How to perform an affine transformation

static void affineTransformation2D_Example()throws Exception{
    //Define control points.
    IPoint[] controlFromPoints = new IPoint[4];
    //To point.
    IPoint[] controlToPoints = new IPoint[4];
    for (int i = 0; i < 4; i++){
        controlFromPoints[i] = new Point();
        controlToPoints[i] = new Point();
    }
    //From points.
    controlFromPoints[0].putCoords(0, 0);
    controlFromPoints[1].putCoords(0, 1);
    controlFromPoints[2].putCoords(1, 0);
    controlFromPoints[3].putCoords(1, 1);
    //To points.
    controlToPoints[0].putCoords(5, 5);
    controlToPoints[1].putCoords(5, 6);
    controlToPoints[2].putCoords(6, 5);
    controlToPoints[3].putCoords(6, 6);

    //Create an AffineTransformation2D object.
    //You have to use the IAffineTransformation2D3GEN because DefineFromControlPoints
    // uses C-Style Arrays in IAffineTransformation2D, which are not usable in .NET.
    IAffineTransformation2D3GEN affineTransformation2D = new AffineTransformation2D()
        ;
    affineTransformation2D.defineFromControlPoints(controlFromPoints,
        controlToPoints);

    double fromError[] = {
        0
    };
    double toError[] = {
        0
    };
    affineTransformation2D.getRMSError(fromError, toError);
    if (fromError[0] > 0.05)
        System.out.println(
            "RMS error is too large; please redigitize control points");


    //Create a polygon.
    ISegmentCollection tranformPolygon = new Polygon();
    IEnvelope envelope = new Envelope();
    envelope.putCoords(0, 0, 10, 10);
    tranformPolygon.setRectangle(envelope);

    ITransform2D transformee = (ITransform2D)tranformPolygon;
    transformee.transform(esriTransformDirection.esriTransformForward, 
        (ITransformation)affineTransformation2D);

    //DigitizedGeometry is now in the destination coordinate system and should be assigned a 
    //spatial reference.
    //Now you will apply the same transformation directly to an array of double precision values 
    //representing (x,y) points.
    //The x,y values are assumed to be interleaved in the array: fromPoints(0) is the x-coordinate 
    //for the first point, fromPoints(1) is the y-coordinate, etc.
    int length = 50;
    double[][] fromPoints = new double[1][length];
    for (int i = 0; i < length; i++)
        fromPoints[0][i] = (i + 1) * 2;
    double[][] toPoints = new double[1][length];

    affineTransformation2D.transformPointsFF
        (esriTransformDirection.esriTransformForward, fromPoints, toPoints);
    //Print results.
    String report = "";
    for (int i = 0; i < length; i++)
        report = report + "Coordinate before = " + fromPoints[0][i] + 
            " and after transformation = " + toPoints[0][i] + "\n";

    System.out.println(report);

}