问题描述:

I am trying to take a set of angles from 0 to 359 and get the average direction of the angles. I have searched everywhere and some of the examples work but for some reason my code isn't working.

For example the average of the set of {355,355,15,15} should be 5 degrees but they I get a bunch of varying answers that don't make much sense.

I'm using this equation courtesy of wiki:

https://en.wikipedia.org/wiki/Mean_of_circular_quantities

`public static void main(String[] args) {`

//ATAN2(sum_of_sin(theta), sum_of_cos(theta))

double[] numbers = {355,355,15,15};

double sin=0.0, cos=0.0, theta=0.0;

for(double d : numbers) {

sin += Math.sin(d);

cos += Math.cos(d);

}

sin = sin / ((double)numbers.length);

cos = cos / ((double)numbers.length);

// Using only atan2

System.out.println("Atan2 Only: " + Math.toDegrees(Math.atan2(sin, cos)));

// Atan2 Only: 159.71920992022936

// Using the wiki solution

if (sin > 0 && cos > 0) {

theta = Math.atan(sin/cos);

} else if(cos < 0) {

theta = Math.atan(sin/cos) + 180;

} else if(sin < 0 && cos > 0) {

theta = Math.atan(sin/cos) + 360;

}

System.out.println("Wiki Answer: " + theta);

// Wiki Answer: 179.6460334382022

}

You need to convert from degrees to radians for the input to sin and cos then back again for the result:

```
double[] numbers = {355, 5, 15 };
double sin=0.0, cos=0.0, theta=0.0;
for(double d : numbers) {
double s = Math.sin(Math.toRadians(d));
sin += s;
double c = Math.cos(Math.toRadians(d));
cos += c;
}
sin = sin / ((double)numbers.length);
cos = cos / ((double)numbers.length);
// Using only atan2
System.out.println("Atan2 Only: " + Math.toDegrees(Math.atan2(sin, cos)));
// Atan2 Only: 159.71920992022936
// Using the wiki solution
if (sin > 0 && cos > 0) {
theta = Math.atan(sin/cos);
} else if(cos < 0) {
theta = Math.atan(sin/cos) + 180;
} else if(sin < 0 && cos > 0) {
theta = Math.atan(sin/cos) + 360;
}
System.out.println("Wiki Answer: " + theta);
System.out.println("Wiki Answer in degrees: " + Math.toDegrees(theta));
```

output:

```
Atan2 Only: 4.9999999999999964
Wiki Answer: 0.08726646259971642
Wiki Answer in degrees: 4.9999999999999964
```

The math methods in Java assume that you're working in radians, not degrees. Try converting all your values to radians by multiplying them by π / 180 and see if that fixes things.

NOTE: There are considerable flaws to this approach; leaving this answer here so that others understand these flaws. Please see comments between @LutzL and me (@Nadesri) for details.

Perhaps I am missing something... I think you should be able to add all the numbers, take the sum modulo 360 (assuming degrees), and then divide by n

```
private double avgOfAngles(List<int> numbers) {
int n = numbers.size();
int sum = 0;
for (int i=0; i<numbers; i++) {
sum += numbers.get(i);
}
return (double) (sum % 360) / n;
}
```

Of course, the above assumes that acceptable answers range between 0 to 359, inclusive; if you prefer a different range (such as -180 to 179), then the above solution would need to be offset by the appropriate amount.

The wiki notes [0, 360] as a possibly counterintuitive example (since the arithmetic mean is 180 despite that 360 degrees is for most purposes the same thing as 0 degrees); I think the above solution still handles at least this example.

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