#include <stdlib.h>#include <stdio.h>#include <math.h>#include <float.h>#include "area.h"#include "basic_grid.h"#include "clipping.h"#include "geometry.h"#include "utils_core.h"#include "ensure_array_size.h"
Go to the source code of this file.
Functions | |
| static double | scalar_product (double a[], double b[]) |
| double | yac_triangle_area (struct yac_grid_cell cell) |
| Calculate the area of a triangle on a unit sphere. | |
| static struct sin_cos_angle | tri_area_quarter_angle (struct sin_cos_angle angle) |
| static double | tri_area_ (struct sin_cos_angle angle_a, struct sin_cos_angle angle_b, struct sin_cos_angle angle_c) |
| static double | tri_area (double u[3], double v[3], double w[3]) |
| static int | compute_norm_vector (double a[], double b[], double norm[]) |
| static double | XYZtoLon (double a[3]) |
| static double | lat_edge_correction (double base_vec[3], double a[3], double b[3]) |
| double | yac_pole_area (struct yac_grid_cell cell) |
| Calculate the area of a cell in a 3d plane on a unit sphere. | |
| double | yac_planar_3dcell_area (struct yac_grid_cell cell) |
| Area calculation on a unit sphere of a planar polygon in 3D. | |
| double | yac_huiliers_area (struct yac_grid_cell cell) |
| Area calculation on a unit sphere taken from ESMF based on L'Huilier's Theorem. | |
| static double | tri_area_info (double ref[3], double a[3], double b[3], double *barycenter, double sign) |
| double | yac_huiliers_area_info (struct yac_grid_cell cell, double *barycenter, double sign) |
Function Documentation
◆ compute_norm_vector()
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inlinestatic |
◆ lat_edge_correction()
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static |
◆ scalar_product()
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inlinestatic |
◆ tri_area()
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static |
◆ tri_area_()
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static |
area of a spherical triangle based on L'Huilier's Theorem
source code is taken from code by Robert Oehmke of Earth System Modeling Framework (www.earthsystemmodeling.org)
it has been extended by a more accurate computation of vector angles
the license statement for this routine is as follows: Earth System Modeling Framework Copyright 2002-2013, University Corporation for Atmospheric Research, Massachusetts Institute of Technology, Geophysical Fluid Dynamics Laboratory, University of Michigan, National Centers for Environmental Prediction, Los Alamos National Laboratory, Argonne National Laboratory, NASA Goddard Space Flight Center. Licensed under the University of Illinois-NCSA License.
- Remarks
- all edges are on great circle
Definition at line 134 of file area.c.
◆ tri_area_info()
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static |
◆ tri_area_quarter_angle()
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inlinestatic |
◆ XYZtoLon()
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inlinestatic |
◆ yac_huiliers_area()
| double yac_huiliers_area | ( | struct yac_grid_cell | cell | ) |
Area calculation on a unit sphere taken from ESMF based on L'Huilier's Theorem.
(http://mathworld.wolfram.com/LHuiliersTheorem.html)
(http://mathforum.org/library/drmath/view/65316.html)
(http://math.stackexchange.com/questions/9819/area-of-a-spherical-triangle)
The cell in split up into triangles that all have one corner in common, then the area for each of the triangle is computed and summed up to build the area of the cell. L'Huilier's Theorem is used to compute the area of the triangles. This seems to be sufficiently accurate for elements on the Earth surface with edge lengths of approx. 100 m and gives results comparable to our implementation of Huilier's algorithm for edge lengths of up to 1 km.
- Examples
- test_area.c, test_basic_grid_data.c, test_clipping.c, test_compute_overlap_area.c, test_lat_clipping.c, and test_partial_areas.c.
Definition at line 396 of file area.c.
◆ yac_huiliers_area_info()
| double yac_huiliers_area_info | ( | struct yac_grid_cell | cell, |
| double * | barycenter, | ||
| double | sign | ||
| ) |
- Examples
- test_compute_overlap_area.c, and test_partial_areas.c.
Definition at line 482 of file area.c.
◆ yac_planar_3dcell_area()
| double yac_planar_3dcell_area | ( | struct yac_grid_cell | cell | ) |
Area calculation on a unit sphere of a planar polygon in 3D.
(http://gaim.umbc.edu/2010/06/03/polygon-area)
This area calculation works for any planar polygon (concave or convex) with non-intersecting edges in 3D. It requires vertex coordinates in Carthesian space. In our case this is applicable for very small elements on the sphere.
- Examples
- test_area.c.
◆ yac_pole_area()
| double yac_pole_area | ( | struct yac_grid_cell | cell | ) |
Calculate the area of a cell in a 3d plane on a unit sphere.
see http://geomalgorithms.com/a01-_area.html
other references:
http://www.mathopenref.com/coordpolygonarea2.html
http://geomalgorithms.com/a01-_area.html
http://stackoverflow.com/questions/2350604/get-the-area-of-a-3d-surface
- Parameters
-
[in] cell cell for which the area shall be calculated
- Returns
- area of the cell
- Examples
- test_area.c.
Definition at line 279 of file area.c.
◆ yac_triangle_area()
| double yac_triangle_area | ( | struct yac_grid_cell | cell | ) |
Calculate the area of a triangle on a unit sphere.
Adopted from the ICON code, mo_base_geometry.f90 provided by Luis Kornblueh, MPI-M.
The algorithm is based on Girards' theorem and formula.
Converted to c by Rene Redler, MPI-M.
Vertex coordinates need to be provided as cartesian coordinates
The algorithm is based on Girards' theorem and formula.
R: Earth radius n: number of vertices pi: guess what Theta: Sum of inner angle of the element (in rad)
The Formula reads as
S = [ Theta - (n-2) * pi ] * R*R
Ad with n=3 for triangles simplifies to
S = [ Theta - pi ] * R*R
- Parameters
-
[in] cell cell for which he area shal be calculated
- Returns
- approximate area of the cell
- Examples
- test_area.c.
Definition at line 21 of file area.c.
