[GRASSSVN] r58164  grass/branches/develbranch_6/lib/gis
svn_grass at osgeo.org
svn_grass at osgeo.org
Thu Nov 7 04:12:03 PST 2013
Author: neteler
Date: 20131107 04:12:02 0800 (Thu, 07 Nov 2013)
New Revision: 58164
Modified:
grass/branches/develbranch_6/lib/gis/area_poly1.c
Log:
area_poly1.c function documentation improved (contributed by Richard Roger richard.roger at water dot nsw dot gov dot au)
Modified: grass/branches/develbranch_6/lib/gis/area_poly1.c
===================================================================
 grass/branches/develbranch_6/lib/gis/area_poly1.c 20131107 12:11:06 UTC (rev 58163)
+++ grass/branches/develbranch_6/lib/gis/area_poly1.c 20131107 12:12:02 UTC (rev 58164)
@@ 1,10 +1,9 @@

/**
* \file area_poly1.c
*
* \brief GIS Library  Polygon area calculation routines.
*
 * (C) 20012008 by the GRASS Development Team
+ * (C) 20012013 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.
@@ 18,7 +17,6 @@
#include <grass/gis.h>
#include "pi.h"

#define TWOPI M_PI + M_PI
static double QA, QB, QC;
@@ 98,9 +96,32 @@
* <b>n</b> pairs of <b>lat,long</b> vertices for latitudelongitude
* grids.
* <br>
 * <b>Note:</b> This routine assumes grid lines on the connecting the
 * vertices (as opposed to geodesics).
+ * <b>Note:</b> 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.integralcalculator.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.
+
+ *
* \param[in] lon array of longitudes
* \param[in] lat array of latitudes
* \param[in] n number of lat,lon pairs
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