Geometry Boost List: Re: [geometry] transformation from ECEF x,y,z to LatLongAlt (LLA)

From: Adam Wulkiewicz (adam.wulkiewicz_at_[hidden])
Date: 2021-07-06 22:54:05

Hi John,

W dniu 06.07.2021 o 22:39, John Mairs via Geometry pisze:
> I've found some online calculators that compute (in 3 dimensions)  
> ECEF x,y,z to LLA and back.
> https://www.oc.nps.edu/oc2902w/coord/llhxyz.htm 
> <https://www.oc.nps.edu/oc2902w/coord/llhxyz.htm>
>
> And I would like to do the same thing using boost geometry.
>
> I watched Adam's 2019 Fos4G in Bucharest and I think I saw that only 
> 2D is supported.
>
> I'm new to GIS so all of the vocabulary terms are quite overwhelming.
>
> I have seen the example (transform_2) in the docs of going from degree 
> (lon-lat) to 3d on the unit circle.  Even with that example i don't 
> understand how (theta 5.0 and phi = 15.0) map to lat/long.

You're talking about this example right?
https://www.boost.org/doc/libs/1_76_0/libs/geometry/doc/html/geometry/reference/algorithms/transform/transform_2.html
The coordinate system used there is spherical polar. See what is theta 
and phi here:
https://en.wikipedia.org/wiki/Spherical_coordinate_system

You either need bg::cs::spherical_equatorial<bg::degree> or 
bg::cs::geographic<bg::degree> to represent a point as longitude and 
latitude. And while cs::spherical_equatorial is supported in transform() 
by default cs::geographic is not. By "by default" I mean "without 
passing an additional parameter - strategy" like that:
https://www.boost.org/doc/libs/1_76_0/libs/geometry/doc/html/geometry/reference/algorithms/transform/transform_3_with_strategy.html

My talk was about SRS transformations, this is a different part of the 
library than transform(), though they can be used together. It's more or 
less Proj (https://proj.org) adapted to work with Boost.Geometry well. 
The 2d/3d support depends on specific projection. Conversion between 3d 
geographic coordinates and 3d ECEF cartesian coordinates is supported.

#include <boost/geometry.hpp>
#include <boost/geometry/srs/transformation.hpp>

int main()
{
 Â Â Â  namespace bg = boost::geometry;
 Â Â Â  using pt_geo_t = bg::model::point<double, 3, 
bg::cs::geographic<bg::degree>>;
 Â Â Â  using pt_car_t = bg::model::point<double, 3, bg::cs::cartesian>;

 Â Â Â  bg::srs::transformation
 Â Â Â Â Â Â Â  <
 Â Â Â Â Â Â Â Â Â Â Â  bg::srs::spar::parameters<bg::srs::spar::proj_lonlat, 
bg::srs::spar::ellps_wgs84>,
bg::srs::spar::parameters<bg::srs::spar::proj_geocent>
 Â Â Â Â Â Â Â  > tr;

 Â Â Â  pt_geo_t pt_geo{ lon, lat, h };
 Â Â Â  pt_car_t pt_car;

 Â Â Â  tr.forward(pt_geo, pt_car);
 Â Â Â  tr.inverse(pt_car, pt_geo);
}

In case you wanted to see how it's done or to implement it by yourself:
https://gssc.esa.int/navipedia//index.php/Ellipsoidal_and_Cartesian_Coordinates_Conversion

Adam