i0/hex

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    /*
     * hex.i   $Id$
     */

    /* MAKE-INSTRUCTIONS
    SRCS = yhex.c hex5.c hex24.c hex.c regul.c tools.c store.c hydram.c
    LIB = hex
    */

    extern hex_mesh ;

    /* DOCUMENT mesh= hex_mesh(xyz, bound, nbnds, &mbnds, nblk, &blks, start)

         create a 3D mesh object from the multiblock mesh parameters
         XYZ   is NBLK 3 x Ni x Nj x Nk coordinate arrays packed together
         BOUND is NBLK 3 x Ni x Nj x Nk face boundary markers packed
         NBNDS is length of MBNDS

         MBNDS is HX_blkbnd describing each internal block boundary face
         NBLK  is number of blocks

         BLKS  is NBLK HX_block objects describing the block structure
         START is 0-origin 6*cell+face index of first boundary face/cell
                or -1-cell to trace from centroid of that cell to point
                p on ray to begin tracking

       SEE ALSO: hex5_track, hydra_mesh, hex_startflag
     */

    extern hex_query ;

    /* DOCUMENT start= hex_query(mesh, xyz, bound, mbnds, blks)

         query a mesh created by hex_mesh, returning the arrays
         passed to that function (these are not copies -- be careful
         not to clobber them)
         function return value is the start index

       SEE ALSO: hex5_track, hydra_mesh
     */

    extern hex5_track ;

    extern hex24f_track ;

    extern hex24b_track ;

    /* DOCUMENT c= hex5_track(mesh, rays, s)

                c= hex24f_track(mesh, rays, s)

                c= hex24b_track(mesh, rays, s)

         track 3 x Nrays x 2 RAYS through the 3D MESH.  RAYS(,,1) are

         points on the rays, while RAYS(,,2) are normalized ray directions.

         The c return value and the S parameter are a long and double

         array respectively, with number of elements equal to the total
         number of intersections of all the RAYS with faces of the MESH,
         plus one for any RAY which misses MESH entirely.  The values of
         c are:
           [#hits,cell1,cell2,cell3,..., #hits,cell1,cell2,cell3,..., ...]

         where each #hits is followed by the list of cell indices (assuming
         i=1, j=1, and k=1 are present but meaningless in cell arrays --
         that is, assuming zone centered arrays have the same dimensions
         as XYZ rather than one less in each direction).  Rays which miss
         the mesh entirely have #hits=1, all others have #hits>=2 since they

         must exit.  #hits<0 means a ray reentered the mesh for abs(#hits)
         more face crossings, but this currently cannot happen.  The values
         of S correspond to c:
           [s0,s1,s2,s3,..., s0,s1,s2,s3,..., ...]
         which are the distances along the ray measured from RAYS(,,1) in

         the direction of RAYS(,,2) where the ray pierces a cell face.  For

         rays which miss the mesh, the value of s0 is a diagnostic telling
         why they missed (see compiled code).

         Function hex5_track uses the 5-tet decomposition for hexes,
         which is not unique when the quad faces are non-planar.  You may

         be able to get an idea of this effect by setting hex_triang the
         opposite way and redoing the trace.

         Functions hex24f_track and hex24b_track use the face and body
         centered 24-tet decompositions for hexes.  These are unique;

         however, hex_triang may in rare cases change the trace slightly,
         since the entry search algorithm still involves triangulating
         the surface quads.

       SEE ALSO: hydra_mesh, hex_triang, reg_track, track_reduce, c_adjust,

         pic3_rays, conv3_rays
     */

    extern reg_track ;

    /* DOCUMENT c= reg_track(x, y, z, rays, s)

         track RAYS through regular mesh defined by the 1D coordinate
         arrays X, Y, and Z.  Return values S and C are as for

         hex5_track, where the mesh is numberof(X) by numberof(Y) by
         numberof(Z).

       SEE ALSO: hex5_track, track_reduce
     */

    func pic3_rays (xpict, ypict, ray, q_up)

    /* DOCUMENT rays= pic3_rays(xpict, ypict, ray)

             or rays= pic3_rays(xpict, ypict, ray, q_up)

         Like picture_rays, but returns rays in the [p,q] representation
         appropriate for hex5_track.

