<font color='black' size='3' face='Georgia, Times New Roman, Times, Serif'><font size="3">Thanks, Charles. Equivalence is the equal-area property.
</font>
<div> <font size="3"><br>
</font>
</div>
<font size="3">
</font>
<div><font size="3"> — daan<br>
<br>
</font>
</div>
<div> <br>
</div>
<div style="font-family:helvetica,arial;font-size:10pt;color:black">-----Original Message-----<br>
From: Charles Karney <charles.karney@sri.com><br>
To: proj <proj@lists.maptools.org><br>
Sent: Thu, Jan 1, 2015 3:18 pm<br>
Subject: Re: [Proj] Jacobi + Guyou projections; conformal map of ellipsoid to sphere<br>
<br>
<div id="AOLMsgPart_0_a93b141c-0eb9-43d0-b4d3-19f457688ef1" style="margin: 0px;font-family: Tahoma, Verdana, Arial, Sans-Serif;font-size: 12px;color: #000;background-color: #fff;">
<pre style="font-size: 9pt;"><tt>Other than Nyrstov <a href="https://dx.doi.org/10.1007/978-3-642-32618-9_17" target="_blank">https://dx.doi.org/10.1007/978-3-642-32618-9_17</a> ,
there's
<a href="http://geocnt.geonet.ru/en/3_axial" target="_blank">http://geocnt.geonet.ru/en/3_axial</a>
J. P. Snyder, Survey Review 38(217), 130-148 (1985)
and references therein
but Snyder's method seems to be much more complicated that Jacobi's
projection (converted into elliptic integrals). I'm not aware of
any work talking about mapping a trixial ellipsoid to a sphere.
However, once you've mapped the ellipsoid to a rectangle, the
mapping to a sphere is straightforward.
BTW, what does "equivalence" mean in this context?
--Charles
On 01/01/2015 04:38 PM, <a href="mailto:strebe@aol.com">strebe@aol.com</a> wrote:
> Hello Charles. Good stuff; thanks.
>
> Do you know of any literature around triaxial-to-spherical mappings in
> general (including other techniques to preserve conformality, as well as
> ones to preserve other traits such as equivalence)?
>
> — daan
>
> -----Original Message-----
> From: Charles Karney <<a href="mailto:charles.karney@sri.com">charles.karney@sri.com</a>>
> To: proj <<a href="mailto:proj@lists.maptools.org">proj@lists.maptools.org</a>>
> Sent: Thu, Jan 1, 2015 1:20 pm
> Subject: [Proj] Jacobi + Guyou projections; conformal map of ellipsoid
> to sphere
>
> I've updated my notes on Jacobi's conformal projection of a triaxial
> ellipsoid; see
>
> <a href="http://geographiclib.sourceforge.net/1.41/jacobi.html" target="_blank">http://geographiclib.sourceforge.net/1.41/jacobi.html</a>
>
> New stuff:
>
> * the limits, ellipsoid of revolution and sphere, are easily obtained;
>
> * the Guyou projection (and hence the Peirce quincuncial projection) are
> special cases of Jacobi's projection (which predates both of these);
>
> * Jacobi + Guyou can be used to map a triaxial ellipsoid conformally
> onto a sphere.
>
> --Charles
>
\
_______________________________________________
Proj mailing list
<a href="mailto:Proj@lists.maptools.org">Proj@lists.maptools.org</a>
<a href="http://lists.maptools.org/mailman/listinfo/proj" target="_blank">http://lists.maptools.org/mailman/listinfo/proj</a>
</tt></pre>
</div>
<!-- end of AOLMsgPart_0_a93b141c-0eb9-43d0-b4d3-19f457688ef1 -->
</div>
</font>