
Geometry : 
From: Adam Wulkiewicz (adam.wulkiewicz_at_[hidden])
Date: 20210706 22:54:05
Hi John,
W dniu 06.07.2021 oÂ 22:39, John Mairs via Geometry pisze:
> I've found some onlineÂ calculators that compute (in 3 dimensions)Â
> 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
> (lonlat) to 3d on the unit circle.Â 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
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