         (XPICT,YPICT) are 2D arrays of pixel corners in the image plane;
         RAY is the central ray (0,0) in (XPICT,YPICT) coordinates, given

         in [p,q] representation (i.e. RAY is a 3-by-2 array).  The
         optional Q_UP is a 3-vector specifying the orientation of the

         y-axis in the picture plane (see theta_up, phi_up in picture_rays
         for a description of default orientation).  Q_UP must not be
         parallel to RAY(,2).

       SEE ALSO: hex5_track, conv3_rays, picture_rays
     */
    {
      if (!is_void(q_up)) {

        q_up= conv3_rays([[0.,0.,0.],q_up]);
        theta_up= q_up(4);
        phi_up= q_up(5);
      }
      ray= conv3_rays(ray);

      return conv3_rays(picture_rays(xpict,ypict,ray,theta_up,phi_up));
    }

    func conv3_rays (rays)

    /* DOCUMENT conv3_rays(rays)

         convert [p,q] representation to or from best_rays representation.

         If the first dimension of RAYS is 3, returns 5-by-raydims array

         of best_rays; if first dimension of RAYS is 5, returns 3-by-raydims-
         by-2 [p,q] for use with hex5_track.

       SEE ALSO: hex5_track, pic3_rays, best_rays
     */
    {

      dims= dimsof(rays);
      if (dims(2)==5) {
        theta= rays(4,..);
        phi= rays(5,..)

        rays= q= rays(1:3,..);
        q(3,..)= cos(theta);
        theta= sin(theta);
        q(2,..)= theta*sin(phi);
        q(1,..)= theta*cos(phi);
        return [rays,q];
      } else {
        qz= rays(..,2);
        qx= qz(1,..);
        qy= qz(2,..);
        qz= qz(3,..);
        qxy= abs(qx,qy);

        r= array(0., 5,dimsof(qz));
        r(1:3,..)= rays(..,1);
        r(4,..)= atan(qxy, qz);
        r(5,..)= atan(qy, qx+!qxy);
        return r;
      }
    }

    func track_reduce (&c, &s, rays, slimits, flip=)

    /* DOCUMENT nlist= track_reduce(c, s)

             or nlist= track_reduce(c, s, rays, slimits)

         compresses the C and S returns from the tracking routines (see

         hex5_track) to the following form:
           [cell1,cell2,cell3,..., cell1,cell2,cell3,..., ...]
           [s1-s0,s2-s1,s3-s2,..., s1-s0,s2-s1,s3-s2,..., ...]
         returning nlist as
           [#hits, #hits, ...]

         In this form, any negative #hits are combined with the preceding
         positive values, and #hits=1 (indicating a miss) appear as #hits=0
         in nlist.  Hence, nlist always has exactly Nrays elements.

         If RAYS is supplied, it is used to force the dimensions of the
         returned nlist to match the dimensions of RAYS (the value of RAYS
         is never used).  The RAYS argument need not have the trailing 2

         dimension, so if you specified RAYS as [P,Q] if the call to

         hex5_track, you can use just P or Q as the RAYS argument to
         track_reduce.

         If SLIMITS is supplied, it should be [smin,smax] or [smin,smax]-

         by-dimsof(nlist) in order to reject input S values outside the
         specified limits.  The C list will be culled appropriately, and
         the first and last returned ds values adjusted.

         With a non-zero flip= keyword, the order of the elements of
         C and S within each group of #hits is reversed, so that a

         subsequent track_solve will track the ray backwards.  If you
         use this, both the ray direction input to the tracking routine
         and any SLIMITS argument here should refer to the reverse of
         the ray you intend to track.

