remap_conserv.c 35.3 KB
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#include "cdo.h"
#include "cdo_int.h"
#include "grid.h"
#include "remap.h"
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#include "remap_store_link.h"
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "clipping/clipping.h"
#include "clipping/area.h"
#include "clipping/geometry.h"
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#ifdef __cplusplus
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}
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#endif
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//#define STIMER
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#ifdef STIMER
#include <time.h>
#endif

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typedef struct {
  enum yac_edge_type *src_edge_type;
  long srch_corners;
  long max_srch_cells;
  double *partial_areas;
  double *partial_weights;
  struct grid_cell *src_grid_cells;
  struct grid_cell *overlap_buffer;
} search_t;

static
void search_realloc(long num_srch_cells, search_t *search)
{
  long max_srch_cells  = search->max_srch_cells;
  double *partial_areas   = search->partial_areas;
  double *partial_weights = search->partial_weights;
  struct grid_cell *overlap_buffer = search->overlap_buffer;
  struct grid_cell *src_grid_cells = search->src_grid_cells;

  if ( num_srch_cells > max_srch_cells )
    {
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      partial_areas   = (double*) Realloc(partial_areas,   num_srch_cells*sizeof(double));
      partial_weights = (double*) Realloc(partial_weights, num_srch_cells*sizeof(double));
      overlap_buffer = (struct grid_cell*) Realloc(overlap_buffer, num_srch_cells*sizeof(struct grid_cell));
      src_grid_cells = (struct grid_cell*) Realloc(src_grid_cells, num_srch_cells*sizeof(struct grid_cell));
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      for ( long n = max_srch_cells; n < num_srch_cells; ++n )
        {
          overlap_buffer[n].array_size      = 0;
          overlap_buffer[n].num_corners     = 0;
          overlap_buffer[n].edge_type       = NULL;
          overlap_buffer[n].coordinates_x   = NULL;
          overlap_buffer[n].coordinates_y   = NULL;
          overlap_buffer[n].coordinates_xyz = NULL;
        }

      for ( long n = max_srch_cells; n < num_srch_cells; ++n )
        {
          src_grid_cells[n].array_size      = search->srch_corners;
          src_grid_cells[n].num_corners     = search->srch_corners;
          src_grid_cells[n].edge_type       = search->src_edge_type;
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          src_grid_cells[n].coordinates_x   = (double*) Malloc(search->srch_corners*sizeof(double));
          src_grid_cells[n].coordinates_y   = (double*) Malloc(search->srch_corners*sizeof(double));
          src_grid_cells[n].coordinates_xyz = (double*) Malloc(3*search->srch_corners*sizeof(double));
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        }

      max_srch_cells = num_srch_cells;

      search->max_srch_cells  = max_srch_cells;
      search->partial_areas   = partial_areas;
      search->partial_weights = partial_weights;
      search->overlap_buffer  = overlap_buffer;
      search->src_grid_cells  = src_grid_cells;
    }
}

static
void search_free(search_t *search)
{
  long max_srch_cells  = search->max_srch_cells;
  double *partial_areas   = search->partial_areas;
  double *partial_weights = search->partial_weights;
  struct grid_cell *overlap_buffer = search->overlap_buffer;
  struct grid_cell *src_grid_cells = search->src_grid_cells;

  for ( long n = 0; n < max_srch_cells; n++ )
    {
      if ( overlap_buffer[n].array_size > 0 )
        {
          Free(overlap_buffer[n].coordinates_x);
          Free(overlap_buffer[n].coordinates_y);
          if ( overlap_buffer[n].coordinates_xyz ) Free(overlap_buffer[n].coordinates_xyz);
          if ( overlap_buffer[n].edge_type ) Free(overlap_buffer[n].edge_type);
        }
      
      Free(src_grid_cells[n].coordinates_x);
      Free(src_grid_cells[n].coordinates_y);
      Free(src_grid_cells[n].coordinates_xyz);
    }

  Free(partial_areas);
  Free(partial_weights);
}

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int rect_grid_search2(long *imin, long *imax, double xmin, double xmax, long nxm, const double *restrict xm);

static
long get_srch_cells_reg2d(const int *restrict src_grid_dims, 
			  const double *restrict src_corner_lat, const double *restrict src_corner_lon,
			  const double *restrict tgt_cell_bound_box, int *srch_add)
{
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  int debug = 0;
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  long nx = src_grid_dims[0];
  long ny = src_grid_dims[1];
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  long num_srch_cells = 0;  // num cells in restricted search arrays
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  long nxp1 = nx+1;
  long nyp1 = ny+1;
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  double src_lon_min = src_corner_lon[0];
  double src_lon_max = src_corner_lon[nx];
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  long imin = nxp1, imax = -1, jmin = nyp1, jmax = -1;

