Biel Simon - 1 month ago 17

Java Question

I know there are lots of questions and answers about this topic or related but i've beenn trying for 2 hours and still haven't benn able to figure it.

I would like to get a function that looks like this:

`public static Vector rotateVector(Vector v, Vector axis, double angle){`

}

Where the axis is a unit vector that defines the plane of rotation (the vector v rotates towards the vector axis if angle is positive)

I have already taken a look at rotation matrices but haven't been able to implement those to the above function

Answer

Rotating (x, y, z) counter clockwise around **unit** vector (u, v, w) by angle theta produces a vector (xPrime, yPrime, zPrime):

```
double xPrime = u*(u*x + v*y + w*z)*(1d - Math.cos(theta))
+ x*Math.cos(theta)
+ (-w*y + v*z)*Math.sin(theta);
double yPrime = v*(u*x + v*y + w*z)*(1d - Math.cos(theta))
+ y*Math.cos(theta)
+ (w*x - u*z)*Math.sin(theta);
double zPrime = w*(u*x + v*y + w*z)*(1d - Math.cos(theta))
+ z*Math.cos(theta)
+ (-v*x + u*y)*Math.sin(theta);
```

Source here.