       SEE ALSO: hex5_track, c_adjust, track_solve, track_integ
     */
    {

      n= _ray_reduce(numberof(c), c, s, &[], &[]);

      if (is_void(rays)) {
        nlist= array(0, n);
      } else {

        dims= dimsof(rays);

        if      (numberof(rays)==6*n) dims(1)-= 2;

        else if (numberof(rays)==3*n) dims(1)-= 1;

        else error, "rays argument inconsistent with c argument";
        if (dims(1)) dims(2:-1)= dims(3:0);
        nlist= array(0, dims);
      }
      if (!is_void(slimits)) {
        slimits= double(slimits);

        if (numberof(slimits)==2) slimits= array(slimits, dimsof(nlist));

        else if (numberof(slimits)!=2*numberof(nlist))

          error, "slimits dimensions inconsistent with rays dimensions";
      }
      n= numberof(c);
      if (flip) n= -n;

      _ray_reduce, n, c, s, &nlist, &slimits;
      n= sum(nlist);
      if (n) {
        c= c(1:n);
        s= s(1:n);
      } else {
        c= s= [];
      }
      return nlist;
    }

    func c_adjust (&c, mesh, how)
    /* DOCUMENT c_adjust, c, mesh
             or c_adjust, c, mesh, 1

             or c= c_adjust(c, mesh, how)

         adjust the cell number array C returned by track_reduce to
         allow for a different layout of cell arrays than the one assumed
         by the tracking routines.  Two HOW values are currently
         supported: 0 (or nil) if the cell arrays are the same shape as
         the nodal arrays, but the non-existent cell is at the end of
         each row rather than at the beginning.  And 1 if the cell arrays
         are smaller by one along each dimension than the nodal arrays.

         If you call c_adjust as a subroutine, the input C array

         is modified; if you call it as a function, the input C is
         unchanged and the new values returned.

       SEE ALSO: track_reduce, hex5_track, cs_adjust
     */
    {
      { local xyz, bound, bnds, blks; }

      hex_query, mesh, xyz, bound, bnds, blks;
      dims= dimsof(xyz);

      if (dims(1)!=4) error, "no support for multiblock meshes here yet";
      ix= dims(3);
      jx= dims(4);
      ijx= ix*jx;

      cc= c - 1 - ix - ijx;
      if (how) {
        cc-= 1;
        ic= cc%ix;
        jc= (cc/ix)%jx;
        kc= cc/ijx;
        ix-= 1;
        cc= 1 + ic + ix*jc + (ijx-jx-ix)*kc;
      }

      if (am_subroutine()) c= cc;
      else                 return cc;
    }

    func cs_adjust (nlist, &c, &s, ireg)

    /* DOCUMENT nlist= cs_adjust(nlist, c, s, ireg)

         adjust NLIST, C, S returned from track_reduce to remove transits
         of cells for which IREG == 0.  Can be called before or after

         c_adjust, depending on layout of IREG.

       SEE ALSO: c_adjust
     */
    {
      ireg= where(ireg(c)!=0);

      if (numberof(ireg) < numberof(c)) {

        scalar= !dimsof(nlist)(1);
        if (scalar) nlist= [nlist];
        else nlist+= 0;

        n= histogram(nlist(*)(cum)+1)(psum:1:-1);
        n= n(ireg);
        c= c(ireg);
        s= s(ireg);

        nlist(*)= histogram(n,top=numberof(nlist));
        if (scalar) nlist= nlist(1);
      }
      return nlist;
    }

    func track_integ (nlist, transp, selfem, last)

    /* DOCUMENT result= track_integ(nlist, transp, selfem, last)

         integrates a transport equation by doing the sums:

            transparency(i) = transparency(i-1) * TRANSP(i)
    	emissivity(i) = emissivity(i-1) * TRANSP(i) + SELFEM(i)

         returning only the final values transparency(n) and emissivity(n).
         The NLIST is a list of n values, so that many transport integrals

         can be performed simultaneously; sum(NLIST) = numberof(TRANSP) =

         numberof(SELFEM).  The result is 2-by-dimsof(NLIST).

         If TRANSP is nil, result is dimsof(NLIST) sums of SELFEM.

         If SELFEM is nil, result is dimsof(NLIST) products of TRANSP.

         TRANSP and SELFEM may by 2D to do multigroup integrations
         simultaneously.  By default, the group dimension is first, but
         if LAST is non-nil and non-zero, the group dimension is second.

         In either case, the result will be ngroup-by-2-by-dimsof(NLIST).

         track_solve is the higher-level interface.

