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

Questions & Answers
1

I drew this graphic:

55626-circle1.png
55626-circle1.png900×485 19.4 KB

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.

2

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.

4

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.

3

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: Rotate a vector around a certain point. - Questions & Answers - Unity Discussions