Random Direction Vector Relative To Current Direction

Question

I have a 2D vector where the x and y values are randomly generated using a range between -1 and 1 respectively. I use this as the direction to move an object in which works great.

var direction = Vector2(Random.Range(-1f, 1f), Random.Range(-1f, 1f));

What I would like to do is after some period of time, randomly generate a new direction vector, but this time keep the same "relative" direction that it currently has. Probably within 45 degrees or so on either side of the current direction.

So I'd like to randomly generate a new direction vector within a range of 45 degrees on either side of it's current direction vector, and start moving in that new direction. Does that make sense?

I'm not quite sure how to go about this, but I'm sure this isn't too difficult if someone could help get me started. Thanks!

Answer 1

Random direction relative to current direction:

Assuming you already have an initial direction vector prepared, as per DMGregory's comment on the OP:

1. Generate a random float that will represent the angle to change the direction by. Since the angle should be constrained to a 90 degree arc "forward" of the initial direction, we restrain the range of the random value to be from -45 to 45:
   • var angle = Random.Range(-45f, 45f);
2. Since you're working with 2D rather than 3D, the axis used for the rotation necessary for the new angle is already known: Z. Because of this, a cross-product calculation is unnecessary.
3. Unity already implements rotation matrices, in the form of the Quaternion class. Since the rotation is done through the Z axis, we can generate the quaternion for the rotation using the Euler() static method.
   • var quaternion = Quaternion.Euler(0, 0, angle);
4. Finally, we multiply the quaternion by the original direction vector, to get a new, rotated vector:
   • var newDirection = quaternion * direction;
   • Important note: To rotate a vector by a quaternion, it's important that the quaternion always comes first in the multiplication.
5. Now that each step of the operation is clear, we can simplify it by making it inline:
   • direction = Quaternion.Euler(0, 0, Random.Range(-45f, 45f)) * direction;

---

Extra:

If you intend to "stack" these operations on top of each-other, it's important to note that the constraint will be relative to the current direction in the current step, and so, overall, the 90 degree cone might not be respected; in fact it's hypothetically possible to get a 90 degree turn (180 cone) with two operations, a full "U-turn" with 4, and a circle with 8.

To get consecutive operations to always generate new angles within the initial 90 degree cone, you need to make the constraint be determined relative to the current step's angle with respect to an "ideal" direction (the initial direction, in this case):

var point = Vector2.zero;
var idealDirection = Vector2.up;
var direction = idealDirection;
for(var i = 0; i < 10; i++){
    var constraint = Vector2.SignedAngle(direction, idealDirection);
    direction = Quaternion.Euler(0, 0, Random.Range(-45f + constraint, 45f +
 constraint)) * direction;
    var newPoint = point + direction;
    Debug.DrawLine(point, newPoint, Color.yellow, 1f);
    point = newPoint;
}
//Done this in cellphone, from memory, but hopefully creates something resembling a directional "lighting bolt".
//It should work, but if I made any mistakes due to lacking VS's intellisense, do tell!
//And regardless of that, the most important: Have fun!

Answer 2

I've done this, and its not too hard.

1. Firstly, generate a random non 0 length vector. Normalise it.
2. Cross product with your current direction vector to create a rotation axis.
3. Generate a random value in your -45 to 45 degree range (radians usually I do!)
4. Depending on your flavour, I usually generate a matrix with the angle and the rotation matrix.
5. Multiply your direction vector with said matrix.

Im sure someone has a better method, but this is what I have done in past.