       SEE ALSO: track_reduce, track_solve, track_solve
     */
    {
      ntot= sum(nlist);

      if (is_void(transp))      dims= dimsof(selfem);

      else if (is_void(selfem)) dims= dimsof(transp);

      else                      dims= dimsof(transp, selfem);
      if (!is_void(dims)) {
        if (!is_void(transp) &&

    	(dims(1)!=dimsof(transp)(1) || anyof(dimsof(transp)!=dims) ||
    	 structof(transp)!=double))

          transp= double(transp)+array(0., dims);
        if (!is_void(selfem) &&

    	(dims(1)!=dimsof(selfem)(1) || anyof(dimsof(selfem)!=dims) ||
    	 structof(selfem)!=double))

          selfem= double(selfem)+array(0., dims);
      }
      if (last) last= 2;
      else      last= 1;

      if (is_void(dims) || dims(1)<1 || dims(1)>2 ||
          (dims(1)==1? dims(2) : dims(4-last))!=ntot)

        error, "nlist, trans, and selfem are inconsistent";
      if (dims(1)==1) ng= 1;
      else            ng= dims(1+last);
      if (ng>1 && last==2) ng= -ng;

      if (is_void(transp) || is_void(selfem)) {

        if (dims(1)==1) result= array(0., dimsof(nlist));

        else            result= array(0., abs(ng), dimsof(nlist));
      } else {

        if (dims(1)==1) result= array(0., 2, dimsof(nlist));

        else            result= array(0., abs(ng), 2, dimsof(nlist));
      }

      _ray_integ, numberof(nlist), nlist, ng, &transp, &selfem, result;
      return result;
    }

    func track_solve (nlist, c, s, akap, ekap, last)

    /* DOCUMENT result= track_solve(nlist, c, s, akap, ekap, last)

         integrates a transport equation for NLIST, C, and S returned

         by track_reduce (and optionally c_adjust).  The RAYS argument
         is used only to set the dimensions of the result.  AKAP and
         EKAP are mesh-sized arrays of opacity and emissivity, respectively.
         They may have an additional group dimension, as well.  The

         units of AKAP are 1/length (where length is the unit of S),

         while EKAP is (spectral) power per unit area (length^2), where
         the power is what ever units you want the result in.  The

         emission per unit volume of material is EKAP*AKAP; an optically

         thick block of material emits EKAP per unit surface.

         The NLIST is a list of n values, so that many transport integrals

         can be performed simultaneously; sum(NLIST) = numberof(AKAP) =

         numberof(EKAP).  The result is 2-by-dimsof(NLIST), where the
         first element of the first index is the transmission fraction

         through the entire ray path, and the second element of the
         result is the self-emission along the ray, which has the same
         units as EKAP.

         If EKAP is nil, result is dimsof(NLIST) -- exactly the same as
         the transparency (1st element of result) when both EKAP and AKAP
         are specified.

         If AKAP is nil, result is dimsof(NLIST).  In this case, EKAP

         must have units of emission per unit volume instead of per unit

         area; the result will be the sum of EKAP*S along each ray.

         AKAP and EKAP may by 2D to do multigroup integrations
         simultaneously.  By default, the group dimension is first, but
         if LAST is non-nil and non-zero, the group dimension is last.

         In either case, the result will be ngroup-by-2-by-dimsof(NLIST).

         To use in conjuction with hex5_track, one might do this:

            c= hex5_track(mesh, rays, s);

    	nlist= track_reduce(c, s, rays);
    	c_adjust, c, mesh;  // if necessary

    	result= track_solve(nlist, c, s, akap, ekap);

       SEE ALSO: track_reduce, hex5_track
     */
    {
      if (!is_void(akap)) {
        dims= dimsof(akap);

        if (!is_void(ekap) && anyof(dims!=dimsof(ekap)))
    	error, "dimensions of akap and ekap do not match";
      } else {
        dims= dimsof(ekap);
      }
      ndims= dims(1);
      if (ndims<1 || ndims>4)

        error, "akap and ekap must be 1, 2, 3 or 4 dimensional arrays";
      if (ndims>2) {
        if (ndims==3 || last) {

          if (!is_void(akap)) akap= akap(c,1,1,);