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  int lfound = rect_grid_search2(&jmin, &jmax, tgt_cell_bound_box[0], tgt_cell_bound_box[1], nyp1, src_corner_lat);
  if ( !lfound ) return 0;
  // printf("lfound, jmin, jmax %d %ld %ld\n", lfound, jmin, jmax);
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  // if ( jmin > 0 ) jmin--;
  // if ( jmax < (ny-2) ) jmax++;
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  double bound_lon1 = tgt_cell_bound_box[2];
  double bound_lon2 = tgt_cell_bound_box[3];
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  if ( bound_lon1 <= src_lon_max && bound_lon2 >= src_lon_min )
    {
      if ( debug ) printf("  b1 %g %g\n", bound_lon1*RAD2DEG, bound_lon2*RAD2DEG);
      if ( bound_lon1 < src_lon_min && bound_lon2 > src_lon_min ) bound_lon1 = src_lon_min;
      if ( bound_lon2 > src_lon_max && bound_lon1 < src_lon_max ) bound_lon2 = src_lon_max;
      lfound = rect_grid_search2(&imin, &imax, bound_lon1, bound_lon2, nxp1, src_corner_lon);
      if ( lfound )
	{
	  if ( debug )
	    printf("   %g %g imin %ld  imax %ld  jmin %ld jmax %ld\n", RAD2DEG*src_corner_lon[imin], RAD2DEG*src_corner_lon[imax+1], imin, imax, jmin, jmax);
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	  for ( long jm = jmin; jm <= jmax; ++jm )
	    for ( long im = imin; im <= imax; ++im )
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	      srch_add[num_srch_cells++] = jm*nx + im;
	}
    }

  bound_lon1 = tgt_cell_bound_box[2];
  bound_lon2 = tgt_cell_bound_box[3];
  if ( bound_lon1 <= src_lon_min && bound_lon2 >= src_lon_min )
    {
      long imin2 = nxp1, imax2 = -1;
      bound_lon1 += 2*M_PI;
      bound_lon2 += 2*M_PI;
      if ( debug ) printf("  b2 %g %g\n", bound_lon1*RAD2DEG, bound_lon2*RAD2DEG);
      if ( bound_lon1 < src_lon_min && bound_lon2 > src_lon_min ) bound_lon1 = src_lon_min;
      if ( bound_lon2 > src_lon_max && bound_lon1 < src_lon_max ) bound_lon2 = src_lon_max;
      lfound = rect_grid_search2(&imin2, &imax2, bound_lon1, bound_lon2, nxp1, src_corner_lon);
      if ( lfound )
	{
	  if ( imax != -1 && imin2 <= imax ) imin2 = imax+1;
	  if ( imax != -1 && imax2 <= imax ) imax2 = imax+1;
	  if ( imin2 >= 0 && imax2 < nxp1 )
	    {
	      if ( debug )
		printf("   %g %g imin %ld  imax %ld  jmin %ld jmax %ld\n", RAD2DEG*src_corner_lon[imin2], RAD2DEG*src_corner_lon[imax2+1], imin2, imax2, jmin, jmax);
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	      for ( long jm = jmin; jm <= jmax; ++jm )
		for ( long im = imin2; im <= imax2; ++im )
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		  srch_add[num_srch_cells++] = jm*nx + im;
	    }
	}
    }

  bound_lon1 = tgt_cell_bound_box[2];
  bound_lon2 = tgt_cell_bound_box[3];
  if ( bound_lon1 <= src_lon_max && bound_lon2 >= src_lon_max )
    {
      long imin3 = nxp1, imax3 = -1;
      bound_lon1 -= 2*M_PI;
      bound_lon2 -= 2*M_PI;
      if ( debug ) printf("  b3 %g %g\n", bound_lon1*RAD2DEG, bound_lon2*RAD2DEG);
      if ( bound_lon1 < src_lon_min && bound_lon2 > src_lon_min ) bound_lon1 = src_lon_min;
      if ( bound_lon2 > src_lon_max && bound_lon1 < src_lon_max ) bound_lon2 = src_lon_max;
      lfound = rect_grid_search2(&imin3, &imax3, bound_lon1, bound_lon2, nxp1, src_corner_lon);
      if ( lfound )
	{
	  if ( imin != nxp1 && imin3 >= imin ) imin3 = imin-1;
	  if ( imax != nxp1 && imax3 >= imin ) imax3 = imin-1;
	  if ( imin3 >= 0 && imin3 < nxp1 )
	    {
	      if ( debug )
		printf("   %g %g imin %ld  imax %ld  jmin %ld jmax %ld\n", RAD2DEG*src_corner_lon[imin3], RAD2DEG*src_corner_lon[imax3+1], imin3, imax3, jmin, jmax);
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	      for ( long jm = jmin; jm <= jmax; ++jm )
		for ( long im = imin3; im <= imax3; ++im )
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		  srch_add[num_srch_cells++] = jm*nx + im;
	    }
	}
    }

  if ( debug ) printf(" -> num_srch_cells: %ld\n", num_srch_cells);

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  return num_srch_cells;
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}

static
void restrict_boundbox(const double *restrict grid_bound_box, double *restrict bound_box)
{
  if ( bound_box[0] < grid_bound_box[0] && bound_box[1] > grid_bound_box[0] ) bound_box[0] = grid_bound_box[0];
  if ( bound_box[1] > grid_bound_box[1] && bound_box[0] < grid_bound_box[1] ) bound_box[1] = grid_bound_box[1];

  if ( bound_box[2] >= grid_bound_box[3] && (bound_box[3]-2*M_PI) > grid_bound_box[2] ) { bound_box[2] -= 2*M_PI; bound_box[3] -= 2*M_PI; }
  if ( bound_box[3] <= grid_bound_box[2] && (bound_box[2]-2*M_PI) < grid_bound_box[3] ) { bound_box[2] += 2*M_PI; bound_box[3] += 2*M_PI; }
  //  if ( bound_box[2] < grid_bound_box[2] && bound_box[3] > grid_bound_box[2] ) bound_box[2] = grid_bound_box[2];
  //  if ( bound_box[3] > grid_bound_box[3] && bound_box[2] < grid_bound_box[3] ) bound_box[3] = grid_bound_box[3];
}

