Align a plane with 3 normal

Questions & Answers
1

I have a region with 3 normals and now I want to align a plane in this region. The two shown in the picture and one perpendicular facing up (created with pca, but that doesent matter)

112376-region-with-3-normal.png
112376-region-with-3-normal.png1056×417 189 KB 

GameObject Gplane = GameObject.CreatePrimitive(PrimitiveType.Plane);
Transform t = Gplane.transform;
t.position = segment.middle;
t.localScale = new Vector3((2*segment.dist_pc1)/10, 0, (2*segment.dist_pc2)/10);
t.rotation = Quaternion.FromToRotation(Vector3.right, segment.middle - segment.pc1);
t.rotation *= Quaternion.FromToRotation(Vector3.forward, segment.middle - segment.pc2);
t.rotation *= Quaternion.FromToRotation(Vector3.up, segment.normal)

I create a newgameobject from primitivetype plane. get transform and set its position and scale (segment is a object which contains all information about this region).
Then I want to align the plane with the three normal, each rotation works fine and aligns the plane with the axis, but multiplied its messed up.

112377-region-with-3-normal-pls-plane.png
112377-region-with-3-normal-pls-plane.png935×549 144 KB

As you can see the plane is kind of between the two normals (blue and red, which you can hardly see but i am sure you can image)
Any advice in what i am doing wrong is appreciated since i am not too familiar with quaternions and rotations.
Thanks in advance.

2

After digging some more I found a working solution.

Instead of calclating the angle one can set the right, forward und up vector of any transform. This will do rotation automatically

t.right = segment.pc1

But since the vector is rotated by itself (Vector3, two defining position in space, the third may let the vector rotate around itself) the plane may be rotated around the this axis (and t.forward is not alinged with segment.pc2)
To fix this i calculated the angle between t.forward and segment.pc2

float angle = Vector3.Angle(t.forward, segment.pc2);
t.RotateAround(segment.middle, t.right, - angle);

RotateAround allowed me to keep the axis that was already set and correct.

I tried to align a plane with two vector3 that is facing in the corresponding directions of the two vectors. Maybe this can help anybyody.