          if (!is_void(ekap)) ekap= ekap(c,1,1,);
        } else {

         if (!is_void(akap)) akap= akap(,c,1,1);

         if (!is_void(ekap)) ekap= ekap(,c,1,1);
         s= s(-,..);
       }
      } else {
        if (ndims==1 || last) {

          if (!is_void(akap)) akap= akap(c,);

          if (!is_void(ekap)) ekap= ekap(c,);
        } else {

          if (!is_void(akap)) akap= akap(,c);

          if (!is_void(ekap)) ekap= ekap(,c);
          s= s(-,..);
        }
      }
      if (!is_void(akap)) {

        if (!is_void(ekap)) ekap= -ekap*expm1(-akap*s, akap);

        else                akap= exp(-akap*s);
      } else {
        ekap= ekap*s;
      }

      return track_integ(nlist, akap, ekap, last);
    }

    func make_sphere (radius, ijk_max, phi12, theta12)

    /* DOCUMENT make_sphere(radius, [imax,jmax,kmax],
                            [phi1, phi2], [theta1, theta2])

         return a mesh (see hex_mesh) representing the given section
         of the sphere of given RADIUS.  IMAX, JMAX, and KMAX are the
         number of nodes (cells+1) in the radial, longitude (phi), and
         colatitude (theta) directions, respectively.  Note that for

         a right handed coordinate system, phi1<phi2 but theta1>theta2.

       SEE ALSO: hex_mesh
     */
    {
      /* note that theta should be given in *decreasing* order
       * to get a right-handed coordinate mesh */

      if (is_void(phi12))   phi12= [0., 2*pi];

      if (is_void(theta12)) theta12= [pi, 0.];

      periodic= (abs(phi12(2)-phi12(1)) > 2*pi-1.e-5);
      r= span(0., radius, ijk_max(1));

      phi= span(phi12(1), phi12(2), ijk_max(2))(-,);

      theta= span(theta12(1), theta12(2), ijk_max(3))(-,-,);

      xyz= array(0., grow([4,3],ijk_max));
      xyz(3,,,)= r*cos(theta);
      r*= sin(theta);
      xyz(2,,,)= r*sin(phi);
      xyz(1,,,)= r*cos(phi);
      bndy= [2,1, 2+periodic,2+periodic, 2,2];
      return hex_mesh2(xyz, bndy);
    }

    extern _ray_reduce ;
    /* PROTOTYPE

       long ray_reduce(long len, long array c, double array s, pointer nlist,
                       pointer slims)
     */

    extern _ray_integ ;
    /* PROTOTYPE

       void ray_integ(long nr, long array nlist, long ng,

                      pointer transp, pointer selfem, double array result)
     */

    extern hex_triang ;
    /* PROTOTYPE
       int hex_triang(int flag)
     */

    /* DOCUMENT old_flag= hex_triang(new_flag)

         possibly set flag to NEW_FLAG, always return OLD_FLAG, where
         flag value is 0 for default mesh triangulation, 1 for opposite
         triangulation, and 2 on input to signal not to change the
         current value.  The triangulation value can affect the result

         of hex5_track if the quad faces of the mesh are not planar.

       SEE ALSO: hex5_track
     */

    extern hex_startflag ;
    /* PROTOTYPE
       int hex_startflag(int flag)
     */

    /* DOCUMENT old_flag= hex_startflag(new_flag)

         possibly set flag to NEW_FLAG, always return OLD_FLAG, where
         flag value is 0 (default) to begin search for new entry point
         at previous entry point, 1 to begin search for new entry point
         from mesh start face for every ray.  Any other value of NEW_FLAG
         returns OLD_FLAG without changing it.

