void FormTheBridgeShape()
    {
        startVerticesCoordinates = ((GameObject)vertexStart).GetComponent<VertexController>().GetTriodVerticesArray(triodStart);//local coordinates of triods vertices
        endVerticesCoordinates = ((GameObject)vertexEnd).GetComponent<VertexController>().GetTriodVerticesArray(triodEnd);
        startShape = ((GameObject)vertexStart).GetComponent<VertexController>().GetTriodShape(triodStart);//in the local coordinates of the vertex
        endShape = ((GameObject)vertexEnd).GetComponent<VertexController>().GetTriodShape(triodEnd);
        ShapeClass originalEndShape = ((GameObject)vertexEnd).GetComponent<VertexController>().GetTriodShape(triodEnd);

        UpdateLineRendererPositions();

        //------------------------------
        //------------------------------
        //generate shapes fo the bridge
        ShapeClass profile = new ShapeClass();
        profile.CopyFrom(startShape);
        bridgeShapes = new List<ShapeClass>();
        startQ = localStartTriodTransfom.rotation;
        endQ = localEndTriodTransform.rotation;
        Quaternion originalEndQ = endQ;

        Matrix4x4 eM = Matrix4x4.TRS(new Vector3(), endQ * GetTwistQuaternion(), new Vector3(-1, -1, 1));
        endQ = QuaternionFromMatrix(eM);
        endQ = MultiplyByScalar(endQ, 1f / GetQuaternionLength(endQ));

        if(vertexStart == vertexEnd && !isNew)
        {
            middlePointDistance = middlePointDistanceSelfe;
        }
        isNew = true;

        startMatrix = Matrix4x4.TRS(localStartTriodTransfom.position, startQ, new Vector3(1, 1, 1));
        endMatrix = Matrix4x4.TRS(localEndTriodTransform.position, endQ, new Vector3(1, 1, 1));
        Matrix4x4 orignalEndMatrix = Matrix4x4.TRS(localEndTriodTransform.position, originalEndQ * GetTwistQuaternion(), new Vector3(1, 1, 1));
        originalEndShape.MapsTo(orignalEndMatrix);

        startShape.MapsTo(startMatrix);
        endShape.MapsTo(endMatrix);

        bridgeShapes.Add(startShape);

        Quaternion currentRotation = startQ;

        List<ShapeClass> firstPassShapes = new List<ShapeClass>();
        firstPassShapes.Add(startShape);
        for (int i = 1; i <= segmentsCount; i++)
        {
            Quaternion middleQ = currentRotation;
            Matrix4x4 middleMatrix = Matrix4x4.TRS(knotPositions[i], middleQ, new Vector3(1, 1, 1));
            Quaternion delta;
            if (i < segmentsCount)
            {
                delta = Quaternion.FromToRotation(middleMatrix.GetColumn(1), (knotPositions[i + 1] - knotPositions[i - 1]).normalized);
            }
            else
            {
                delta = Quaternion.FromToRotation(middleMatrix.GetColumn(1), (knotPositions[i] - knotPositions[i - 1]).normalized);
            }
            middleQ = delta * middleQ;
            middleMatrix = Matrix4x4.TRS(knotPositions[i], middleQ, new Vector3(1, 1, 1));
            Quaternion twistRotation = Quaternion.AngleAxis(GetTwistAngle() / (float)segmentsCount, middleMatrix.GetColumn(1));
            middleQ = twistRotation * middleQ;
            middleMatrix = Matrix4x4.TRS(knotPositions[i], middleQ, new Vector3(1, 1, 1));
            ShapeClass middleShape = new ShapeClass();
            middleShape.CopyFrom(profile);
            middleShape.MapsTo(middleMatrix);

            firstPassShapes.Add(middleShape);

            currentRotation = middleQ;
        }
        //find angle between end shape and target shape
        float errorAngle = ShapeClass.GetAngleBetween(firstPassShapes[firstPassShapes.Count - 1], originalEndShape);
        //print(errorAngle);
        //bridgeShapesTemp = firstPassShapes;

        currentRotation = startQ;