static
void boundbox_from_corners_reg2d(long grid_add, const int *restrict grid_dims, const double *restrict corner_lon,
				 const double *restrict corner_lat, double *restrict bound_box)
{
  long nx = grid_dims[0];
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  long iy = grid_add/nx;
  long ix = grid_add - iy*nx;
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  double clat1 = corner_lat[iy  ];
  double clat2 = corner_lat[iy+1];
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  if ( clat2 > clat1 )
    {
      bound_box[0] = clat1;
      bound_box[1] = clat2;
    }
  else
    {
      bound_box[0] = clat2;
      bound_box[1] = clat1;
    }

  bound_box[2] = corner_lon[ix  ];
  bound_box[3] = corner_lon[ix+1];
}

static
void boundbox_from_corners1(long ic, long nc, const double *restrict corner_lon,
			    const double *restrict corner_lat, double *restrict bound_box)
{
  long inc, j;
  double clon, clat;

  inc = ic*nc;

  clat = corner_lat[inc];
  clon = corner_lon[inc];

  bound_box[0] = clat;
  bound_box[1] = clat;
  bound_box[2] = clon;
  bound_box[3] = clon;

  for ( j = 1; j < nc; ++j )
    {
      clat = corner_lat[inc+j];
      clon = corner_lon[inc+j];

      if ( clat < bound_box[0] ) bound_box[0] = clat;
      if ( clat > bound_box[1] ) bound_box[1] = clat;
      if ( clon < bound_box[2] ) bound_box[2] = clon;
      if ( clon > bound_box[3] ) bound_box[3] = clon;
    }

  if ( fabs(bound_box[3] - bound_box[2]) > PI )
    {
      bound_box[2] = 0;
      bound_box[3] = PI2;
    }

  /*
  double dlon = fabs(bound_box[3] - bound_box[2]);

  if ( dlon > PI )
    {
      if ( bound_box[3] > bound_box[2] && (bound_box[3]-PI2) < 0. )
	{
	  double tmp = bound_box[2];
	  bound_box[2] = bound_box[3] - PI2;
	  bound_box[3] = tmp;
	}
      else
	{
	  bound_box[2] = 0;
	  bound_box[3] = PI2;
	}
    }
  */
}

static
void boundbox_from_corners1r(long ic, long nc, const double *restrict corner_lon,
			     const double *restrict corner_lat, restr_t *restrict bound_box)
{
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  long inc = ic*nc;
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  restr_t clat = RESTR_SCALE(corner_lat[inc]);
  restr_t clon = RESTR_SCALE(corner_lon[inc]);
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  bound_box[0] = clat;
  bound_box[1] = clat;
  bound_box[2] = clon;
  bound_box[3] = clon;

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  for ( long j = 1; j < nc; ++j )
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    {
      clat = RESTR_SCALE(corner_lat[inc+j]);
      clon = RESTR_SCALE(corner_lon[inc+j]);

      if ( clat < bound_box[0] ) bound_box[0] = clat;
      if ( clat > bound_box[1] ) bound_box[1] = clat;
      if ( clon < bound_box[2] ) bound_box[2] = clon;
      if ( clon > bound_box[3] ) bound_box[3] = clon;
    }

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  if ( RESTR_ABS(bound_box[3] - bound_box[2]) > RESTR_SCALE(PI) )
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    {
      bound_box[2] = 0;
      bound_box[3] = RESTR_SCALE(PI2);
    }
  /*
  if ( RESTR_ABS(bound_box[3] - bound_box[2]) > RESTR_SCALE(PI) )
    {
      if ( bound_box[3] > bound_box[2] && (bound_box[3]-RESTR_SCALE(PI2)) < RESTR_SCALE(0.) )
	{
	  restr_t tmp = bound_box[2];
	  bound_box[2] = bound_box[3] - RESTR_SCALE(PI2);
	  bound_box[3] = tmp;
	}
    }
  */
}

//#if defined(HAVE_LIBYAC)

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static
double gridcell_area(struct grid_cell cell)
{
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  return yac_huiliers_area(cell);
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}

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static
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void cdo_compute_overlap_areas(unsigned N, search_t *search, struct grid_cell target_cell)
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{
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  double *partial_areas   = search->partial_areas;
  struct grid_cell *overlap_buffer = search->overlap_buffer;
  struct grid_cell *source_cells = search->src_grid_cells;

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  /* Do the clipping and get the cell for the overlapping area */

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  yac_cell_clipping(N, source_cells, target_cell, overlap_buffer);
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  /* Get the partial areas for the overlapping regions */

  for ( unsigned n = 0; n < N; n++ )
    {
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      partial_areas[n] = gridcell_area(overlap_buffer[n]);
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    }

#ifdef VERBOSE
  for ( unsigned n = 0; n < N; n++ )
    printf("overlap area : %lf\n", partial_areas[n]);
#endif
}
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static double const tol = 1.0e-12;

enum cell_type {
  UNDEF_CELL,
  LON_LAT_CELL,
  LAT_CELL,
  GREAT_CIRCLE_CELL,
  MIXED_CELL
};
/*
static enum cell_type get_cell_type(struct grid_cell target_cell) {

  int count_lat_edges = 0, count_great_circle_edges = 0;

   if ((target_cell.num_corners == 4) &&
       ((target_cell.edge_type[0] == LAT_CIRCLE &&
         target_cell.edge_type[1] == LON_CIRCLE &&
         target_cell.edge_type[2] == LAT_CIRCLE &&
         target_cell.edge_type[3] == LON_CIRCLE) ||
        (target_cell.edge_type[0] == LON_CIRCLE &&
         target_cell.edge_type[1] == LAT_CIRCLE &&
         target_cell.edge_type[2] == LON_CIRCLE &&
         target_cell.edge_type[3] == LAT_CIRCLE)))
      return LON_LAT_CELL;
   else
      for (unsigned i = 0; i < target_cell.num_corners; ++i)
         if (target_cell.edge_type[i] == LON_CIRCLE ||
             target_cell.edge_type[i] == GREAT_CIRCLE)
            count_great_circle_edges++;
         else
            count_lat_edges++;