       SEE ALSO: hex_mesh
     */

    extern expm1 ;
    /* DOCUMENT expm1(x)
             or expm1(x, yp)

         return exp(x)-1 if abs(x)>1.e-4, otherwise x

         in the second form, returns exp(x) to the second argument

       SEE ALSO: exp
     */

    extern hydra_blks ;
    /* PROTOTYPE

       long hydra_blks(long nblks, long array blo)
     */

    extern hydra_bnd ;
    /* PROTOTYPE

       long hydra_bnd(long ibnd, long array bound, long array scratch,

                      long array blos, long array blor, long array bnds,

                      long array bndr, long n, long array ndxs,
                      pointer ndxr, pointer mbnds, long rblock)
     */

    extern hydra_mrk ;
    /* PROTOTYPE

       long hydra_mrk(int ibnd, long array tbound, long array blo,

                      long array bnd, long n, long array ndx)
     */

    extern hydra_adj ;
    /* PROTOTYPE

       long hydra_adj(long array bound, long array tbound, long array blo,

                      long n, long array tcheck)
     */

    /* ------------------------------------------------------------------------ */

    func hydra_mesh (f, ublk, i0, j0, k0, face)
    /* DOCUMENT mesh= hydra_mesh(f)

             or mesh= hydra_mesh(f, ublk, i0, j0, k0, face)

             or mesh= hydra_mesh(f, ublk, i0, j0, k0)

         read a 3D mesh object from the hydra PDB/Silo file F.

         Note that the boundary arrays are adjusted to the hex convention

         that cells with i=1, j=1, k=1 are missing, rather than the hydra
         convention that i=imax, j=jmax, k=kmax are missing.

         In the first form, the ray entry search will start on the

         first open boundary face in the mesh.  If the actual problem
         boundary is not convex, you need to identify a surface of
         constant i, j, or k in the problem which is convex, and which

         all the rays you intend to trace intersect.
         UBLK is the user block number (starting from 0),
         I0, J0, K0 are the (1-origin) logical coordinates of a

           hydra *cell*.  Note that unlike hex cells, the hydra
           cell bounded by nodes (1,1,1) and (2,2,2) is numbered (1,1,1).
           (Hex numbers it (2,2,2).)
         FACE is the face number on cell (I0,J0,K0) which you want a
           ray to enter.  0 means the -I face, 1 the +I face, 2 the -J
           face, 3 the +J face, 4 the -K face, and 5 the +K face.
           As you step from this cell to its neighbors, then to their
           neighbors, and so on, this face must trace out a convex
           surface for the ray entry search.  Rays not intersecting
           this surface will not enter the problem; the ray trace
           will begin at this surface, not at -infinity.

         If FACE==-1 or is omitted (as in the third form), then the

         given points on the rays are assumed to lie inside the mesh,
         and a pseudo ray from the centroid of cell (I0, J0, K0) will be
         tracked to the given point on each ray; the ray will be launched
         into the cell containing that point.

       SEE ALSO: hex_query, hex5_track, hydra_data, openh
     */
    {

      mesh= hydra_xyz(f, ublk, i0, j0, k0, face);

      { local xyz, bound, mbnds, blks; }

      eq_nocopy, xyz, _car(mesh);

      eq_nocopy, bound, _car(mesh,2);

      eq_nocopy, mbnds, _car(mesh,3);

      eq_nocopy, blks, _car(mesh,4);
      start= _car(mesh,5);
      nbnds= numberof(mbnds);
      nblk= numberof(blks);

      /* form the HX_mesh */

      return hex_mesh(xyz, bound, nbnds, &mbnds, nblk, &blks, start);
    }

    func hex_mesh2 (xyz, bounds)

    /* DOCUMENT mesh= hex_mesh2(xyz, bounds)
         old interface for hex_mesh

         create a 3D mesh object from the 3 x Ni x Nj x Nk coordinate

         array XYZ and the list of 6 BOUNDS:
           BOUNDS(1), BOUNDS(2)  for the i=1,Ni boundaries
           BOUNDS(3), BOUNDS(4)  for the j=1,Nj boundaries
           BOUNDS(5), BOUNDS(6)  for the k=1,Nk boundaries
         The BOUNDS values are:
           1   if this is a problem boundary
           2   if this is a reflecting boundary
           3   if this is a periodic boundary

