test_area.c

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// Copyright (c) 2024 The YAC Authors
//
// SPDX-License-Identifier: BSD-3-Clause
 
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "test_common.h"
#include "clipping.h"
#include "area.h"
#include "tests.h"
#include "geometry.h"
 
#define YAC_EARTH_RADIUS (6371.2290)
 
static int utest_compare_area(double a, double b);
static void utest_test_area(struct yac_grid_cell cell, double ref_area,
                            double (*area_func)(struct yac_grid_cell));
 
int main (void) {
 
  enum yac_edge_type gc_edges[] =
    {YAC_GREAT_CIRCLE_EDGE, YAC_GREAT_CIRCLE_EDGE, YAC_GREAT_CIRCLE_EDGE,
     YAC_GREAT_CIRCLE_EDGE, YAC_GREAT_CIRCLE_EDGE, YAC_GREAT_CIRCLE_EDGE,
     YAC_GREAT_CIRCLE_EDGE, YAC_GREAT_CIRCLE_EDGE, YAC_GREAT_CIRCLE_EDGE};
  enum yac_edge_type lat_edges[4] =
    {YAC_LAT_CIRCLE_EDGE, YAC_LON_CIRCLE_EDGE, YAC_LAT_CIRCLE_EDGE, YAC_LON_CIRCLE_EDGE};
 
  double area;
 
  puts ("----- calculating area -----\n");
 
  {
    /* set the test data over the Equator
 
               0.0 (lon)
               0.5 (lat)
               / \
              /   \
    -0.5     /     \  0.5
     0.0     \     /  0.0
              \   /
               \ /
               0.0
              -0.5         
    */
 
    struct yac_grid_cell Quad =
      generate_cell_deg((double[4]){0.5, 0.0, -0.5, 0.0},
                        (double[4]){0.0, 0.5, 0.0, -0.5}, gc_edges, 4);
 
    area = yac_pole_area ( Quad );
    printf ( "pole     area of quad   over Equator    is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    area = yac_huiliers_area ( Quad );
    printf ( "huiliers area of quad   over Equator    is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
    yac_free_grid_cell(&Quad);
  }
 
  {
  /* Triangle, half of the above Quad */
 
    struct yac_grid_cell Tri =
      generate_cell_deg((double[3]){0.5, 0.0, -0.5},
                        (double[3]){0.0, 0.5, 0.0}, gc_edges, 3);
 
    area = yac_triangle_area ( Tri );
    printf ( "ICON     area of triangle over Equator  is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    area = yac_pole_area ( Tri );
    printf ( "pole     area of triangle over Equator  is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    area = yac_huiliers_area ( Tri );
    printf ( "huiliers area of triangle over Equator  is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
    yac_free_grid_cell(&Tri);
  }
 
  {
    /* set the test data over the Equator
 
    -0.5               0.5 (lon)
    0.5  -----------  0.5 (lat)
         |         |
         |         |
         |         |
         |         |
         |         |
    -0.5  -----------  0.5
    -0.5              -0.5
 
    */
 
    struct yac_grid_cell Quad =
      generate_cell_deg((double[4]){-0.5, 0.5, 0.5, -0.5},
                        (double[4]){-0.5, -0.5, 0.5, 0.5}, gc_edges, 4);
 
    area = yac_pole_area ( Quad );
    printf ( "pole     area of quad   over Equator    is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    area = yac_huiliers_area ( Quad );
    printf ( "huiliers area of quad   over Equator    is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    double ref_area = yac_pole_area(Quad);
 
    utest_test_area(Quad, ref_area, yac_pole_area);
    utest_test_area(Quad, ref_area, yac_huiliers_area);
 
    yac_free_grid_cell(&Quad);
  }
 
  {
    /* Half of the above Quad */
 
    struct yac_grid_cell Tri =
      generate_cell_deg((double[3]){-0.5, 0.5, 0.5},
                        (double[3]){-0.5, -0.5, 0.5}, gc_edges, 3);
 
    area = yac_triangle_area ( Tri );
    printf ( "ICON     area of triangle over Equator  is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    area = yac_pole_area ( Tri );
    printf ( "pole     area of triangle over Equator  is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    area = yac_huiliers_area ( Tri );
    printf ( "huiliers area of triangle over Equator  is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    yac_free_grid_cell(&Tri);
  }
 