   if (count_lat_edges && count_great_circle_edges)
      return MIXED_CELL;
   else if (count_lat_edges)
      return LAT_CELL;
   else
      return GREAT_CIRCLE_CELL;
}
*/
static
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void cdo_compute_concave_overlap_areas(unsigned N, search_t *search, struct grid_cell target_cell,
				       double target_node_x, double target_node_y)
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{
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  double *partial_areas   = search->partial_areas;
  struct grid_cell *overlap_buffer = search->overlap_buffer;
  struct grid_cell *source_cell = search->src_grid_cells;

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  /*
  enum cell_type target_cell_type = UNDEF_CELL;

  if ( target_cell.num_corners > 3 )
    target_cell_type = get_cell_type(target_cell);

  if ( target_cell.num_corners < 4 || target_cell_type == LON_LAT_CELL )
    {
      cdo_compute_overlap_areas(N, overlap_buffer, source_cell, target_cell, partial_areas);
      return;
    }

  if ( target_node_x == NULL || target_node_y == NULL )
    cdoAbort("Internal problem (cdo_compute_concave_overlap_areas): missing target point coordinates!");
  */
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  /*
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  struct grid_cell target_partial_cell =
    {.coordinates_x   = (double[3]){-1, -1, -1},
     .coordinates_y   = (double[3]){-1, -1, -1},
     .coordinates_xyz = (double[3*3]){-1, -1, -1},
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     .edge_type       = (enum yac_edge_type[3]) {GREAT_CIRCLE, GREAT_CIRCLE, GREAT_CIRCLE},
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     .num_corners     = 3};
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  */
  double coordinates_x[3] = {-1, -1, -1};
  double coordinates_y[3] = {-1, -1, -1};
  double coordinates_xyz[9] = {-1, -1, -1};
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  enum yac_edge_type edge_types[3] = {GREAT_CIRCLE, GREAT_CIRCLE, GREAT_CIRCLE};
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  struct grid_cell target_partial_cell =
    {.coordinates_x   = coordinates_x,
     .coordinates_y   = coordinates_y,
     .coordinates_xyz = coordinates_xyz,
     .edge_type       = edge_types,
     .num_corners     = 3};
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  /* Do the clipping and get the cell for the overlapping area */

  for ( unsigned n = 0; n < N; n++) partial_areas[n] = 0.0;

  // common node point to all partial target cells
  target_partial_cell.coordinates_x[0] = target_node_x;
  target_partial_cell.coordinates_y[0] = target_node_y;

  LLtoXYZ ( target_node_x, target_node_y, target_partial_cell.coordinates_xyz );

  for ( unsigned num_corners = 0; num_corners < target_cell.num_corners; ++num_corners )
    {
      unsigned corner_a = num_corners;
      unsigned corner_b = (num_corners+1)%target_cell.num_corners;

      // skip clipping and area calculation for degenerated triangles
      //
      // If this is not sufficient, instead we can try something like:
      //
      //     struct point_list target_list
      //     init_point_list(&target_list);
      //     generate_point_list(&target_list, target_cell);
      //     struct grid_cell temp_target_cell;
      //     generate_overlap_cell(target_list, temp_target_cell);
      //     free_point_list(&target_list);
      //
      // and use temp_target_cell for triangulation.
      //
      // Compared to the if statement below the alternative seems
      // to be quite costly.

      if ( ( ( fabs(target_cell.coordinates_xyz[0+3*corner_a]-target_cell.coordinates_xyz[0+3*corner_b]) < tol ) &&
	     ( fabs(target_cell.coordinates_xyz[1+3*corner_a]-target_cell.coordinates_xyz[1+3*corner_b]) < tol ) &&
	     ( fabs(target_cell.coordinates_xyz[2+3*corner_a]-target_cell.coordinates_xyz[2+3*corner_b]) < tol ) ) ||
	   ( ( fabs(target_cell.coordinates_xyz[0+3*corner_a]-target_partial_cell.coordinates_xyz[0]) < tol    ) &&
	     ( fabs(target_cell.coordinates_xyz[1+3*corner_a]-target_partial_cell.coordinates_xyz[1]) < tol    ) &&
	     ( fabs(target_cell.coordinates_xyz[2+3*corner_a]-target_partial_cell.coordinates_xyz[2]) < tol    ) ) ||
	   ( ( fabs(target_cell.coordinates_xyz[0+3*corner_b]-target_partial_cell.coordinates_xyz[0]) < tol    ) &&
	     ( fabs(target_cell.coordinates_xyz[1+3*corner_b]-target_partial_cell.coordinates_xyz[1]) < tol    ) &&
	     ( fabs(target_cell.coordinates_xyz[2+3*corner_b]-target_partial_cell.coordinates_xyz[2]) < tol    ) ) )
	continue;

      target_partial_cell.coordinates_x[1] = target_cell.coordinates_x[corner_a];
      target_partial_cell.coordinates_y[1] = target_cell.coordinates_y[corner_a];
      target_partial_cell.coordinates_x[2] = target_cell.coordinates_x[corner_b];
      target_partial_cell.coordinates_y[2] = target_cell.coordinates_y[corner_b];

      target_partial_cell.coordinates_xyz[0+3*1] = target_cell.coordinates_xyz[0+3*corner_a];
      target_partial_cell.coordinates_xyz[1+3*1] = target_cell.coordinates_xyz[1+3*corner_a];
      target_partial_cell.coordinates_xyz[2+3*1] = target_cell.coordinates_xyz[2+3*corner_a];
      target_partial_cell.coordinates_xyz[0+3*2] = target_cell.coordinates_xyz[0+3*corner_b];
      target_partial_cell.coordinates_xyz[1+3*2] = target_cell.coordinates_xyz[1+3*corner_b];
      target_partial_cell.coordinates_xyz[2+3*2] = target_cell.coordinates_xyz[2+3*corner_b];