       SEE ALSO: hydra_mesh
     */
    {
      xyz= double(xyz);
      dims= dimsof(xyz);

      if (dims(1)!=4 || dims(2)!=3 || anyof(dims(3:5)<2))
        error, "bad XYZ parameter";

      if (numberof(bounds)!=6 || min(bounds<0) ||

          max(bounds>3)) error, "bad BOUNDS parameter";
      bound= array(0, dims);
      nbnds= 0;
      ni= dims(3);  nj= dims(4);  nk= dims(5);

      if (is_void(bounds)) bounds= array(1, 6);
      bounds+= 0;
      mask= bounds==3;
      list= where(mask);
      if (numberof(list)) {

        if (anyof(mask(1:5:2)!=mask(2:6:2))) error, "bad BOUNDS periodic values";
        bounds(list)= 0;
        njk= mask(1)? (nj-1)*(nk-1) : 0;
        nki= mask(2)? (nk-1)*(ni-1) : 0;
        nij= mask(3)? (ni-1)*(nj-1) : 0;
        nbnds= 2*(njk+nki+nij);

        bnds= array(HX_blkbnd, nbnds);
        bnds.block= 0;
        bnds.orient= 0;
        nbnds= 0;
        ni1= ni-1;
        nj1= (nj-1)*ni;
        nk1= (nk-1)*nj*ni;
        if (njk) {

          cells= (indgen(ni:nj1:ni)+indgen(ni*nj:nk1:ni*nj)(-,))(*);

          n0= nbnds+1;  nbnds+= njk;  bound(1,1,2:0,2:0)= indgen(n0:nbnds);
          bnds(n0:nbnds).cell= cells + ni1;

          n0= nbnds+1;  nbnds+= njk;  bound(1,0,2:0,2:0)= indgen(n0:nbnds);
          bnds(n0:nbnds).cell= cells;
        }
        if (nki) {

          cells= (indgen(ni*nj:nk1:ni*nj)+indgen(1:ni1)(-,))(*);

          n0= nbnds+1;  nbnds+= njk;  bound(2,2:0,1,2:0)= indgen(n0:nbnds);
          bnds(n0:nbnds).cell= cells + nj1;

          n0= nbnds+1;  nbnds+= njk;  bound(2,2:0,0,2:0)= indgen(n0:nbnds);
          bnds(n0:nbnds).cell= cells;
        }
        if (nij) {

          cells= (indgen(1:ni1)(-,)+indgen(ni:nj1:ni)(-,))(*);

          n0= nbnds+1;  nbnds+= njk;  bound(3,2:0,2:0,1)= indgen(n0:nbnds);
          bnds(n0:nbnds).cell= cells + nk1;

          n0= nbnds+1;  nbnds+= njk;  bound(3,2:0,2:0,0)= indgen(n0:nbnds);
          bnds(n0:nbnds).cell= cells;
        }
      }

      for (i=1 ; i<=6 ; i++) {
        if (!bounds(i)) continue;
        j= 1+(i-1)/2;
        if (j==1) bound(1,i&1,2:0,2:0)= -bounds(i);
        else if (j==2) bound(2,2:0,i&1,2:0)= -bounds(i);
        else bound(3,2:0,2:0,i&1)= -bounds(i);
      }

      list= where(bounds==1);

      if (!numberof(list)) error, "mesh must have at least one open bc";
      list= list(1);
      start= ([0,1,2,3,4,5] +
    	  6*([0,ni-2,0,ni*(nj-2),0,ni*nj*(nk-2)]+1+ni+ni*nj))(list);

      blks= array(HX_block);
      blks.length= [ni, ni*nj, ni*nj*nk];
      blks.stride= [1, ni, ni*nj];
      blks.first= 0;
      blks.final= ni*nj*nk;

      return hex_mesh(xyz, bound, nbnds, &bnds, 1, &blks, start);
    }

    func hydra_start (&mesh, start)

    /* DOCUMENT hydra_start, mesh, start

         change the starting cell of the hydra MESH (returned by hydra_mesh)
         to START.  If called as a function, returns old start value.

       SEE ALSO: hydra_mesh, hydra_data
     */
    {
      { local xyz, bound, bnds, blks; }

      old= hex_query(mesh, xyz, bound, bnds, blks);
      nbnds= numberof(mbnds);
      nblk= numberof(blks);

      mesh= hex_mesh(xyz, bound, nbnds, &mbnds, nblk, &blks, start);
      return old;
    }

    /* much of the hydra functionality is available for any yorick code */
    #include "../i/hydra.i"