/// <summary>
/// Converts the toric representation to world coordinates
/// </summary>
/// <returns>Vector3 in world coordinates</returns>
public Vector3 ToWorldPosition()
{
Vector3 C;
float last = (vecAB.magnitude * Mathf.Sin(_alpha.toRad() + _theta.toRad() / 2)) / Mathf.Sin(_alpha.toRad());
Vector3 n = -vecAB;
n = n.normalized;
Vector2 n2 = new Vector2(n.x, n.z);
float tmp = n2[0];
n2[0] = -n2[1];
n2[1] = tmp;
Vector3 z = new Vector3(n2.x, 0, n2.y);
z = z.normalized;
Vector3 t = Vector3.Cross(z, n);
//horizontal rotation
Quaternion qT = Quaternion.AngleAxis(_theta.angle() / 2, t.normalized);
//vertical rotation
Quaternion qP = Quaternion.AngleAxis(_phi.angle(), n);
Vector3 res = qP * qT * vecAB;
C = res * last / vecAB.magnitude + A;
return(C);
}
private Quaternion computeTiltAngle(float tilt)
{
FixAngle phi = new FixAngle(tilt);
return(Quaternion.AngleAxis(phi.angle(), _mainCamera.transform.forward));
}
//Returns the maximum value of theta for a given alpha
public float getMaxTheta()
{
return(2 * (180 - _alpha.angle()));
}