  {
 
    struct yac_grid_cell Tri =
      generate_cell_deg((double[3]){150.0, 180.0, 180.0},
                        (double[3]){-60.0, -60.0, -90.0}, gc_edges, 3);
 
    area = yac_triangle_area ( Tri );
    printf ( "ICON     area of triangle over South Pole is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    area = yac_pole_area ( Tri );
    printf ( "pole     area of triangle over South Pole is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    area = yac_huiliers_area ( Tri );
    printf ( "huiliers area of triangle over South Pole is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    yac_free_grid_cell(&Tri);
  }
 
  {
    /* set the test data over the North Pole
 
    90.0                0.0 (lon)
    89.5  -----------  89.5 (lat)
          |         |
          |         |
          |    x    |
          |         |
          |         |
    180.0  ----------- 270.0
    89.5               89.5
 
    */
 
    struct yac_grid_cell Quad =
      generate_cell_deg((double[4]){0.0, 90.0, -180.0, -90.0},
                        (double[4]){89.5, 89.5, 89.5, 89.5}, gc_edges, 4);
 
    area = yac_pole_area ( Quad );
    printf ( "pole   area of quad     over North Pole is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    area = yac_huiliers_area ( Quad );
    printf ( "huiliers area of quad   over North Pole is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    yac_free_grid_cell(&Quad);
  }
 
  {
    struct yac_grid_cell Quad =
      generate_cell_deg((double[4]){-180.0, -150.0, -150.0, -180.0},
                        (double[4]){60.0, 60.0, 90.0, 90.0}, gc_edges, 4);
 
    area = yac_pole_area ( Quad );
    printf ( "pole     area of quad   near North Pole is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    area = yac_huiliers_area ( Quad );
    printf ( "huiliers area of quad   near North Pole is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    yac_free_grid_cell(&Quad);
  }
 
  {
    struct yac_grid_cell Quad =
      generate_cell_deg((double[4]){-180.0, -150.0, -150.0, -180.0},
                        (double[4]){-90.0, -90.0, -60.0, -60.0}, gc_edges, 4);
 
    printf ( "ICON     area of quad   near South Pole is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    area = yac_pole_area ( Quad );
    printf ( "pole     area of quad   near South Pole is %f sqr Km \n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    area = yac_huiliers_area ( Quad );
    printf ( "huiliers area of quad   near South Pole is %f sqr Km \n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    yac_free_grid_cell(&Quad);
  }
 
  {
    struct yac_grid_cell Quin =
      generate_cell_deg((double[5]){-180.0, -150.0, 0.0, -150.0, -180.0},
                        (double[5]){60.0, 60.0, 90.0, 90.0, 90.0}, gc_edges, 5);
 
    area = yac_pole_area ( Quin );
    printf ( "pole     area of quin   near North Pole is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    area = yac_huiliers_area ( Quin );
    printf ( "huiliers area of quin   near North Pole is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    yac_free_grid_cell(&Quin);
  }
 