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      yac_cell_clipping(N, source_cell, target_partial_cell, overlap_buffer);
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      /* Get the partial areas for the overlapping regions as sum over the partial target cells. */

      for (unsigned n = 0; n < N; n++)
	{
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	  partial_areas[n] += gridcell_area(overlap_buffer[n]);
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	  // we cannot use pole_area because it is rather inaccurate for great circle
	  // edges that are nearly circles of longitude
	  //partial_areas[n] = pole_area (overlap_buffer[n]);
	}
    }

#ifdef VERBOSE
  for (unsigned n = 0; n < N; n++)
    printf("overlap area %i: %lf \n", n, partial_areas[n]);
#endif
}

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//#endif

static
int get_lonlat_circle_index(remapgrid_t *remap_grid)
{
  int lonlat_circle_index = -1;

  if ( remap_grid->num_cell_corners == 4 )
    {
      if ( remap_grid->remap_grid_type == REMAP_GRID_TYPE_REG2D )
	{
	  lonlat_circle_index = 1;
 	}
      else
	{
	  const double* cell_corner_lon = remap_grid->cell_corner_lon;
	  const double* cell_corner_lat = remap_grid->cell_corner_lat;
	  int gridsize = remap_grid->size;
	  int num_i = 0, num_eq0 = 0, num_eq1 = 0;
	  int iadd = gridsize/3-1;

	  if ( iadd == 0 ) iadd++;

	  for ( int i = 0; i < gridsize; i += iadd )
	    {
	      num_i++;

	      if ( IS_EQUAL(cell_corner_lon[i*4+1], cell_corner_lon[i*4+2]) &&
		   IS_EQUAL(cell_corner_lon[i*4+3], cell_corner_lon[i*4+0]) &&
		   IS_EQUAL(cell_corner_lat[i*4+0], cell_corner_lat[i*4+1]) &&
		   IS_EQUAL(cell_corner_lat[i*4+2], cell_corner_lat[i*4+3]) )
		{  
		  num_eq1++;
		}
	      else if ( IS_EQUAL(cell_corner_lon[i*4+0], cell_corner_lon[i*4+1]) &&
			IS_EQUAL(cell_corner_lon[i*4+2], cell_corner_lon[i*4+3]) &&
			IS_EQUAL(cell_corner_lat[i*4+1], cell_corner_lat[i*4+2]) &&
			IS_EQUAL(cell_corner_lat[i*4+3], cell_corner_lat[i*4+0]) )
		{
		  num_eq0++;
		}
	    }

	  if ( num_i == num_eq1 ) lonlat_circle_index = 1;
	  if ( num_i == num_eq0 ) lonlat_circle_index = 0;	      
	}
    }

  //printf("lonlat_circle_index %d\n", lonlat_circle_index);

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  return lonlat_circle_index;
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}


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static
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void remapNormalizeWeights(remapgrid_t *tgt_grid, remapvars_t *rv)
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{
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  // Include centroids in weights and normalize using destination area if requested
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  long num_links = rv->num_links;
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  int num_wts = rv->num_wts;
  int tgt_cell_add;       // current linear address for target grid cell
  double norm_factor = 0; // factor for normalizing wts
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  if ( rv->norm_opt == NORM_OPT_DESTAREA )
    {
#if defined(SX)
#pragma vdir nodep
#endif
#if defined(_OPENMP)
#pragma omp parallel for default(none) \
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  shared(num_wts, num_links, rv, tgt_grid) \
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  private(tgt_cell_add, norm_factor)
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#endif
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      for ( long n = 0; n < num_links; ++n )
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	{
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	  tgt_cell_add = rv->tgt_cell_add[n];
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          if ( IS_NOT_EQUAL(tgt_grid->cell_area[tgt_cell_add], 0) )
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	    norm_factor = 1./tgt_grid->cell_area[tgt_cell_add];
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          else
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            norm_factor = 0.;
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	  rv->wts[n*num_wts] *= norm_factor;
	}
    }
  else if ( rv->norm_opt == NORM_OPT_FRACAREA )
    {
#if defined(SX)
#pragma vdir nodep
#endif
#if defined(_OPENMP)
#pragma omp parallel for default(none) \
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  private(tgt_cell_add, norm_factor)
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#endif
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      for ( long n = 0; n < num_links; ++n )
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	{
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	  tgt_cell_add = rv->tgt_cell_add[n];
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          if ( IS_NOT_EQUAL(tgt_grid->cell_frac[tgt_cell_add], 0) )
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	    norm_factor = 1./tgt_grid->cell_frac[tgt_cell_add];
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          else
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            norm_factor = 0.;
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	  rv->wts[n*num_wts] *= norm_factor;
	}
    }
  else if ( rv->norm_opt == NORM_OPT_NONE )
    {
    }
}

