<html><head></head><body name="Mail Message Editor"><div><span class="Apple-style-span" style="">Oscar:<br><div><span class="Apple-style-span" style=""><br></span></div><div><span class="Apple-style-span" style="">Not to answer the question about proj specifically, since I do not know, but to talk about the Bonne in general: The Bonne is highly unstable when the standard parallel is near the equator. The formulas must get recast from the usual forms, and, once recast, must further get developed as a (very complicated) series for latitudes close to the equator. If proj is not doing this then gross errors should be expected.<div><span class="Apple-style-span" style=""><br></span></div><div><span class="Apple-style-span" style="">Why do you say that the difference probably cannot be attributed to instabilities?<div><span class="Apple-style-span" style=""><br></span></div><div><span class="Apple-style-span" style="">The Bonne with a standard parallel of 0° is identical to the sinusoidal.</span></div></span></div></span></div><div><span class="Apple-style-span" style=""><br></span></div><div><span class="Apple-style-span" style="">Regards,<div><span class="Apple-style-span" style="">— daan Strebe</span></div></span></div></span></div><div><span class="Apple-style-span" style=""><br></span></div><div><span class="Apple-style-span"><br></span></div><div id="replyPrefaceElement">On Nov 21, 2010, at 3:24:01 AM, OvV_HN <ovv@hetnet.nl> wrote:</div><br><blockquote style="padding-left: 5px; margin-left: 5px; border-left-width: 2px; border-left-style: solid; border-left-color: blue; color: blue; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><span class="Apple-style-span" style="font-family: monospace; font-size: 11px; ">There is probably a more serious problem in one of the other projections,<span class="Apple-converted-space"> </span><br>namely the Bonne projection.<br>If lat_0 is close to 0, the Sinuoidal projection is taken.<br>If one compares in a limiting case the northing, produced by the Sinusoidal,<span class="Apple-converted-space"> </span><br>and for the same set of parameters the northing, produced by the Bonne<span class="Apple-converted-space"> </span><br>projection, a difference of perhaps 300 meters will be obtained. This<span class="Apple-converted-space"> </span><br>observation is valid for both the ellipsoidal and the spherical projections.<br>This difference can probably not be attributed to instabilities in the<span class="Apple-converted-space"> </span><br>calculation or a difference between a limiting lat_0 (of 1e-10 deg) and<span class="Apple-converted-space"> </span><br>zero.<br>Can somebody enlighten me? Does the Sinusoidal projection differ a bit too<span class="Apple-converted-space"> </span><br>much from the Bonne (but no one cares)?<br>Is there something wrong in the proj/libproj code?<br>Or did I do something wrong?<br><br>My test case:<br><br>Bessel 1841 ellipsoid<br>lat=40d 32m; lon=-7d 16m;<br>lat0=1e-10; lon0=-8.131906111111112;<br>x0=20000; y0=10000; [meters]<br>bonne ellipsoidal projection<br>Result: x = 93299.284; y = 4497999.829; [meters]<br><br>for lat0=0 the Sinusoidal projection is taken.<br>Result: x = 93299.284; y = 4498299.575;<br>Difference in y: 299.75 m<br><br>Oscar van Vlijmen<br><br></span></span></blockquote><div><span class="Apple-style-span"><br></span></div><div class="aol_ad_footer" id="uDB5A0EB4F1A445A98B285DD87F074471"></div></body></html>