  {
    /* Triangle that contains an edge of length zero */
 
    struct yac_grid_cell Tri =
      generate_cell_deg((double[3]){-0.5,  0.5, -0.5},
                        (double[3]){-0.5, -0.5, -0.5}, gc_edges, 3);
 
    area = yac_triangle_area ( Tri );
    printf ( "ICON     area of triangle over Equator  is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    area = yac_pole_area ( Tri );
    printf ( "pole     area of triangle over Equator  is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    area = yac_huiliers_area ( Tri );
    printf ( "huiliers area of triangle over Equator  is %f sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    if ((area < 0.0) || (area > 1e-9))
      PUT_ERR("ERROR in yac_huiliers_area for zero size triangle");
 
    yac_free_grid_cell(&Tri);
  }
 
  {
    struct yac_grid_cell Quad =
      generate_cell_deg((double[4]){0, 1, 1, 0},
                        (double[4]){0, 0, 1, 1}, gc_edges, 4);
    struct yac_grid_cell Tri =
      generate_cell_deg((double[3]){1, 1, 1},
                        (double[3]){0, 0, 1}, gc_edges, 3);
 
    double base_area = yac_huiliers_area(Quad);
 
    yac_free_grid_cell(&Quad);
    yac_free_grid_cell(&Tri);
 
    /* A dx of 1e-8 deg corresponds to a dx of ~1 mm on the Earth surface */
 
    double dx[] = {1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1,
                   0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9};
 
    for (size_t i = 0; i < sizeof(dx) / sizeof(dx[0]); ++i) {
 
 
      struct yac_grid_cell Quad =
        generate_cell_deg((double[4]){0, 1.0-dx[i], 1, 0},
                          (double[4]){0, 0, 1, 1}, gc_edges, 4);
      struct yac_grid_cell Tri =
        generate_cell_deg((double[3]){1.0-dx[i], 1, 1},
                          (double[3]){0, 0, 1}, gc_edges, 3);
 
      double partial_area = yac_huiliers_area(Quad);
      partial_area += yac_huiliers_area(Tri);
 
      yac_free_grid_cell(&Quad);
      yac_free_grid_cell(&Tri);
 
      if (utest_compare_area(base_area, partial_area))
        PUT_ERR("yac_huiliers_area computed wrong area\n");
 
      printf ("accuracy check for (base_area - partial_area) %8.1e sqr km for dx %.1e\n",
              base_area - partial_area, dx[i]);
    }
  }
 
  {
    struct yac_grid_cell Tri =
      generate_cell_deg(
        (double[3]){0.09817477/YAC_RAD, 0.09817477/YAC_RAD, 0.098174496/YAC_RAD},
        (double[3]){0.353325247/YAC_RAD, 0.353335501/YAC_RAD, 0.353335609/YAC_RAD},
        gc_edges, 3);
 
    area = yac_pole_area(Tri);
 
    if (area < 0)
       PUT_ERR("pole_area computed wrong area\n");
 
    printf ("pole   accuracy check of very small area %.2e sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    area = yac_huiliers_area(Tri);
 
    if (area < 0)
       PUT_ERR("huiliers_area computed wrong area\n");
 
    printf ("huiliers accuracy check of very small area %.2e sqr km\n", area * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS );
 
    yac_free_grid_cell(&Tri);
  }
 
  {
    double edge_length_deg = 1.0e-8; // ~1.11 mm
 
     printf ("\n accuracy check for a unit square\n");
     printf (" edge length [m] |        plain       |       simple       |        pole        |      huiliers\n");
     printf (" ----------------+--------------------+--------------------+--------------------+--------------------\n");
     for ( unsigned i = 1; i < 11; ++i ) {
 
        double edge_length_m =
          edge_length_deg * YAC_RAD * YAC_EARTH_RADIUS * 1.0e3;
 
        struct yac_grid_cell Quad =
          generate_cell_deg((double[4]){0, edge_length_deg, edge_length_deg, 0},
                            (double[4]){0, 0, edge_length_deg, edge_length_deg},
                            gc_edges, 4);
 
        double t_area = edge_length_m                * edge_length_m;
        double p_area = yac_planar_3dcell_area(Quad) * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS * 1.0e6;
        double s_area = yac_pole_area(Quad)          * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS * 1.0e6;
        double h_area = yac_huiliers_area(Quad)      * YAC_EARTH_RADIUS * YAC_EARTH_RADIUS * 1.0e6;
 
