TestsCalibratePhysicalVrScene.cs

using UnityEngine;
using System.Collections;

public class CalibrationScript : MonoBehaviour
{
    public Transform P1; //Physic
    public Transform P2; //Physic
    public Transform P3; //Physic

    public Transform V1; //Virtual
    public Transform V2; //Virtual
    public Transform V3; //Virtual

	// Use this for initialization
	void Start () {
        StartCoroutine(Calibrate());
	}

    IEnumerator Calibrate()
    {
        yield return new WaitForSeconds(1);
        
        // 1) Remove all rotation (we will add it manually later)
        transform.rotation = Quaternion.identity;

        yield return new WaitForSeconds(0.5f);

        // 2) translate the Chaperon in a vector that begin at the virtual point to the physical point
        var p1 = P1.position;
        var p2 = P2.position;
        var p3 = P3.position;

        var v1 = V1.position;
        var v2 = V2.position;
        var v3 = V3.position;
                
        var translationVector = new Vector3(p1.x - v1.x, p1.y - v1.y, p1.z - v1.z);
        transform.Translate(translationVector, Space.World);

        yield return new WaitForSeconds(0.5f);

        // 3) Rotate the Chaperon so v2 and p2 touch each other (p1 et v1 already touch so we use this position as the center of rotation)
        // Perpendicular vector calculated by cross. See: https://docs.unity3d.com/Manual/ComputingNormalPerpendicularVector.html
        var rotationVector1 = new Vector3(p1.x - p2.x, p1.y - p2.y, p1.z - p2.z);
        var rotationVector2 = new Vector3(p1.x - v2.x, p1.y - v2.y, p1.z - v2.z);
                
        // Precision problem?
        var parentCenter = createParent(p1);
        parentCenter.transform.rotation = Quaternion.FromToRotation(-rotationVector1, rotationVector2);
        parentCenter.transform.rotation = Quaternion.FromToRotation(p1 - p2, -p1 - v2);
        
        
        
        
        //StartCoroutine(TestSomething(p1, cross, angle));   
                
        //transform.RotateAround(parentCenter.transform.position, cross, angle.magnitude);
        
        //parentCenter.transform.rotation = Quaternion.FromToRotation(p1, rotationVector1, rotationVector2);

        //var cross = Vector3.Cross(rotationVector1, rotationVector2);
        //var angle = Quaternion.ToEulerAngles(Quaternion.FromToRotation(rotationVector1, rotationVector2));
        //transform.RotateAround(cross, angle.magnitude);
        //StartCoroutine(TestSomething(p1, rotationVector1, -rotationVector2));
        yield return new WaitForSeconds(1);

        //yield return new WaitForSeconds(0.5f);
        //var go = createParent(transform.position);
        //yield return new WaitForSeconds(0.5f);

        //go.transform.rotation = Quaternion.FromToRotation(rotationVector1, rotationVector2);

        //yield return new WaitForSeconds(0.5f);
        //removeLastParent();
        //yield return new WaitForSeconds(0.5f);

        
    }

    IEnumerator TestSomething(Vector3 center, Vector3 cross, Vector3 angle)
    {
        var parentCenter = createParent(center);
        while (true)
        {
            parentCenter.transform.RotateAround(cross, angle.magnitude);

            //parentCenter.transform.rotation = Quaternion.FromToRotation(rotationVector1, rotationVector2);
            //transform.RotateAround(parentCenter.transform.position, cross, magnitude);
            yield return new WaitForSeconds(0.5f);
        }
    }

    private GameObject parentGameObject;
    private GameObject createParent(Vector3 position)
    {
        parentGameObject = new GameObject("Center of rotation");
        parentGameObject.transform.position = position;
        transform.parent = parentGameObject.transform;
        return parentGameObject;
    }

    private void removeLastParent()
    {
        transform.parent = parentGameObject.transform.parent;
        GameObject.Destroy(parentGameObject);
    }

    
}