random.onUnitCircle ?

Questions & Answers
1

there's random onUnitSphere, but it doesn't work as random.onUnitCircle if it's being reduced from Vector3 to Vector2.

what are there other ways of choosing a random point on a circle.(not inside it, not outside, just on the very edge)

6

THE EASIEST WAY IS THIS:

Random.insideUnitCircle.normalized;

Just random inside unit circle first, and then normalized it. This will convert the vector to be 1 in magnitude, which is the same as random on unit circle. Hope this helps!

3

Similar to Peter’s answer, you could get a random angle and pass that to a custom function that accepts an angle and radius.

It would be akin to something like:

Vector2 GetUnitOnCircle(float angleDegrees, float radius) {

    // initialize calculation variables
    float _x = 0;
    float _y = 0;
    float angleRadians = 0;
    Vector2 _returnVector;

    // convert degrees to radians
    angleRadians = angleDegrees * Mathf.PI / 180.0f;

    // get the 2D dimensional coordinates
    _x = radius * Mathf.Cos(angleRadians);
    _y = radius * Mathf.Sin(angleRadians);

    // derive the 2D vector
    _returnVector = new Vector2(_x, _y);

    // return the vector info
    return _returnVector;
}
2

You could get a random value between `0` and `2pi` radians then find the sin and cos of that and make them your values in a `Vector2`.

5

Another way:

  1. Use Unity methods to get a random point.

  2. Normalize the vector to be one unit long.

  3. Multiply by radius to get desired length.

    public static Vector2 RandomOnUnitCircle2( float radius) 
{
	Vector2 randomPointOnCircle = Random.insideUnitCircle;
	randomPointOnCircle.Normalize();
	randomPointOnCircle *= radius;
	return randomPointOnCircle;
}
public static Vector3 RandomOnUnitSphere( float radius) 
{
	Vector3 randomPointOnCircle = Random.insideUnitSphere;
	randomPointOnCircle.Normalize();
	randomPointOnCircle *= radius;
	return randomPointOnCircle;
}
7

I was surprised to see so much resistance to trig here. As game programmers, we should either strive to make our code optimal (not use a bunch of high-level calls that bring in extra overhead) as well as improve what we know as far as not just programming, but mathematics. Peter G deserves the answer to this thread, as he provided the answer. I can’t say whether or not it is the absolute best option, but it is most certainly hard to think of something that can compete. Using Peter G’s suggestion, I was able to produce this:

float randomAngle = Random.Range(0f, Mathf.PI * 2f);
Vector2 randomPointAround2DCircumference = new Vector2(Mathf.Sin(randomAngle), Mathf.Cos(randomAngle)).normalized;

Wrapping this in a function should now be fairly easy:

 public Vector2 GetPointOnUnitCircleCircumference()
 {
     float randomAngle = Random.Range(0f, Mathf.PI * 2f);
     return new Vector2(Mathf.Sin(randomAngle), Mathf.Cos(randomAngle)).normalized;
 }

I have tested this in Unity and I am seeing the intended results. Enjoy!

4

I must say I got scared away when I saw the answer about sinuses and cosinues and "pi" and radians, and converting them to vectors

so I just did something low-tech, but it works. for reference:

var circleCentre = Vector3.zero;
var circleDirection = Vector3.zero;
var ray = new Ray(circleCentre, circleDirection);

function Update () {
    if(Input.GetKeyDown(KeyCode.Return))
    {
        ray.direction = Vector3(Random.Range(-1.0,1.0), Random.Range(-1.0,1.0), 0);


//and just to have some visual clue:
        var cube = GameObject.CreatePrimitive(PrimitiveType.Cube);
        cube.transform.position = ray.GetPoint(2);
        cube.transform.localScale = Vector3(.1,.1,.1);
    }
}

Thank you for those high-tech answers though. I hope I'll be able to work on such hardcore mathematical stuff soon enough.