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<DIV>Dear Dev list,</DIV>
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<DIV>I hope this is the correct place to post a request for an update to two comments in /lib/gis/area_poly1.c, and replace it with something more informative.</DIV>
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<DIV>My remarks are based on reading /lib/gis/area_poly1.c from grass-7.0.svn_src_snapshot_2013_07_13.</DIV>
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<DIV>This file has routines for computing areas of polygons on the ellipsoid. The algorithm is hardly described, and it is not trivial to work out what is going on. My comment addresses that deficiency.</DIV>
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<DIV>Regards,</DIV>
<DIV>Richard Roger</DIV>
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<DIV>1. The comment before the routine <FONT face="Courier New">G_begin_ellipsoid_polygon_area</FONT> reads:</DIV>
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<DIV> <FONT face="Courier New">* \brief Begin area calculations.<BR> *<BR> * This initializes the polygon area calculations for the<BR> * ellipsoid with semi-major axis <i>a</i> (in meters) and ellipsoid<BR> * eccentricity squared <i>e2</i>.<BR> *<BR> * \param a semi-major axis<BR> * \param e2 ellipsoid eccentricity</FONT></DIV>
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<DIV>For the comment to be self-consistent, the last line should be:</DIV>
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<DIV><FONT face="Courier New"> * \param e2 ellipsoid eccentricity squared</FONT></DIV>
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<DIV>2. The comment before the routine <FONT face="Courier New">G_ellipsoid_polygon_area</FONT> describes briefly what it<BR>computes:</DIV>
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<DIV> <FONT face="Courier New">* <b>Note:</b> This routine assumes grid lines on the connecting the <BR> * vertices (as opposed to geodesics).</FONT></DIV>
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<DIV>I find this comment less than useful. The method this routine implements for computing area is<BR>not one that I have been able to find explicitly in the literature, i.e., I did not recognize the Qbar<BR>function nor the QBarA, QbarB, etc., constants. As such, it is not at all obvious just what area this<BR>routine computes. With some work, I have been able to figure out what is going on. I suggest<BR>the Note be replaced with, e.g.,</DIV>
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<DIV> <FONT face="Courier New">* <b>Note:</b> This routine computes the area of a polygon on the<BR> * ellipsoid. The sides of the polygon are, in general, not geodesics.<BR> * Each side is actually defined by a linear relationship between<BR> * latitude and longitude, i.e., on a rectangular/equidistant<BR> * cylindrical/Plate Carr{'e}e grid, the side would appear as a<BR> * straight line. For two consecutive vertices of the polygon, <BR> * (lat_1, long1) and (lat_2,long_2), the line joining them (i.e., the<BR> * polygon's side) is defined by:<BR> * lat_2 - lat_1 <BR> * lat = lat_1 + (long - long_1) * ---------------<BR> * long_2 - long_1<BR> * where long_1 < long < long_2. This is not a straight line on <BR> * the ellipsoid.<BR> * The values of QbarA, etc., are determined by the integration of<BR> * the Q function. Into </FONT><A href="http://www.integral-calculator.com"><FONT face="Courier New">www.integral-calculator.com</FONT></A><FONT face="Courier New">, paste this <BR> * expression :<BR> *<BR> * sin(x)+ (2/3)e^2(sin(x))^3 + (3/5)e^4(sin(x))^5 + (4/7)e^6(sin(x))^7<BR> *<BR> * and you'll get their values. (Last checked 30 Oct 2013). <BR> *<BR> * This function correctly computes (within the limits of the series<BR> * approximation) the area of a quadrilateral on the ellipsoid when<BR> * two of its sides run along meridians and the other two sides run<BR> * along parallels of latitude.</FONT></DIV>
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<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><FONT face=Arial><FONT size=2><SPAN class=Redtext><SPAN style="COLOR: #c60c30; mso-bidi-font-family: 'Times New Roman'" lang=EN-US>Dr. R. E. Roger</SPAN></SPAN><SPAN style="COLOR: #002664" lang=EN-US> | Senior Spatial Analyst</SPAN></FONT></FONT></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><FONT face=Arial><FONT size=2><SPAN class=Redtext><SPAN style="COLOR: #c60c30; mso-bidi-font-family: 'Times New Roman'" lang=EN-US>NSW Department of Primary Industries </SPAN></SPAN><SPAN style="COLOR: #002664" lang=EN-US>|</SPAN><SPAN class=Redtext><SPAN style="COLOR: #c60c30; mso-bidi-font-family: 'Times New Roman'" lang=EN-US> NSW Office of Water</SPAN></SPAN></FONT></FONT><SPAN lang=EN-US><FONT color=#003e7e><FONT face=Arial><FONT size=2> <BR><?xml:namespace prefix = st1 ns = "urn:schemas-microsoft-com:office:smarttags" /><st1:Street w:st="on"><st1:address w:st="on">181 <SPAN style="mso-bidi-font-family: Arial">-</SPAN> 183 Anson Street</st1:address></st1:Street></FONT></FONT></FONT></SPAN><FONT face=Arial><FONT size=2><SPAN style="COLOR: #002664" lang=EN-US> | Orange NSW 2800 | <st1:address w:st="on"><st1:Street w:st="on">PO Box</st1:Street> 53</st1:address> | Orange NSW 2800<BR></SPAN><SPAN class=Redtext><SPAN style="COLOR: #c60c30; mso-bidi-font-family: 'Times New Roman'" lang=EN-US>T</SPAN></SPAN><SPAN style="COLOR: #002664" lang=EN-US>: 02 6363 8729 |</SPAN><SPAN lang=EN-US><FONT color=#003e7e> </FONT></SPAN><SPAN class=Redtext><SPAN style="COLOR: #c60c30; mso-bidi-font-family: 'Times New Roman'" lang=EN-US>F</SPAN></SPAN><SPAN style="COLOR: #002664" lang=EN-US>: 02 6361 3839 |</SPAN><SPAN lang=EN-US><FONT color=#003e7e> </FONT></SPAN><SPAN class=Redtext><SPAN style="COLOR: #c60c30; mso-bidi-font-family: 'Times New Roman'" lang=EN-US>E</SPAN></SPAN><SPAN style="COLOR: #002664" lang=EN-US>: <A href="mailto:Richard.Roger@water.nsw.gov.au">Richard.Roger@water.nsw.gov.au</A></SPAN></FONT></FONT><FONT face=Arial><FONT size=2><SPAN lang=EN-US><FONT color=#003e7e> <BR></FONT></SPAN><SPAN class=Redtext><SPAN style="COLOR: #c60c30; mso-bidi-font-family: 'Times New Roman'" lang=EN-US>W</SPAN></SPAN><SPAN style="COLOR: #002664" lang=EN-US>: <A href="http://www.trade.nsw.gov.au/"><SPAN style="COLOR: #002664; TEXT-DECORATION: none; text-underline: none">www.water.nsw.gov.au</SPAN></A></SPAN></FONT></FONT></P>
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