[Proj] triaxial ellipsoid

Aleksander Yanovskiy yanouski at yandex.by
Thu Jan 10 03:00:25 EST 2013

```Thank you Charles for the explanation! It seems the visualization could be done in SciLab (http://www.scilab.org/).

09.01.2013, 23:57, "Charles Karney" <charles.karney at sri.com>:
> On 2013-01-09 15:06, Aleksander Yanovskiy wrote:
>
>>  Thank you both Charles and Jean-Marc for your work!
>>  The visualizations at http://geographiclib.sourceforge.net/1.29/triaxial.html are really helpfull for understanding the material. Could you please advise me some free software to generate the figures with another initial conditions ?
>>
>>  Aleksander
>
> I can tell you what I did to make the plots:
>
> (1) Compute the path of geodesic using Matlab.  The code for transpolar
> and circumpolar geodesics is straightforward: tabulate the two integrals
> over a period and then use interp1q to interpolate and reverse
> interpolate these integrals, e.g., for circumpolar geodesics:
>
>    sigma -> integral -> omega
>
> Umbilical geodesics are trickier because the rules for traversing the
> umbilical points need to be worked out and coded up.  In addition the
> line isn't well parameterized by either beta or omega when it lies near
> the middle ellipse, so I ended up combining both parameterizations to
> get a smooth result.
>
> (2) To plot, I converted beta,omega to cartesian coordinates, projected
> these to a 2d orthographic plane, replaced the back portions of the
> geodesics by NaN, and used Matlab's 2d plot function.  (I suppose I
> could have used the 3d graphics capabilities of Matlab; but I liked the
> control that I had over the output doing the 2d conversion myself.)
>
> You can equally well use octave for these tasks if you want a free
> solution.
>
> I might end up coding these routines for public consumption.  However
> that's on a back burner for me.  First, I need to write up my algorithm
> for exact sampling from a normal distribution.  See
>
>    http://randomlib.sf.net/html/classRandomLib_1_1ExactNormal.html
```