area_poly1.c File Reference

GIS Library - Polygon area calculation routines. More...

#include <math.h>
#include <grass/gis.h>
#include "pi.h"

Include dependency graph for area_poly1.c:

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Macros
#define	TWOPI   M_PI + M_PI

Functions
int	G_begin_ellipsoid_polygon_area (double a, double e2)
	Begin area calculations. More...
double	G_ellipsoid_polygon_area (const double *lon, const double *lat, int n)
	Area of lat-long polygon. More...

Detailed Description

GIS Library - Polygon area calculation routines.

(C) 2001-2013 by the GRASS Development Team

This program is free software under the GNU General Public License (>=v2). Read the file COPYING that comes with GRASS for details.

Author

GRASS GIS Development Team

Date

1999-2008

Definition in file area_poly1.c.

Macro Definition Documentation

#define TWOPI   M_PI + M_PI

Definition at line 20 of file area_poly1.c.

Referenced by G_ellipsoid_polygon_area().

Function Documentation

int G_begin_ellipsoid_polygon_area	(	double	a,
		double	e2
	)

Begin area calculations.

This initializes the polygon area calculations for the ellipsoid with semi-major axis a (in meters) and ellipsoid eccentricity squared e2.

Parameters

[in]	a	semi-major axis
[in]	e2	ellipsoid eccentricity

Returns

always returns 0

Definition at line 65 of file area_poly1.c.

Referenced by G_begin_polygon_area_calculations().

double G_ellipsoid_polygon_area	(	const double *	lon,
		const double *	lat,
		int	n
	)

Area of lat-long polygon.

Returns the area in square meters of the polygon described by the n pairs of lat,long vertices for latitude-longitude grids.
Note: This routine computes the area of a polygon on the ellipsoid. The sides of the polygon are rhumb lines and, in general, not geodesics. Each side is actually defined by a linear relationship between latitude and longitude, i.e., on a rectangular/equidistant cylindrical/Plate Carr{'e}e grid, the side would appear as a straight line. For two consecutive vertices of the polygon, (lat_1, long1) and (lat_2,long_2), the line joining them (i.e., the polygon's side) is defined by:

                                    lat_2  -  lat_1 
    lat = lat_1 + (long - long_1) * ---------------
                                    long_2 - long_1

where long_1 < long < long_2. The values of QbarA, etc., are determined by the integration of the Q function. Into www.integral-calculator.com, paste this expression :

sin(x)+ (2/3)e^2(sin(x))^3 + (3/5)e^4(sin(x))^5 + (4/7)e^6(sin(x))^7

and you'll get their values. (Last checked 30 Oct 2013).

This function correctly computes (within the limits of the series approximation) the area of a quadrilateral on the ellipsoid when two of its sides run along meridians and the other two sides run along parallels of latitude.

Parameters

[in]	lon	array of longitudes
[in]	lat	array of latitudes
[in]	n	number of lat,lon pairs

Returns

double Area in square meters

Definition at line 137 of file area_poly1.c.

References Radians, and TWOPI.

Referenced by G_area_of_polygon().