        if (0)
          printf (" %.8e m|%.8e sqr m|%.8e sqr m|%.8e sqr m|%.8e sqr m\n",
                  edge_length_m, p_area, t_area, s_area, h_area);
 
        edge_length_deg *= 10.0;
 
        yac_free_grid_cell(&Quad);
     }
 
  }
 
  { // cell with two edges (one great circle and one circle of latitude)
 
    for (int y = -90; y <= 90; y += 5) {
 
      struct yac_grid_cell cell =
        generate_cell_deg((double[2]){0.0, 20.0},
                          (double[2]){(double)y, (double)y},
                          (enum yac_edge_type[]){
                            YAC_GREAT_CIRCLE_EDGE, YAC_LAT_CIRCLE_EDGE}, 2);
 
      // compute reference area
      double ref_area;
 
      {
        double coordinates_x[3] = {0.0, 20.0, 0.0};
        double coordinates_y[3] = {(double)y, (double)y, 0};
 
        if ((y == -90) || (y == 90) || (y == 0)) {
 
          ref_area = 0.0;
 
        } else {
 
          if (y < 0) {
            ref_area = (coordinates_x[1]*YAC_RAD - coordinates_x[0]*YAC_RAD) *
                        (1 - cos(M_PI_2 + coordinates_y[0]*YAC_RAD));
            coordinates_y[2] = -90.0;
          } else {
            ref_area = (coordinates_x[1]*YAC_RAD - coordinates_x[0]*YAC_RAD) *
                        (1 - cos(M_PI_2 - coordinates_y[0]*YAC_RAD));
            coordinates_y[2] = 90.0;
          }
 
          struct yac_grid_cell tmp_cell =
            generate_cell_deg(coordinates_x, coordinates_y, gc_edges, 3);
          // ref_area *= YAC_EARTH_RADIUS * YAC_EARTH_RADIUS;
          ref_area -= yac_huiliers_area(tmp_cell);
 
          yac_free_grid_cell(&tmp_cell);
        }
      }
 
      utest_test_area(cell, ref_area, yac_pole_area);
      utest_test_area(cell, ref_area, yac_huiliers_area);
 
      yac_free_grid_cell(&cell);
    }
  }
 
  { // cell with lon lat edges and one edge on the equator
 
    double ref_area = sin(0.5 * YAC_RAD) * (0.5 * YAC_RAD);
    // ref_area *= YAC_EARTH_RADIUS * YAC_EARTH_RADIUS;
 
    double coordinates_x[2][4] = {{-0.5, 0.0, 0.0, -0.5},
                                  { 0.0, 0.5, 0.5,  0.0}};
    double coordinates_y[2][4] = {{-0.5, -0.5, 0.0, 0.0},
                                  { 0.0,  0.0, 0.5, 0.5}};
 
    for (int x = 0; x < 2; ++x) {
      for (int y = 0; y < 2; ++y) {
        struct yac_grid_cell cell =
          generate_cell_deg(coordinates_x[x], coordinates_y[y], lat_edges, 4);
 
        utest_test_area(cell, ref_area, yac_pole_area);
        utest_test_area(cell, ref_area, yac_huiliers_area);
 
        yac_free_grid_cell(&cell);
      }
    }
  }
 
  { // cell with lon lat edges (both lat edges on the different side of the
    // equator)
    double ref_area = (2.0 * sin(0.5 * YAC_RAD)) * (1.0 * YAC_RAD);
    // ref_area *= YAC_EARTH_RADIUS * YAC_EARTH_RADIUS;
 
    struct yac_grid_cell cell =
      generate_cell_deg((double[4]){-0.5, 0.5, 0.5, -0.5},
                        (double[4]){-0.5, -0.5, 0.5, 0.5}, lat_edges, 4);
 
    utest_test_area(cell, ref_area, yac_pole_area);
    utest_test_area(cell, ref_area, yac_huiliers_area);
 
