Euler Angles and Vectors

Questions & Answers
1

Hi, I am learning how to make a third-person game and I noticed that Euler Angles uses vectors in order to rotate objects. (Look at the marked area in the screenshot, mine is almost the same as that.) I am having trouble to understand how vectors can be used to represent the rotation of the object. Thank you in advance.

169309-unity.png
169309-unity.png1537×764 52.7 KB

2

Any rotation can be represented by a sum of rotations about the 3 main axis (X, Y, and Z axis). For example if I wanted to represent a rotation about the y axis in the positive direction, or in other words a rotation to the right, I could use the vector (0, y, 0) where y represents how large of an angle in degrees I want to rotate. Similarly if I want to tilt forward or backward I could rotate about the x axis. A rotation of (0, 0, 0) represents an object that is aligned with the 3 axis (“forward” for the object is along the world Z axis, “up” for the object is along the world Y axis, and “right” for the object is along the world X axis). Therefore, the orientation of any object can be represented as an offset in degrees along some combination of the 3 axis, relative to this default orientation. So if I wanted to represent a more complex rotation, I could simply find which combination of basic axial rotations add up to represent the overall rotation.
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It is worth noting that given any orientation there are multiple sets of Vector3’s (what we call Euler Angles) that represent that orientation. For example, the default orientation can be represented by (0, 0, 0) OR (0, 360, 0) OR (360, 360, 360) etc.
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Also worth noting is that it matters in what order you apply each axial rotation. When you give Unity a rotation of (10, 20, 30) it will first take the rotation about the X axis, then apply the rotation about the Y axis, then apply the rotation about the Z axis. Other programs may not use this convention. To see why the order matters, imagine a rotation of (90, 90, 0). Rotating about the X axis then the Y axis (IMPORTANT: this is the new local Y axis after applying the rotation, NOT the world Y axis) will give a different rotation than first rotating on the Y axis, then rotating on the X axis. Edit: The order is actually Z, then X, Then Y

3

Thanks for your reply. I still can’t get this topic. Let’s say we have a script like this:
169318-basicscript.png

As we know it makes the character move forward 1 unity if we press “W”. Right ?
The thing that I don’t get is that how those x, y, z are converted when we write something like this:

target.eulerAngles = new Vector3(0, 90, 0);

4

to convert to true vector degree in the inspector use

    if(transform.localEulerAngles.x != lastXDegree)
    {
        lastXDegree = transform.localEulerAngles.x;

        Debug.Log("transform.localEulerAngles.x = " + transform.localEulerAngles.x);

        float xDegree = ((lastXDegree + 540) % 360) - 180;

        Debug.Log("Convert X Degree = " + xDegree);

        Debug.Log("Sin X = " + Mathf.Sin(xDegree));
        Debug.Log("Cos X = " + Mathf.Cos(xDegree));
    }