nside_ + ip;
}
else // North & South polar caps
{
double tp = tt-int(tt);
double tmp = nside_*sqrt(3*(1-za));
int64 jp = int64(tp*tmp); // increasing edge line index
int64 jm = int64((1.0-tp)*tmp); // decreasing edge line index
int64 ir = jp+jm+1; // ring number counted from the closest pole
int64 ip = int64(tt*ir); // in {0,4*ir-1}
ip = imodulo<int64>(ip,4*ir);
if (z>0)
return 2*ir*(ir-1) + ip;
else
return npix_ - 2*ir*(ir+1) + ip;
}
}
else // scheme_ == NEST
{
int face_num, ix, iy;
if (za<=twothird) // Equatorial region
{
double temp1 = nside_*(0.5+tt);
double temp2 = nside_*(z*0.75);
int64 jp = int64(temp1-temp2); // index of ascending edge line
int64 jm = int64(temp1+temp2); // index of descending edge line
int64 ifp = jp >> order_; // in {0,4}
int64 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
{
int ntt = int(tt);
if (ntt>=4) ntt=3;
double tp = tt-ntt;
double tmp = nside_*sqrt(3*(1-za));
int64 jp = int64(tp*tmp); // increasing edge line index
int64 jm = int64((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;
}
}
return xyf2nest(ix,iy,face_num);
}
}
void Healpix_Base2::pix2ang_z_phi (int64 pix, double &z, double &phi) const
{
if (scheme_==RING)
{
if (pix<ncap_) // North Polar cap
{
int64 iring = int64(0.5*(1+isqrt(1+2*pix))); //counted from North pole
int64 iphi = (pix+1) - 2*iring*(iring-1);
z = 1.0 - (iring*iring)*fact2_;
phi = (iphi-0.5) * halfpi/iring;
}
else if (pix<(npix_-ncap_)) // Equatorial region
{
int64 ip = pix - ncap_;
int64 iring = ip/(4*nside_) + nside_; // counted from North pole
int64 iphi = ip%(4*nside_) + 1;
// 1 if iring+nside is odd, 1/2 otherwise
double fodd = ((iring+nside_)&1) ? 1 : 0.5;
int64 nl2 = 2*nside_;
z = (nl2-iring)*fact1_;
phi = (iphi-fodd) * pi/nl2;
}
else // South Polar cap
{
int64 ip = npix_ - pix;
int64 iring = int64(0.5*(1+isqrt(2*ip-1))); //counted from South pole
int64 iphi = 4*iring + 1 - (ip - 2*iring*(iring-1));
z = -1.0 + (iring*iring)*fact2_;
phi = (iphi-0.5) * halfpi/iring;
}
}
else
{
int64 nl4 = nside_*4;
int face_num, ix, iy;
nest2xyf(pix,ix,iy,face_num);
int64 jr = (int64(jrll[face_num])<<order_) - ix - iy - 1;
int64 nr;
int 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;
}
int64 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)*(halfpi/nr);
}
}
void Healpix_Base2::get_ring_info (int64 ring, int64 &startpix, int64 &ringpix,
double &costheta, double &sintheta, bool &shifted) const
{
planck_assert(scheme_==RING,"map must be in RING scheme");
int64 northring = (ring>2*nside_) ? 4*nside_-ring : ring;
if (northring < nside_)
{
double tmp = northring*northring*fact2_;
costheta = 1 - tmp;
sintheta = sqrt(tmp*(2-tmp));
ringpix = 4*northring;
shifted = true;
startpix = 2*northring*(northring-1);
}
else
{
costheta = (2*nside_-northring)*fact1_;
sintheta = sqrt((1+costheta)*(1-costheta));
ringpix = 4*nside_;
shifted = ((northring-nside_) & 1) == 0;
startpix = ncap_ + (northring-nside_)*ringpix;
}
if (northring != ring) // southern hemisphere
{
costheta = -costheta;
startpix = npix_ - startpix - ringpix;
}
}
void Healpix_Base2::neighbors (int64 pix, fix_arr<int64,8> &result) const
{
static const int xoffset[] = { -1,-1, 0, 1, 1, 1, 0,-1 };
static const int yoffset[] = { 0, 1, 1, 1, 0,-1,-1,-1 };
static const int 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 int 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
int ix, iy, face_num;
(scheme_==RING) ?