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static
void set_yac_coordinates(int remap_grid_type, int cell_add, int num_cell_corners, remapgrid_t *remap_grid, struct grid_cell *yac_grid_cell)
{
  if ( remap_grid_type == REMAP_GRID_TYPE_REG2D )
    {
      int nx = remap_grid->dims[0];
      int iy = cell_add/nx;
      int ix = cell_add - iy*nx;
      const double *restrict reg2d_corner_lon = remap_grid->reg2d_corner_lon;
      const double *restrict reg2d_corner_lat = remap_grid->reg2d_corner_lat;
      double *restrict coordinates_x = yac_grid_cell->coordinates_x;
      double *restrict coordinates_y = yac_grid_cell->coordinates_y;

      coordinates_x[0] = reg2d_corner_lon[ix  ];
      coordinates_y[0] = reg2d_corner_lat[iy  ];
      coordinates_x[1] = reg2d_corner_lon[ix+1];
      coordinates_y[1] = reg2d_corner_lat[iy  ];
      coordinates_x[2] = reg2d_corner_lon[ix+1];
      coordinates_y[2] = reg2d_corner_lat[iy+1];
      coordinates_x[3] = reg2d_corner_lon[ix  ];
      coordinates_y[3] = reg2d_corner_lat[iy+1];
    }
  else
    {
      const double *restrict cell_corner_lon = remap_grid->cell_corner_lon;
      const double *restrict cell_corner_lat = remap_grid->cell_corner_lat;
      double *restrict coordinates_x = yac_grid_cell->coordinates_x;
      double *restrict coordinates_y = yac_grid_cell->coordinates_y;
      for ( int ic = 0; ic < num_cell_corners; ++ic )
        {
          coordinates_x[ic] = cell_corner_lon[cell_add*num_cell_corners+ic];
          coordinates_y[ic] = cell_corner_lat[cell_add*num_cell_corners+ic];
        }
    }
      
  const double *restrict coordinates_x = yac_grid_cell->coordinates_x;
  const double *restrict coordinates_y = yac_grid_cell->coordinates_y;
  double *restrict coordinates_xyz = yac_grid_cell->coordinates_xyz;
  for ( int ic = 0; ic < num_cell_corners; ++ic )
    LLtoXYZ(coordinates_x[ic], coordinates_y[ic], coordinates_xyz+ic*3);
}

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static
void reg2d_bound_box(remapgrid_t *remap_grid, double *grid_bound_box)
{
  int nx = remap_grid->dims[0];
  int ny = remap_grid->dims[1];
  const double *restrict reg2d_corner_lon = remap_grid->reg2d_corner_lon;
  const double *restrict reg2d_corner_lat = remap_grid->reg2d_corner_lat;

  grid_bound_box[0] = reg2d_corner_lat[0];
  grid_bound_box[1] = reg2d_corner_lat[ny];
  if ( grid_bound_box[0] > grid_bound_box[1] )
    {
      grid_bound_box[0] = reg2d_corner_lat[ny];
      grid_bound_box[1] = reg2d_corner_lat[0];
    }
  grid_bound_box[2] = reg2d_corner_lon[0];
  grid_bound_box[3] = reg2d_corner_lon[nx];
}

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void remap_conserv_weights(remapgrid_t *src_grid, remapgrid_t *tgt_grid, remapvars_t *rv)
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{
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  int lcheck = TRUE;
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  int srch_corners;  // num of corners of srch cells
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  /* Variables necessary if segment manages to hit pole */
  int src_remap_grid_type = src_grid->remap_grid_type;
  int tgt_remap_grid_type = tgt_grid->remap_grid_type;
  extern int timer_remap_con;

  if ( cdoVerbose ) cdoPrint("Called %s()", __func__);

  progressInit();

  if ( cdoTimer ) timer_start(timer_remap_con);

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  int src_grid_size = src_grid->size;
  int tgt_grid_size = tgt_grid->size;
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  int src_num_cell_corners = src_grid->num_cell_corners;
  int tgt_num_cell_corners = tgt_grid->num_cell_corners;
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  int max_num_cell_corners = src_num_cell_corners;
  if ( tgt_num_cell_corners > max_num_cell_corners ) max_num_cell_corners = tgt_num_cell_corners;

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  enum yac_edge_type great_circle_type[max_num_cell_corners];
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  for ( int i = 0; i < max_num_cell_corners; ++i ) great_circle_type[i] = GREAT_CIRCLE;

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  enum yac_edge_type lonlat_circle_type[] = {LON_CIRCLE, LAT_CIRCLE, LON_CIRCLE, LAT_CIRCLE, LON_CIRCLE};
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  enum yac_edge_type *src_edge_type = great_circle_type;
  enum yac_edge_type *tgt_edge_type = great_circle_type;
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  enum cell_type target_cell_type = UNDEF_CELL;

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  if ( src_num_cell_corners == 4 )
    {
      int lonlat_circle_index = get_lonlat_circle_index(src_grid);
      if ( lonlat_circle_index >= 0 ) src_edge_type = &lonlat_circle_type[lonlat_circle_index];
    }

  if ( tgt_num_cell_corners == 4 )
    {
      int lonlat_circle_index = get_lonlat_circle_index(tgt_grid);
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      if ( lonlat_circle_index >= 0 )
	{
	  target_cell_type = LON_LAT_CELL;
	  tgt_edge_type = &lonlat_circle_type[lonlat_circle_index];
	}
    }

  if ( !(tgt_num_cell_corners < 4 || target_cell_type == LON_LAT_CELL) )
    {
      if ( tgt_grid->cell_center_lon == NULL || tgt_grid->cell_center_lat == NULL )
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	cdoAbort("Internal problem (%s): missing target point coordinates!", __func__);
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    }


