Projection is almost ECEF but on a pure sphere not an ellipsoid in usual GIS systems?

[ecopirate]

It looks like that the mesh is on an ECEF coordinate system, but on a pure sphere not an ellipsoid in usual GIS systems.

Originally posted by @LexSong in #4 (comment)

Greetings LexSong

Following your insight into the use of ECEF projection I tried firing-up BlueMarble Geographic Calculator and started experimenting. My workflow is to:

1. Copy out the object file's "v: X Y Z" coordinates into a plain CSV file using Notepad++.
2. In BlueMarble set source projection as "Geocentric WGS 84"
3. Set output projection as "Geodetic WGS 84"
4. Import into ArcGIS and check the positioning.

Tried on two areas in the UK and the Bahamas.
So far area extent and Longitude positions of the results looks okay
HOWEVER Latitude in both test cases is about 20 km off in a Northerly direction.

So...really great if you could please explain a little bit more what you mean when you say the exact ECEF projection used is "a pure sphere not an ellipsoid in usual GIS systems."?
And any suggestion on

how to handle that??

Thanks!

Ian

Example showing projection error for the Bahama test:

[LexSong]

What I mean it's that you shouldn't use projections like WGS84. Just calculate latitudes and longitudes directly from XYZ, assume that the Google earth is a perfect sphere.

[LexSong]

The formula is:

R = sqrt (x^2+y^2+z^2)
Latitude = arcsin(z/R)

[ecopirate]

Thanks Lex Song,

Assuming Radius of Earth is exactly: 6,371 km (6371000 meters)

The full formulae would then be :
R = sqrt (x^2+y^2+z^2)    
Latitude = arcsin(z/R)  
Longitude = arctan(y/x)
Height = R - 6371000

Quick Google Sheets calculator based on the above here:
https://docs.google.com/spreadsheets/d/1CVc_ldL6gmUG51IYMtCQbr88_Yo9Y1458bw1CAglfgA/edit?usp=sharing

Cheers,

ian

[LexSong]

Height = R - 6371000

Well, it's way more complicated than that. I'm not sure about how Google did choose their height reference. I can't even get a good estimation from the low-resolution mesh of the whole globe. In some places, I think the sea level may even have several Kms differences. The height is not as useful as latitude and longitude here.

[ecopirate]

Yep, I also haven't find been able to find much detail on how Google chose there spatial references.
But quite happy here with the results of replacing the lines calculating vertices x,y,x points in dump_obj.js with the following:

EDITED
let pi = Math.PI;
let R = 0;

	R = Math.sqrt((_x * _x) + (_y * _y) + (_z * _z)); 
            x = 180.0 / pi * Math.atan2(_y ,_x);
	y = 180.0 / pi * Math.asin(_z / R);
	
	z = R - 6371010;

[retroplasma]

They use 6371010 for the radius.

[desmondCTNG]

Yep, I also haven't find been able to find much detail on how Google chose there spatial references.
But quite happy here with the results of replacing the lines calculating vertices x,y,x points in dump_obj.js with the following:

EDITED
let pi = Math.PI;
let R = 0;

	R = Math.sqrt((_x * _x) + (_y * _y) + (_z * _z)); 
            x = 180.0 / pi * Math.atan2(_y ,_x);
	y = 180.0 / pi * Math.asin(_z / R);
	
	z = R - 6371010;

Are these edits refering to line 212 to line 214 of dump_obj.js? Or also line 262 to 264 of dump_obj.js?