Rotate Vector3 Manually?

Questions & Answers
1

Hi all, i need to find a way to reproduce unity3 rotation on a simply server that dosn’t have fancy unity3 functionality.

So far i have come up with:

`public static Vector3 Rotate(Vector3 x, float _x, float _y, float _z)
{
float angle = _z;
x = new Vector3(
x.x * Mathf.Cos(Mathf.Deg2Rad * angle) - x.y * Mathf.Sin(Mathf.Deg2Rad * angle),
x.x * Mathf.Sin(Mathf.Deg2Rad * angle) + x.y * Mathf.Cos(Mathf.Deg2Rad * angle),
x.z);
angle = _y;
x = new Vector3(
x.x * Mathf.Cos(Mathf.Deg2Rad * angle) + x.z * Mathf.Sin(Mathf.Deg2Rad * angle),
x.y,
-x.x * Mathf.Sin(Mathf.Deg2Rad * angle) + x.z * Mathf.Cos(Mathf.Deg2Rad * angle));
angle = _x;
x = new Vector3(
x.x,
x.y * Mathf.Cos(Mathf.Deg2Rad * angle) - x.z * Mathf.Sin(Mathf.Deg2Rad * angle),
x.y * Mathf.Sin(Mathf.Deg2Rad * angle) + x.z * Mathf.Cos(Mathf.Deg2Rad * angle));

    return x;
}`

However i can’t reproduce rotation angles that i input from transform.rotation.eulerAngles, on some angles it works on some not, any idea why?

3

This one will exactly replicate the rotation that a Transform experiences with the given worldspace eulerangles:

public static Vector3 Rotate(Vector3 aVec, Vector3 aAngles)
{
    aAngles *= Mathf.Deg2Rad;
    float sx = Mathf.Sin(aAngles.x);
    float cx = Mathf.Cos(aAngles.x);
    float sy = Mathf.Sin(aAngles.y);
    float cy = Mathf.Cos(aAngles.y);
    float sz = Mathf.Sin(aAngles.z);
    float cz = Mathf.Cos(aAngles.z);
    aVec = new Vector3(aVec.x * cz - aVec.y * sz, aVec.x * sz + aVec.y * cz, aVec.z                    );
    aVec = new Vector3(aVec.x                   , aVec.y * cx - aVec.z * sx, aVec.y * sx + aVec.z * cx );
    aVec = new Vector3(aVec.x * cy + aVec.z * sy, aVec.y                   , -aVec.x * sy + aVec.z * cy);
    return aVec;
}

So those two lines will result in the same vector:

Vector3 input; // some vector

Vector3 v1 = transform.TranslateDirection(input);
Vector3 v2 = Rotate(input, transform.eulerAngles);

As others have said the order in which you apply the rotations matters. Unity uses the local order Y - X - Z. The worldspace order is always the reverse, so Z - X - Y.

2

What you’re trying to do is like rotating the bits in a bitmap on the surface of a cube in 3-space. It works if the cube’s surface is aligned with the global X-Y plane, but not generally. General rotations require quaternions, to be generally useful your Rotate() function needs to use quaternion multiplication.

Try this experiment: rotate the vector (0,0,1) by (90°,45°,45°). 1st, rotate 45° about the Z axis. In Yaw/Pitch/Roll terms, a roll. Still at (0,0,1). 2nd, rotate 90° about the X-axis, a pitch. Now we’re at (0,1,0). Last, rotate 45° about the Y axis, another roll. Still at (0,1,0). This might not be the anticipated result. So the question is what does a rotation by (90°,45°,45°) mean? Rotate 45° about an axis tilted (90°,45°,0)? By Yaw = 90°,Pitch = 45°, Roll = 45°? Rotate 1st about X then Y then Z? They all give different answers.

The transformation first Z then X then Y is the transform.rotation.eulerAngles() transform using degrees and is equivalent to

Quaternion.Euler(0, 0, z) * Quaternion.Euler(x, 0, 0) * Quaternion.Euler(0, y, 0)

so to duplicate transform.rotation.eulerAngles(), the Rotate() function in psudocode might look like

return x * Quaternion.Euler(0, 0, _z) * Quaternion.Euler(_x, 0, 0) * Quaternion.Euler(0, _y, 0);

Other transforms are useful, for a camera azimuth/altitude transformation try

transform.rotation = Quaternion.Euler(0, Az, 0) * Quaternion.Euler(-Alt, 0, 0);

or Yaw/Pitch/Roll:

transform.rotation = Quaternion.Euler(0, Yaw, 0) * Quaternion.Euler(Pitch, 0, 0) * Quaternion.Euler(0, 0, Roll);
4

The others have given you the full answer, but you will have to dramatically improve your understanding of quaternions before you can work in this realm.