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  struct grid_cell *tgt_grid_cell2[ompNumThreads];  
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  for ( int i = 0; i < ompNumThreads; ++i )
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    {
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      tgt_grid_cell2[i] = (struct grid_cell*) Malloc(sizeof(struct grid_cell));
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      tgt_grid_cell2[i]->array_size      = tgt_num_cell_corners;
      tgt_grid_cell2[i]->num_corners     = tgt_num_cell_corners;
      tgt_grid_cell2[i]->edge_type       = tgt_edge_type;
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      tgt_grid_cell2[i]->coordinates_x   = (double*) Malloc(tgt_num_cell_corners*sizeof(double));
      tgt_grid_cell2[i]->coordinates_y   = (double*) Malloc(tgt_num_cell_corners*sizeof(double));
      tgt_grid_cell2[i]->coordinates_xyz = (double*) Malloc(3*tgt_num_cell_corners*sizeof(double));
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    }

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  search_t search[ompNumThreads];
  for ( int i = 0; i < ompNumThreads; ++i )
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    {
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      search[i].srch_corners    = src_num_cell_corners;
      search[i].src_edge_type   = src_edge_type;
      search[i].max_srch_cells  = 0;
      search[i].partial_areas   = NULL;
      search[i].partial_weights = NULL;
      search[i].src_grid_cells  = NULL;
      search[i].overlap_buffer  = NULL;
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    }

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  int *srch_add2[ompNumThreads];
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  for ( int i = 0; i < ompNumThreads; ++i )
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    srch_add2[i] = (int*) Malloc(src_grid_size*sizeof(int));
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  srch_corners = src_num_cell_corners;

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  double src_grid_bound_box[4];
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  if ( src_remap_grid_type == REMAP_GRID_TYPE_REG2D )
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    reg2d_bound_box(src_grid, src_grid_bound_box);
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  weightlinks_t *weightlinks = (weightlinks_t *) Malloc(tgt_grid_size*sizeof(weightlinks_t));
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  double findex = 0;
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  long sum_srch_cells = 0;
  long sum_srch_cells2 = 0;
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#ifdef STIMER
  double stimer = 0;
#endif
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  /* Loop over destination grid */

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#if defined(_OPENMP)
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#pragma omp parallel for schedule(dynamic) default(none)                   \
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  shared(ompNumThreads, src_remap_grid_type, tgt_remap_grid_type, src_grid_bound_box, \
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	 rv, cdoVerbose, tgt_num_cell_corners, target_cell_type, \
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         weightlinks,  srch_corners, src_grid, tgt_grid, tgt_grid_size, src_grid_size, \
	 search, srch_add2, tgt_grid_cell2, findex, sum_srch_cells, sum_srch_cells2)
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#endif
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  for ( long tgt_cell_add = 0; tgt_cell_add < tgt_grid_size; ++tgt_cell_add )
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    {
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      double partial_weight;
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      long src_cell_add;       /* current linear address for source grid cell   */
      long num_srch_cells;
      long n, num_weights, num_weights_old;
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      int ompthID = cdo_omp_get_thread_num();
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#if defined(_OPENMP)
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#include "pragma_omp_atomic_update.h"
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#endif
      findex++;
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      if ( ompthID == 0 ) progressStatus(0, 1, findex/tgt_grid_size);
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      weightlinks[tgt_cell_add].nlinks = 0;	

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      int *srch_add = srch_add2[ompthID];
      struct grid_cell *tgt_grid_cell = tgt_grid_cell2[ompthID];
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      /* Get search cells */
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#ifdef STIMER
      clock_t start = clock();
#endif
          
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      if ( src_remap_grid_type == REMAP_GRID_TYPE_REG2D && tgt_remap_grid_type == REMAP_GRID_TYPE_REG2D )
	{
	  double tgt_cell_bound_box[4];
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	  boundbox_from_corners_reg2d(tgt_cell_add, tgt_grid->dims, tgt_grid->reg2d_corner_lon, tgt_grid->reg2d_corner_lat, tgt_cell_bound_box);
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	  restrict_boundbox(src_grid_bound_box, tgt_cell_bound_box);
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	  num_srch_cells = get_srch_cells_reg2d(src_grid->dims, src_grid->reg2d_corner_lat, src_grid->reg2d_corner_lon,
						tgt_cell_bound_box, srch_add);
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	  if ( num_srch_cells == 1 && src_grid->dims[0] == 1 && src_grid->dims[1] == 1 &&
	       IS_EQUAL(src_grid->reg2d_corner_lat[0], src_grid->reg2d_corner_lat[1]) && 
	       IS_EQUAL(src_grid->reg2d_corner_lon[0], src_grid->reg2d_corner_lon[1]) ) num_srch_cells = 0;
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	}
      else if ( src_remap_grid_type == REMAP_GRID_TYPE_REG2D )
	{
	  double tgt_cell_bound_box[4];
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	  boundbox_from_corners1(tgt_cell_add, tgt_num_cell_corners, tgt_grid->cell_corner_lon, tgt_grid->cell_corner_lat, tgt_cell_bound_box);
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	  restrict_boundbox(src_grid_bound_box, tgt_cell_bound_box);
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	  num_srch_cells = get_srch_cells_reg2d(src_grid->dims, src_grid->reg2d_corner_lat, src_grid->reg2d_corner_lon,
						tgt_cell_bound_box, srch_add);
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	  if ( num_srch_cells == 1 && src_grid->dims[0] == 1 && src_grid->dims[1] == 1 &&
	       IS_EQUAL(src_grid->reg2d_corner_lat[0], src_grid->reg2d_corner_lat[1]) && 
	       IS_EQUAL(src_grid->reg2d_corner_lon[0], src_grid->reg2d_corner_lon[1]) ) num_srch_cells = 0;
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	}
      else
	{
	  restr_t tgt_cell_bound_box_r[4];
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	  boundbox_from_corners1r(tgt_cell_add, tgt_num_cell_corners, tgt_grid->cell_corner_lon, tgt_grid->cell_corner_lat, tgt_cell_bound_box_r);
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          long nbins = src_grid->num_srch_bins;
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	  num_srch_cells = get_srch_cells(tgt_cell_add, nbins, tgt_grid->bin_addr, src_grid->bin_addr,
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					  tgt_cell_bound_box_r, src_grid->cell_bound_box, src_grid_size, srch_add);
	}
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#ifdef STIMER
      clock_t finish = clock();
      stimer += ((double)(finish-start))/CLOCKS_PER_SEC;
#endif
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      if ( 0 && cdoVerbose ) sum_srch_cells += num_srch_cells;
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      if ( 0 && cdoVerbose )
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	printf("tgt_cell_add %ld  num_srch_cells %ld\n", tgt_cell_add, num_srch_cells);
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      if ( num_srch_cells == 0 ) continue;