    yac_free_grid_cell(&cell);
  }
 
  { // cell with lon lat edges (both lat edges on the same side of the equator)
    double ref_area = sin(1.0 * YAC_RAD);
    ref_area -= sin(0.5 * YAC_RAD);
    ref_area *= 1.0 * YAC_RAD;
    // ref_area *= YAC_EARTH_RADIUS * YAC_EARTH_RADIUS;
 
    for (int i = 0; i < 2; ++i) {
 
      double coordinates_x[4] = {-0.5, 0.5, 0.5, -0.5};
      double coordinates_y[2][4] = {{ 0.5, 0.5, 1.0,  1.0},
                                    {-0.5,-0.5,-1.0, -1.0}};
      enum yac_edge_type edge_types[4] =
        {YAC_LAT_CIRCLE_EDGE, YAC_LON_CIRCLE_EDGE, YAC_LAT_CIRCLE_EDGE, YAC_LON_CIRCLE_EDGE};
 
      struct yac_grid_cell cell =
        generate_cell_deg(coordinates_x, coordinates_y[i], edge_types, 4);
 
      utest_test_area(cell, ref_area, yac_pole_area);
      utest_test_area(cell, ref_area, yac_huiliers_area);
 
      yac_free_grid_cell(&cell);
    }
  }
 
  { // concave cell
 
    double intersections[2][3];
 
    if (!intersect(YAC_GREAT_CIRCLE_EDGE, 20.0, 59.0, 0.0, 80.0,
                   YAC_LAT_CIRCLE_EDGE, 0.0, 60.0, 20.0, 60.0,
                   intersections[0]))
      return EXIT_FAILURE;
    if (!intersect(YAC_GREAT_CIRCLE_EDGE, 20.0, 59.0, -20.0, 59.0,
                   YAC_LAT_CIRCLE_EDGE, 0.0, 60.0, 20.0, 60.0,
                   intersections[1]))
      return EXIT_FAILURE;
 
    double intersections_lon[2], intersections_lat[2];
    XYZtoLL(intersections[0], &(intersections_lon[0]), &(intersections_lat[0]));
    XYZtoLL(intersections[1], &(intersections_lon[1]), &(intersections_lat[1]));
 
    // this cell is convex
    struct yac_grid_cell partial_ref_cell =
      generate_cell_deg(
        (double[]){20.0, intersections_lon[0]/YAC_RAD,
                   intersections_lon[1]/YAC_RAD},
        (double[]){59.0, 60.0, 60.0},
        (enum yac_edge_type[]){YAC_GREAT_CIRCLE_EDGE, YAC_LAT_CIRCLE_EDGE, YAC_GREAT_CIRCLE_EDGE}, 3);
 
    double partial_area = yac_pole_area(partial_ref_cell);
 
    if (utest_compare_area(partial_area,
                     yac_huiliers_area(partial_ref_cell)))
      PUT_ERR("pole_area != huiliers_area for convex cell");
 
    double ref_area = 2.0 * partial_area;
 
    struct yac_grid_cell cells[2] =
      {generate_cell_deg(
         (double[]){20.0,
                     intersections_lon[0]/YAC_RAD,
                     intersections_lon[1]/YAC_RAD,
                    -intersections_lon[1]/YAC_RAD,
                    -intersections_lon[0]/YAC_RAD, -20.0},
         (double[]){59.0, 60.0, 60.0, 60.0, 60.0, 59.0},
         (enum yac_edge_type[]){
           YAC_GREAT_CIRCLE_EDGE, YAC_LAT_CIRCLE_EDGE, YAC_GREAT_CIRCLE_EDGE,
           YAC_LAT_CIRCLE_EDGE, YAC_GREAT_CIRCLE_EDGE, YAC_GREAT_CIRCLE_EDGE}, 6),
       generate_cell_deg(
         (double[]){20.0,
                     intersections_lon[0]/YAC_RAD,
                    -intersections_lon[0]/YAC_RAD,
                    -20.0,
                    -intersections_lon[1]/YAC_RAD,
                     intersections_lon[1]/YAC_RAD},
         (double[]){59.0, 60.0, 60.0, 59.0, 60.0, 60.0},
         (enum yac_edge_type[]){
           YAC_GREAT_CIRCLE_EDGE, YAC_LAT_CIRCLE_EDGE, YAC_GREAT_CIRCLE_EDGE,
           YAC_GREAT_CIRCLE_EDGE, YAC_LAT_CIRCLE_EDGE, YAC_GREAT_CIRCLE_EDGE}, 6)};
 
