area.c File Reference

#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"

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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 *middle_lat)
static double	lat_edge_correction (double base_vec[3], double a[3], double b[3])
static double	lat_edge_correction_info (double base_vec[3], double a[3], double b[3], double *barycenter, double sign)
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()

static int compute_norm_vector ( double a[], double b[], double norm[] )

inlinestatic

Definition at line 196 of file area.c.

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lat_edge_correction()

static double lat_edge_correction ( double base_vec[3], double a[3], double b[3] )

static

Definition at line 300 of file area.c.

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lat_edge_correction_()

static double lat_edge_correction_ ( double base_vec[3], double a[3], double b[3], double * middle_lat )

static

Definition at line 217 of file area.c.

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lat_edge_correction_info()

static double lat_edge_correction_info ( double base_vec[3], double a[3], double b[3], double * barycenter, double sign )

static

Definition at line 307 of file area.c.

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scalar_product()

static double scalar_product ( double a[], double b[] )

inlinestatic

Definition at line 592 of file area.c.

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tri_area()

static double tri_area ( double u[3], double v[3], double w[3] )

static

Definition at line 186 of file area.c.

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tri_area_()

static double tri_area_ ( struct sin_cos_angle angle_a, struct sin_cos_angle angle_b, struct sin_cos_angle angle_c )

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.

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tri_area_info()

static double tri_area_info ( double ref[3], double a[3], double b[3], double * barycenter, double sign )

static

Definition at line 504 of file area.c.

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tri_area_quarter_angle()

static struct sin_cos_angle tri_area_quarter_angle ( struct sin_cos_angle angle )

inlinestatic

Definition at line 105 of file area.c.

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XYZtoLon()

static double XYZtoLon ( double a[3] )

inlinestatic

Definition at line 213 of file area.c.

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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 449 of file area.c.

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yac_huiliers_area_info()

double yac_huiliers_area_info	(	struct yac_grid_cell	cell,
		double *	barycenter,
		double	sign )

Examples

test_area.c, test_compute_overlap_area.c, and test_partial_areas.c.

Definition at line 539 of file area.c.

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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.

Definition at line 417 of file 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 332 of file area.c.

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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.

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