ring2xyf(pix,ix,iy,face_num) : nest2xyf(pix,ix,iy,face_num);
const int64 nsm1 = nside_-1;
if ((ix>0)&&(ix<nsm1)&&(iy>0)&&(iy<nsm1))
{
if (scheme_==RING)
for (int m=0; m<8; ++m)
result[m] = xyf2ring(ix+xoffset[m],iy+yoffset[m],face_num);
else
for (int m=0; m<8; ++m)
result[m] = xyf2nest(ix+xoffset[m],iy+yoffset[m],face_num);
}
else
{
for (int i=0; i<8; ++i)
{
int x=ix+xoffset[i];
int y=iy+yoffset[i];
int 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; }
int 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) std::swap(x,y);
result[i] = (scheme_==RING) ? xyf2ring(x,y,f) : xyf2nest(x,y,f);
}
else
result[i] = -1;
}
}
}
void Healpix_Base2::get_ring_info2 (int64 ring, int64 &startpix, int64 &ringpix,
double &theta, bool &shifted) const
{
int64 northring = (ring>2*nside_) ? 4*nside_-ring : ring;
if (northring < nside_)
{
double tmp = northring*northring*fact2_;
double costheta = 1 - tmp;
double sintheta = sqrt(tmp*(2-tmp));
theta = atan2(sintheta,costheta);
ringpix = 4*northring;
shifted = true;
startpix = 2*northring*(northring-1);
}
else
{
theta = acos((2*nside_-northring)*fact1_);
ringpix = 4*nside_;
shifted = ((northring-nside_) & 1) == 0;
startpix = ncap_ + (northring-nside_)*ringpix;
}
if (northring != ring) // southern hemisphere
{
theta = pi-theta;
startpix = npix_ - startpix - ringpix;
}
}
void Healpix_Base2::get_interpol (const pointing &ptg, fix_arr<int64,4> &pix,
fix_arr<double,4> &wgt) const
{
double z = cos (ptg.theta);
int64 ir1 = ring_above(z);
int64 ir2 = ir1+1;
double theta1, theta2, w1, tmp, dphi;
int64 sp,nr;
bool shift;
int64 i1,i2;
if (ir1>0)
{
get_ring_info2 (ir1, sp, nr, theta1, shift);
dphi = twopi/nr;
tmp = (ptg.phi/dphi - .5*shift);
i1 = (tmp<0) ? int64(tmp)-1 : int64(tmp);
w1 = (ptg.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, theta2, shift);
dphi = twopi/nr;
tmp = (ptg.phi/dphi - .5*shift);
i1 = (tmp<0) ? int64(tmp)-1 : int64(tmp);
w1 = (ptg.phi-(i1+.5*shift)*dphi)/dphi;
i2 = i1+1;
if (i1<0) i1 +=nr;
if (i2>=nr) i2 -=nr;
pix[2] = sp+i1; pix[3] = sp+i2;
wgt[2] = 1-w1; wgt[3] = w1;
}
if (ir1==0)
{
double wtheta = ptg.theta/theta2;
wgt[2] *= wtheta; wgt[3] *= wtheta;
double fac = (1-wtheta)*0.25;
wgt[0] = fac; wgt[1] = fac; wgt[2] += fac; wgt[3] +=fac;
pix[0] = (pix[2]+2)%4;
pix[1] = (pix[3]+2)%4;
}
else if (ir2==4*nside_)
{
double wtheta = (ptg.theta-theta1)/(pi-theta1);
wgt[0] *= (1-wtheta); wgt[1] *= (1-wtheta);
double fac = wtheta*0.25;
wgt[0] += fac; wgt[1] += fac; wgt[2] = fac; wgt[3] =fac;
pix[2] = ((pix[0]+2)&3)+npix_-4;
pix[3] = ((pix[1]+2)&3)+npix_-4;
}
else
{
double wtheta = (ptg.theta-theta1)/(theta2-theta1);
wgt[0] *= (1-wtheta); wgt[1] *= (1-wtheta);
wgt[2] *= wtheta; wgt[3] *= wtheta;
}
if (scheme_==NEST)
for (tsize m=0; m<pix.size(); ++m)
pix[m] = ring2nest(pix[m]);
}
double Healpix_Base2::max_pixrad() const
{
vec3 va,vb;
va.set_z_phi (2./3., pi/(4*nside_));
double t1 = 1.-1./nside_;
t1*=t1;
vb.set_z_phi (1-t1/3, 0);
return v_angle(va,vb);
}
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