Changing direction in 3D - unity3d

Question

I am working on a 3D project, in Unity.
I have an object moving in a confined space. The object have a fixed velocity, and it bounces back once they reach the space limit.
I want it to change direction once every n seconds.
The problem I am facing is: How to rotate a 3D vector by a given angle.
In 2D is pretty easy, while in 3D I am not sure how to handle it.
Can someone help me with that?

Answer 1

In 2D this is simple...
In three 3 as well.
You can e.g. simply rotate a Vector3 about any given Euler angles via
var newVector = Quaternion.Euler(x, y, z) * oldVector;
question remains where you get those angles from and whether those are random or you are rather looking for Reflect the vector once the objects reach your defined area constraints.
You can as well simply invert the individual components like e.g.
// Note for simplicity reasons this is not an actual "distance"
// but rather the maximum of each individual axis
public float maxDistance;
private Rigidbody _rigidbody;
private void Start ()
{
_rigidbody = GetComponent<Rigidbody>();
_rigidbody.velocity = Random.insideUnitSphere.normalized;
}
private void FixedUpdate()
{
var vel = _rigidbody.velocity;
var pos = _rigidbody.position;
if(Mathf.Abs(pos.x) >= maxDistance)
{
vel.x *= -1;
}
if(Mathf.Abs(pos.y) >= maxDistance)
{
vel.y *= -1;
}
if(Mathf.Abs(pos.z) >= maxDistance)
{
vel.z *= -1;
}
_rigidbody.velocity = vel;
}

Answer 2

You can change directions by a certain angle on a certain axis, making it similar to 2D.
If you are moving the object with its transform you can easily rotate an object with the Rotate method on the game object transform.
//in a script attached to the game object you want to rotate
transform.Rotate(Vector3.up, Random.Range(90,270), Space.self);
You can now use transform.forward to move the object.
If you want to go deeper into 3D rotation have a look at Quaternions
You can use the Quaternion.operator * to rotate one rotation by another, or to rotate a vector by a rotation.
Consider also looking at the Vector3 class methods such as Reflect and RotateTowards.
Tip: To keep a consistent speed across all directions, consider normalizing the direction vector, (0,1,1) will travel faster than (0,0,1).
You can normalize any vector as follows:
Vector3 direction = Vector3.up + Vector3.forward; //(0,1,1)
direction = direction.normalized; //(0,0.71,0.71)

Answer 3

I managed to do the thing I wanted. Firstly, I computed a Vector3 that was orthogonal to the current transform.forward; then I rotate that angle around itself of a random angle between 0 and 360 degrees, and finally I used that generated vector as axis for the rotation to apply to the velocity of my object.
Here is the code:
public static void ChangeObjectDirection(Rigidbody rb, int angle, float velocity)
{
// get the transform of rb
var t = rb.gameObject.transform;
// get the current velocity direction
var direction = t.forward;
// generate a normalized orthogonal vector wrt the current velocity direction
var orth = OrthogonalVector(direction);
// rotate the orthogonal vector around himself of a random angle between 0 and 360
orth = Quaternion.AngleAxis(Random.Range(0, 360), direction) * orth;
// generate random rotational angle in degrees
var randomAngle = Random.Range(-angle, angle);
// rotate the current velocity direction of randomAngle around the orth vector
direction = Quaternion.AngleAxis(randomAngle, orth) * direction;
// update the velocity direction
t.forward = direction;
rb.velocity = direction * velocity;
}
private static Vector3 OrthogonalVector(Vector3 u)
{
var a = u.x;
var b = u.y;
var c = u.z;
Vector3 v;
if (b == 0 && c == 0)
{
v = new Vector3(0f, 1f, 1f);
}
else if (a == 0 && c == 0)
{
v = new Vector3(1f, 0f, 1f);
}
else if (a == 0 && b == 0)
{
v = new Vector3(1f, 1f, 0f);
}
else
{
if (c != 0)
{
// ax + bx + cz == 0 with x == 1 and y == 1 => z = (-a - b) / c
v = new Vector3(1f, 1f, (-a - b) / c);
}
else
{
// ax + bx + cz == 0 with y == 1 and z == 1 => c = (-b - c) / a
v = new Vector3((-b - c) / a, 1f, 1f);
}
}
v = v.normalized;
return v;
}