        //form the bridge shapes
        for (int i = 1; i <= segmentsCount; i++ )
        {
            Quaternion middleQ = currentRotation;
            Matrix4x4 middleMatrix = Matrix4x4.TRS(knotPositions[i], middleQ, new Vector3(1, 1, 1));
            Quaternion delta;
            if(i < segmentsCount)
            {
                delta = Quaternion.FromToRotation(middleMatrix.GetColumn(1), (knotPositions[i + 1] - knotPositions[i - 1]).normalized);
            }
            else
            {
                delta = Quaternion.FromToRotation(middleMatrix.GetColumn(1), (knotPositions[i] - knotPositions[i - 1]).normalized);
            }
            middleQ = delta * middleQ;
            middleMatrix = Matrix4x4.TRS(knotPositions[i], middleQ, new Vector3(1, 1, 1));
            //Quaternion twistRotation = Quaternion.AngleAxis((GetTwistAngle() / (float)segmentsCount) + (errorAngle / (float)segmentsCount), middleMatrix.GetColumn(1));
            Quaternion twistRotation = Quaternion.AngleAxis(AnglePiClamp(GetTwistAngle() + errorAngle) / (float)segmentsCount, middleMatrix.GetColumn(1));
            middleQ = twistRotation * middleQ;
            middleMatrix = Matrix4x4.TRS(knotPositions[i], middleQ, new Vector3(1, 1, 1));
            ShapeClass middleShape = new ShapeClass();
            middleShape.CopyFrom(profile);
            middleShape.MapsTo(middleMatrix);

            if(i < segmentsCount)
            {
                bridgeShapes.Add(middleShape);
            }
            else
            {
                ShapeClass tsh = new ShapeClass();
                tsh.CopyFrom(middleShape);
                tsh.MatchTo(originalEndShape);

                //and match to vertices of the Vertex
                tsh.WeldToMesh(endVerticesCoordinates, localEndTriodTransform);

                bridgeShapes.Add(tsh);
            }

            currentRotation = middleQ;
        }
    }
    // Use this for initialization
    void Start()
    {
        knotPositions = new Vector3[pointsNumber];
        shapes = new List<ShapeClass>();
        for (int i = 0; i < pointsNumber; i++ )
        {
            knotPositions[i] = GetPointPositionInSpline(new Vector3(), new Vector3(0, 1, 0), new Vector3(2, 3, 0), new Vector3(3, 3, 0), (float)i / (float)(pointsNumber - 1));
        }
        originalShape = new ShapeClass(new Vector3[]{new Vector3(-1, 0, -1), new Vector3(-1, 0, 1), new Vector3(1, 0, 1), new Vector3(1, 0, -1)});

        shapes.Add(originalShape);

        //startQ = new Quaternion(0, 0, 1, 0);
        startQ = Quaternion.Euler(0, 0, 0);
        startMatrix = Matrix4x4.TRS(new Vector3(), startQ, new Vector3(1, 1, 1));
        endQ = Quaternion.Euler(0, 0, -90);
        //endQ = new Quaternion(0, 1, 0, 0);
        endMatrix = Matrix4x4.TRS(new Vector3(3, 3, 0), endQ, new Vector3(1, 1, 1));
        //endQ = QuaternionFromMatrix(endMatrix);

        print("end Quaternion=" + endQ.ToString() + " start Quaternion=" + startQ.ToString());
        print("startMatrix=" + startMatrix.ToString());

        //calculate angle between quaternions
           // float angle = (180 * Mathf.Acos(Quaternion.Dot(startQ, endQ))) / Mathf.PI;
        float angle = Mathf.Acos(Quaternion.Dot(startQ, endQ) / (GetQuaternionLength(startQ) * GetQuaternionLength(endQ)));
        //print("Angle=" + angle.ToString());

        endShape = new ShapeClass();
        endShape.CopyFrom(originalShape);
        endShape.MapsTo(endMatrix);

        //calculate other shapes
        for (int i = 1; i < pointsNumber-1; i++ )
        {
            //Quaternion middleQ = Quaternion.Lerp(startQ, endQ, (float)i * 100 / (float)(pointsNumber - 1));
            Quaternion middleQ = GetInterpolatedQuaternion(startQ, endQ, angle, (float)i / (float)(pointsNumber - 1));
            print(middleQ.ToString() + " " + ((float)i / (float)(pointsNumber - 1)).ToString());
            Matrix4x4 middleMatrix = Matrix4x4.TRS(knotPositions[i], middleQ, new Vector3(1, 1, 1));

            ShapeClass middleShape = new ShapeClass();
            middleShape.CopyFrom(originalShape);
            middleShape.MapsTo(middleMatrix);

            shapes.Add(middleShape);

        }

        shapes.Add(endShape);
    }