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      set_yac_coordinates(tgt_remap_grid_type, tgt_cell_add, tgt_num_cell_corners, tgt_grid, tgt_grid_cell);

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      /* Create search arrays */

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      search_realloc(num_srch_cells, &search[ompthID]);
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      double *partial_areas   = search[ompthID].partial_areas;
      double *partial_weights = search[ompthID].partial_weights;
      struct grid_cell *src_grid_cells = search[ompthID].src_grid_cells;
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      for ( n = 0; n < num_srch_cells; ++n )
	{
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	  int srch_corners_new = srch_corners;
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	  src_cell_add = srch_add[n];
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          set_yac_coordinates(src_remap_grid_type, src_cell_add, srch_corners_new, src_grid, &src_grid_cells[n]);
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	}

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      if ( tgt_num_cell_corners < 4 || target_cell_type == LON_LAT_CELL )
	{
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	  cdo_compute_overlap_areas(num_srch_cells, &search[ompthID], *tgt_grid_cell);
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	}
      else
	{
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	  double cell_center_lon = tgt_grid->cell_center_lon[tgt_cell_add];
	  double cell_center_lat = tgt_grid->cell_center_lat[tgt_cell_add];
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	  cdo_compute_concave_overlap_areas(num_srch_cells, &search[ompthID], *tgt_grid_cell, cell_center_lon, cell_center_lat);
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	}
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      double tgt_area = gridcell_area(*tgt_grid_cell);
      // double tgt_area = cell_area(tgt_grid_cell);
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      for ( num_weights = 0, n = 0; n < num_srch_cells; ++n )
	{
	  if ( partial_areas[n] > 0 )
	    {
	      partial_areas[num_weights] = partial_areas[n];
	      srch_add[num_weights] = srch_add[n];
	      num_weights++;
	    }
	}

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      if ( 0 && cdoVerbose ) sum_srch_cells2 += num_weights;
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      for ( n = 0; n < num_weights; ++n )
	partial_weights[n] = partial_areas[n] / tgt_area;

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      if ( rv->norm_opt == NORM_OPT_FRACAREA )
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	yac_correct_weights((unsigned)num_weights, partial_weights);
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      for ( n = 0; n < num_weights; ++n )
	partial_weights[n] *= tgt_area;
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      num_weights_old = num_weights;
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      num_weights = 0;
      for ( n = 0; n < num_weights_old; ++n )
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	{
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	  src_cell_add = srch_add[n];
	  if ( partial_weights[n] <= 0. ) src_cell_add = -1;
	  if ( src_cell_add != -1 )
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	    {
	      partial_weights[num_weights] = partial_weights[n];
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	      srch_add[num_weights] = src_cell_add;
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	      num_weights++;
	    }
	}

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      for ( n = 0; n < num_weights; ++n )
	{
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	  partial_weight = partial_weights[n];
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	  src_cell_add = srch_add[n];
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#if defined(_OPENMP)
#pragma omp atomic
#endif
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	  src_grid->cell_area[src_cell_add] += partial_weight;
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	}
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      num_weights_old = num_weights;
      for ( num_weights = 0, n = 0; n < num_weights_old; ++n )
	{
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	  src_cell_add = srch_add[n];
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	  /*
	    Store the appropriate addresses and weights. 
	    Also add contributions to cell areas.
	    The source grid mask is the master mask
	  */
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	  if ( src_grid->mask[src_cell_add] )
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	    {
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	      partial_weights[num_weights] = partial_weights[n];
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	      srch_add[num_weights] = src_cell_add;
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	      num_weights++;
	    }
	}

      for ( n = 0; n < num_weights; ++n )
	{
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	  partial_weight = partial_weights[n];
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	  src_cell_add = srch_add[n];
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#if defined(_OPENMP)
#pragma omp atomic
#endif
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	  src_grid->cell_frac[src_cell_add] += partial_weight;
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	  tgt_grid->cell_frac[tgt_cell_add] += partial_weight;
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	}

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      store_weightlinks(1, num_weights, srch_add, partial_weights, tgt_cell_add, weightlinks);
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      tgt_grid->cell_area[tgt_cell_add] = tgt_area; 
      // printf("area %d %g %g\n", tgt_cell_add, tgt_grid->cell_area[tgt_cell_add], tgt_area);
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  }
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