Find two points which are on 120 degrees from a third point.

Question

I drew this graphic: circle-points

If you check better all 4 points including the center of the circle are on Z = z1. I know the center of the circle which is (x1, y1, z1). I also know the top point which is (x1, y1 + r, z1). And I know that the other two points are on angle of 120 degrees. How can I find x2, y2, x3 and y3 using some useful functions from Unity.

Note: I know pytagorean theroem. No need to mention it.

I could possibly make some math with lines on a plane and where they intersect but that seems rather complex.

Answer 1

Best Answer

Answer by Garazbolg · Oct 14, 2015 at 08:48 AM

Or you could do it with trigonometry :

x2 = x1 + cos(30°) * r;

x3 = x1 - cos(30°) * r;

y2 = y3 = y1 - sin(30°) * r;

but to make it even simpler 'sin(30°)' is equal to 1/2

so y2 = y3 = y1 - r/2;

In Unity :

 float cos30_R = Mathf.Cos(30 * Mathf.Deg2Rad) * r;
 
 x2 = x1 + cos30_R;
 x3 = x1 -  cos30_R;
 
 y2 = y3 = y1 - r/2;

It should use less ressources then your method.

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Answer 2

Answer by 0potable · Oct 06, 2015 at 09:18 AM

One quick dirty way on top of my head : use a Transform as a helper.

1) transform.position = circleCenter

2) transform.LookAt(topPoint, Vector3.up)

3) transform.Rotate(Vector3.up * 120f)

4) transform.TransformPoint(Vector3.forward * radius) <<

5) Repeat step 3 & 4 for the last point

Note that the Vector3.up of the second step need to represent the "up" direction of the circle.

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Answer 3

Answer by spinnerbox · Oct 14, 2015 at 07:32 AM

This function works perfectly:

  function RotatePointAroundPivot(point: Vector3, pivot: Vector3, angles: Vector3): Vector3 {
    var dir: Vector3 = point - pivot; // get point direction relative to pivot
    dir = Quaternion.Euler(angles) * dir; // rotate it
    point = dir + pivot; // calculate rotated point
    return point; // return it
  }

From this question: http://answers.unity3d.com/questions/532297/rotate-a-vector-around-a-certain-point.html

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Find two points which are on 120 degrees from a third point.

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