    for (int i = 0; i < 2; ++i) {
      utest_test_area(cells[i], ref_area, yac_pole_area);
      utest_test_area(cells[i], ref_area, yac_huiliers_area);
    }
    yac_free_grid_cell(&(cells[0]));
    yac_free_grid_cell(&(cells[1]));
    yac_free_grid_cell(&partial_ref_cell);
  }
 
  { // case extracted from ICON example, which requires a high accuracy in the
    // area computation
    struct yac_grid_cell cells[] = {
      generate_cell_deg((double[]){-151.1489316535362661,
                                   -151.7087167856307133,
                                   -150.6174180645230933},
                        (double[]){  10.6333746562670566,
                                     11.5836995038666437,
                                     11.6243355661022782}, gc_edges, 3),
      generate_cell_deg((double[]){-152.8132296086113513,
                                   -153.8786613849353557,
                                   -151.6929566531634066},
                        (double[]){  13.4512385235805798,
                                     11.4650630285209161,
                                     11.5568484830228009}, gc_edges, 3),
      generate_cell_deg((double[]){-152.8132296086113513,
                                   -151.6929566531634066,
                                   -150.6265735326831532},
                        (double[]){  13.4512385235805798,
                                     11.5568484830228009,
                                     13.5446528932721275}, gc_edges, 3),
      generate_cell_deg((double[]){-153.8786613849353557,
                                   -151.6929566531634066,
                                   -152.7627337461449031},
                        (double[]){  11.4650630285209161,
                                     11.5568484830228009,
                                      9.5827293336264265}, gc_edges, 3),
      generate_cell_deg((double[]){-151.6929566531634066,
                                   -152.7627337461449031,
                                   -150.5840076321059371},
                        (double[]){  11.5568484830228009,
                                      9.5827293336264265,
                                      9.6520960946755832}, gc_edges, 3),
      generate_cell_deg((double[]){-151.6929566531634066,
                                   -150.6265735326831532,
                                   -149.5139953075027108},
                        (double[]){  11.5568484830228009,
                                     13.5446528932721275,
                                     11.6284420125700851}, gc_edges, 3),
      generate_cell_deg((double[]){-151.6929566531634066,
                                   -149.5139953075027108,
                                   -150.5840076321059371},
                        (double[]){  11.5568484830228009,
                                     11.6284420125700851,
                                      9.6520960946755832}, gc_edges, 3)};
    size_t num_cells = sizeof(cells) / sizeof(cells[0]);
 
    struct yac_grid_cell overlap_cells[sizeof(cells) / sizeof(cells[0]) - 1];
    for (size_t i = 0; i < num_cells-1; ++i)
      yac_init_grid_cell(&overlap_cells[i]);
 
    yac_cell_clipping(num_cells - 1, &cells[1], cells[0], &overlap_cells[0]);
 
    double tgt_area = yac_huiliers_area(cells[0]);
    double area_tol = tgt_area * 1e-8;
    double diff_area = tgt_area;
 
    for (size_t i = 0; i < num_cells-1; ++i)
      diff_area -= yac_huiliers_area(overlap_cells[i]);
 
    if (fabs(diff_area) > area_tol)
      PUT_ERR("yac_huiliers_area is too inaccurate");
 
    for (size_t i = 0; i < num_cells; ++i)
      yac_free_grid_cell(&cells[i]);
    for (size_t i = 0; i < num_cells-1; ++i)
      yac_free_grid_cell(&overlap_cells[i]);
  }
 
