Best way to translate latitude / longitude data into xyz points?

Replies to This Discussion

Permalink Reply by Petras Vestartas on August 26, 2017 at 4:15pm

Lunchbox  converts to datatree or you can write your own script (always the best option for custom needs). Just be caseful with numbers x.xxxxxxxxxxxxxxxxxx, as those strings will be rounded  to doubles that are able to store in memory

Permalink Reply by safda on August 26, 2017 at 4:44pm

Hi Petras,

Thanks for your reply - and I apologize, I realize that I was not at all clear in my initial question! I know how to bring the data in - and would be doing pretty much exactly what you've outlined nicely in your suggestion. My issue is that I believe there needs to be some kind of formula in order to get from lat / long coords to xyz space. When I try plotting as the lat / long coords directly, the geometry looks really off, so I feel like I'm probably missing something? Any geographers out there able to weigh in?

Permalink Reply by Petras Vestartas on August 26, 2017 at 5:19pm

just google this stuff how to convert latitude longitude to cartesian coordinates:

https://stackoverflow.com/questions/1185408/converting-from-longitude-latitude-to-cartesian-coordinates

Because your coordinates are on sphere, while you are mapping to 2D space.

Permalink Reply by Petras Vestartas on August 26, 2017 at 5:20pm

and then smb can say that 

 You are assuming the earth is a sphere, while WGS-84 assumes an ellipsoid

Permalink Reply by Petras Vestartas on August 26, 2017 at 5:21pm

Copy paste:

Just to make the definition complete, in the Cartesian coordinate system:

• the x-axis goes through long,lat (0,0), so longitude 0 meets the equator;
• the y-axis goes through (0,90);
• and the z-axis goes through the poles.

The conversion is:

x = R * cos(lat) * cos(lon)  y = R * cos(lat) * sin(lon)  z = R *sin(lat) 

Where R is the approximate radius of earth (e.g. 6371KM).

If your trigonometric functions expect radians (which they probably do), you will need to convert your longitude and latitude to radians first. You obviously need a decimal representation, not degrees\minutes\seconds (see e.g. here about conversion).

The formula for back conversion:

   lat = asin(z / R)    lon = atan2(y, x) 

asin is of course arc sine. read about atan2 in wikipedia. Don’t forget to convert back from radians to degrees.

Permalink Reply by Petras Vestartas on August 26, 2017 at 5:23pm

So it boils down to:

var earthRadius = 6367; //radius in km
public Point3d convertSphericalToCartesian(latlong)
{
    var lat = DegtoRad (latlong.Latitude);
    var lon = DegtoRad (latlong.Longitude);
    var x = earthRadius * Math.cos(lat)*Math.cos(lon);
    var y = earthRadius * Math.cos(lat)*Math.sin(lon);
    var z = earthRadius * Math.sin(lat);
    return new Point3d(x,y,z);
}

Permalink Reply by safda on August 27, 2017 at 8:04am

Hi Petras,

This is great! Thanks so much for all the info - I really didn't know where to start, but this gives me a lot to work with. I'll dig into it and see how it goes...

Permalink Reply by Petras Vestartas on August 27, 2017 at 10:34am

The last reply is literally math functions achievable though grasshopper component, just read line by line and recreate.