how can I rotate these coordinates to North South?

[red pike]

I have two sets of coordinates in cartesian format which is like x,y,z from the center of the earth. the The first point is a base station which never moves, and the second is a rover which moves.

I want to get coordinates of the rover on a relative plane from the base station which I achieved doing the following:

passing the base station point to this function

    public static List<Double> getTransformAngles(Point3d pointA) {
        double rotationZ = Math.atan2(pointA.getY(), pointA.getX());
        double pow = Math.pow(pointA.getX(), 2) + Math.pow(pointA.getY(), 2);
        double rotationY = Math.atan2(Math.sqrt(pow), pointA.getZ());

        return List.of(-rotationZ, -rotationY);
    }```

then I rotate the rover point by the rotations and do the same with the base station then subtract the two.

this WORKS but the I want the X axis to be N and S. any idea what to rotate it by to make it do that?

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[proper lantern]

Hm... If you're working with spherical geometry, perhaps spherical coordinates are a better idea? Cartesian are harder to work with in this case.

[red pike]

yeah but in the end I just have a 2d plane which assumes the earth is flat

like im working on a super small scale so 2d is actually easier

[proper lantern]

Ohh, flatland, ok. Though, the coordinates won't be from the center of the sphere (as there is none), but from an arbitrary point.
As for the code, can't really help with that. My coding knowledge is quite limited. I recommend looking into rotation matrices in 3D, though.

[red pike]

code wise is fine

just the math

here is visually what I mean

starting position is 10 20 0

first rotation is -1.1071487177940904 rad on the Z

which aligns it on the x

[proper lantern]

Well, no need for so many decimals 😅

[red pike]

im just copy and pasting

[proper lantern]

Oh, ok.

[red pike]

next rotation is -1.5707963267948966 rad on the y

so now it's 0, 0, y height irrelevant

this would be the base station

so imagine another point doing the same rotations but from a slightly different starting point

well it would mean that the relative positon between the two points is on the plane of the base station

make sense?

[proper lantern]

Well, suppose you have a point r0 around which you rotate, and let M be the rotation matrix. Then the result will be:
r' = r0 + M(r - r0)

[red pike]

so here is where im asking for help

i already know my math works and does what I want it to do

but the relative plane isn't north south

[red pike]

i want to rotate the rover around the base in such a way that moving perfectly X mean I was going perfect North

or really so the axis aligns with an axis of the earth which is how we started