  { // check for a bug found by Uwe Schulzweida
 
    struct yac_grid_cell Tri =
      generate_cell_deg((double[3]){0.5, 0.5, -0.5},
                        (double[3]){0.0, 0.0, 0.0}, gc_edges, 3);
 
    if (yac_triangle_area(Tri) != 0.0)
      PUT_ERR("ERROR in yac_triangle_area");
    yac_free_grid_cell(&Tri);
 
    Tri = generate_cell_deg((double[3]){0.5, -0.5, 0.5},
                            (double[3]){0.0, 0.0, 0.0}, gc_edges, 3);
 
    if (yac_triangle_area(Tri) != 0.0)
      PUT_ERR("ERROR in yac_triangle_area");
    yac_free_grid_cell(&Tri);
 
    Tri = generate_cell_deg((double[3]){-0.5, 0.5, 0.5},
                            (double[3]){0.0, 0.0, 0.0}, gc_edges, 3);
 
    if (yac_triangle_area(Tri) != 0.0)
      PUT_ERR("ERROR in yac_triangle_area");
    yac_free_grid_cell(&Tri);
  }
 
  {
    double ref_area = 0.0;
    double ref_barycenter[3] = {0.0, 0.0, 0.0};
 
    {
      struct yac_grid_cell ref_cell =
        generate_cell_deg(
          (double[]){0.0,1.0,1.0, 0.0},
          (double[]){0.0,0.0,1.0, 1.0}, gc_edges, 4);
      ref_area = yac_huiliers_area_info(ref_cell, ref_barycenter, 1.0);
      yac_free_grid_cell(&ref_cell);
      normalise_vector(ref_barycenter);
    }
 
    enum {NUM_CORNERS = 6};
    double coordinates_x[NUM_CORNERS] = {0.0, 1.0, 1.0, 0.0, 1.0, 0.0};
    double coordinates_y[NUM_CORNERS] = {0.0, 0.0, 1.0, 0.0, 1.0, 1.0};
 
    for (size_t i = 0; i < NUM_CORNERS; ++i) {
 
      double temp_coordinates_x[NUM_CORNERS];
      double temp_coordinates_y[NUM_CORNERS];
 
      for (size_t j = 0; j < NUM_CORNERS; ++j) {
        temp_coordinates_x[(i+j)%NUM_CORNERS] = coordinates_x[j];
        temp_coordinates_y[(i+j)%NUM_CORNERS] = coordinates_y[j];
      }
      double area = 0.0, barycenter[3] = {0.0, 0.0, 0.0};
      struct yac_grid_cell cell =
        generate_cell_deg(
          temp_coordinates_x, temp_coordinates_y, gc_edges, NUM_CORNERS);
      area = yac_huiliers_area_info(cell, barycenter, 1.0);
      yac_free_grid_cell(&cell);
 
      normalise_vector(barycenter);
      if (fabs(area - ref_area) > YAC_AREA_TOL)
        PUT_ERR("ERROR in yac_huiliers_area_info (area)");
 
      if (get_vector_angle(barycenter, ref_barycenter) > yac_angle_tol)
        PUT_ERR("ERROR in yac_huiliers_area_info (barycenter)");
 
      // check for NANs
      if ((barycenter[0] != barycenter[0]) ||
          (barycenter[1] != barycenter[1]) ||
          (barycenter[2] != barycenter[2]))
        PUT_ERR("ERROR in yac_huiliers_area_info (barycenter NAN)");
    }
  }
 
