great circle arc

Programming Questions

ijeoma

in Programming Questions • 1 year ago

I've been trying to create a great circle arc between the US and China but I can't get the algorithm/code right. I tried changing the return line to converting latN and lonN to degree but that wasnt right either... so I just kept it how it is in the js code. You can download the example I wrote at http://ekeneijeoma.com/processing/GreatCircleTest.zip

float[] interpolate(float[] latlon1, float[] latlon2, float f) {
float lat1 = radians(latlon1[1]);
float lon1 = radians(latlon1[0]);
float lon2 = radians(latlon2[1]);
float lat2 = radians(latlon2[0]);
float d = 2 * asin(sqrt(pow(sin((lat1 - lat2) / 2), 2) + cos(lat1)
* cos(lat2) * pow(sin((lon1 - lon2) / 2), 2)));
float bearing = atan2(sin(lon1 - lon2) * cos(lat2), cos(lat1)
* sin(lat2) - sin(lat1) * cos(lat2) * cos(lon1 - lon2))
/ -(PI / 180);
bearing = bearing < 0 ? 360 + bearing : bearing;
float A = sin((1 - f) * d) / sin(d);
float B = sin(f * d) / sin(d);
float x = A * cos(lat1) * cos(lon1) + B * cos(lat2) * cos(lon2);
float y = A * cos(lat1) * sin(lon1) + B * cos(lat2) * sin(lon2);
float z = A * sin(lat1) + B * sin(lat2);
float latN = atan2(z, sqrt(pow(x, 2) + pow(y, 2)));
float lonN = atan2(y, x);
return new float[] {
radians(latN), radians(lonN)
};
}

Replies(2)

jbum

Re: great circle arc

1 year ago

I see two bugs.

1) Your code assumes the parameters begin passed in have lat in the [0] index, and lon in the [1] index. This code gets it wrong.

float lat1 = radians(latlon1[1]); // should be 0
float lon1 = radians(latlon1[0]); // should be 1
float lon2 = radians(latlon2[1]); // correct
float lat2 = radians(latlon2[0]); // correct

I would also suggest swapping lines 3 and 4 to avoid trouble.

2) Your function computes lat/lon in radians. But it appears you want them in degrees. Your return statement should be changed from this:

return new float[] { radians(latN), radians(lonN) };

to this:

println(latN + "," + lonN);

return new float[] { degrees(latN), degrees(lonN) };

I added the println so you can see the values.

If something is already in radians. Don't use the radians() function on it. Ditto with degrees.

Functions like atan2() *always* return results in radians.

In my own code, I have gotten into the habit of avoiding the use of degrees entirely (it's an unnatural system invented by humans for human consumption. Ditto with using 100 for percentages). However, I understand how you might find it useful to use degrees for expressing latitude/longitude, and what you're doing here is fine.

ijeoma

Re: great circle arc

1 year ago

thanks for the reply. somehow my last reply got deleted but i talked it out with my co-worker and meant to post an answer but you beat me to it!

great circle arc

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