area.h File Reference

Structs and interfaces for area calculations. More...

#include "basic_grid.h"
#include "clipping.h"

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Macros
#define	YAC_AREA_TOL   ((0.02 * 0.02) / (6371.2290 * 6371.2290))

Functions
double	yac_triangle_area (struct yac_grid_cell cell)
	Calculate the area of a triangle on a unit sphere.
double	yac_cell_area (struct yac_grid_cell cell)
	Calculate the area of a cell on a unit sphere.
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.
double	yac_huiliers_area_info (struct yac_grid_cell cell, double *barycenter, double sign)

Detailed Description

Structs and interfaces for area calculations.

Definition in file area.h.

Macro Definition Documentation

YAC_AREA_TOL

#define YAC_AREA_TOL   ((0.02 * 0.02) / (6371.2290 * 6371.2290))

an area of 20m x 20m on the Earth Surface is equivalent to an area on the unit sphere:

Examples

test_area.c, and test_basic_grid_data.c.

Definition at line 23 of file area.h.

Function Documentation

yac_cell_area()

double yac_cell_area

(

struct yac_grid_cell

cell

)

Calculate the area of a cell on a unit sphere.

Generalized version of triangle_area

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

Parameters

[in]

cell

cell for which he area shall be calculated

Returns

area of the triangle

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.

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 )

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.

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

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

Definition at line 21 of file area.c.

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