  { // check influence of lat circle edges on computation of the barycenter
    // of a cell
 
    for (int pole = -1; pole <= 1; pole += 2) {
      for (int cell_order_a = 0; cell_order_a < 2; ++cell_order_a) {
        for (int cell_order_b = 0; cell_order_b < 2; ++cell_order_b) {
 
          enum yac_edge_type ll_edges[3] =
            {YAC_LON_CIRCLE_EDGE, YAC_LON_CIRCLE_EDGE, YAC_LAT_CIRCLE_EDGE};
          double lon[2][3] = {{0.0,0.0,20.0}, {20.0, 20.0, 0.0}};
          struct yac_grid_cell gc_triangle =
            generate_cell_deg(
              lon[cell_order_a],
              (double[]){copysign(88.0,(double)pole),
                        copysign(90.0,(double)pole),
                        copysign(88.0,(double)pole)}, gc_edges, 3);
          struct yac_grid_cell ll_triangle =
            generate_cell_deg(
              lon[cell_order_b],
              (double[]){copysign(88.0,(double)pole),
                        copysign(90.0,(double)pole),
                        copysign(88.0,(double)pole)}, ll_edges, 3);
 
          double gc_barycenter[3] = {0.0, 0.0, 0.0};
          double gc_area =
            yac_huiliers_area_info(gc_triangle, gc_barycenter, 1.0);
          double ll_barycenter[3] = {0.0, 0.0, 0.0};
          double ll_area =
            yac_huiliers_area_info(ll_triangle, ll_barycenter, 1.0);
 
          if (gc_area < 0.0) {
            gc_area = -gc_area;
            gc_barycenter[0] = -gc_barycenter[0];
            gc_barycenter[1] = -gc_barycenter[1];
            gc_barycenter[2] = -gc_barycenter[2];
          }
          normalise_vector(gc_barycenter);
 
          if (ll_area < 0.0) {
            ll_area = -ll_area;
            ll_barycenter[0] = -ll_barycenter[0];
            ll_barycenter[1] = -ll_barycenter[1];
            ll_barycenter[2] = -ll_barycenter[2];
          }
          normalise_vector(ll_barycenter);
 
          // the triangle with the lat circle edge should be bigger
          if ((ll_area - gc_area) < YAC_AREA_TOL)
            PUT_ERR("ERROR in yac_huiliers_area_info (area)");
 
          // the barycenter of the triangle with the gc edges should be closer
          // to the pole
          if (((gc_barycenter[2] - ll_barycenter[2]) * (double)pole) < 1e-9)
            PUT_ERR("ERROR in yac_huiliers_area_info (barycenter)");
        }
      }
    }
  }
 
  return TEST_EXIT_CODE;
}
 
static void utest_test_area(struct yac_grid_cell cell, double ref_area,
                      double (*area_func)(struct yac_grid_cell)) {
 
  double mem_dummy_[128][3];
  enum yac_edge_type edge_dummy[128];
  struct yac_grid_cell test_cell = {.coordinates_xyz = mem_dummy_,
                                .edge_type = edge_dummy,
                                .num_corners = cell.num_corners};
 
  for (int order = -1; order <= 1; order += 2) {
    for (int start = 0; start < (int)(cell.num_corners); ++start) {
 
      for (int i = 0; i < (int)(cell.num_corners); ++i) {
        int j = ((int)(cell.num_corners)+start+i*order)%(int)(cell.num_corners);
        test_cell.coordinates_xyz[i][0] = cell.coordinates_xyz[j][0];
        test_cell.coordinates_xyz[i][1] = cell.coordinates_xyz[j][1];
        test_cell.coordinates_xyz[i][2] = cell.coordinates_xyz[j][2];
        j = ((int)(cell.num_corners) + j - (order < 0))%(int)(cell.num_corners);
        test_cell.edge_type[i] = cell.edge_type[j];
      }
 
      double area = area_func(test_cell);
 
      if (utest_compare_area(area, ref_area)) PUT_ERR("ERROR: wrong area\n");
    }
  }
}
 
static int utest_compare_area(double a, double b) {
 
  double diff = fabs(a - b);
  double tol = MAX(MIN(a,b)*1e-6, YAC_AREA_TOL);
 
  if (diff < tol) return 0;
  else return (a > b) - (a < b);
}