How to perform an affine transformation

Performing an affine transformation

private void AffineTransformation2D_Example()
{
    // 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 PointClass();
        controlToPoints[i]=new PointClass();
    }
    // 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 IAffineTransformation2D3GEN because DefineFromControlPoints
    // uses C-Style Arrays in IAffineTransformation2D, which are not usable in .NET.
    IAffineTransformation2D3GEN affineTransformation2D=new
        AffineTransformation2DClass();
    affineTransformation2D.DefineFromControlPoints(ref controlFromPoints, ref
        controlToPoints);

    double fromError=0;
    double toError=0;
    affineTransformation2D.GetRMSError(ref fromError, ref toError);
    if (fromError > 0.05)
    {
        System.Windows.Forms.MessageBox.Show(
            "RMS error is too large; please redigitize control points");
    }

    // Create a polygon.
    ISegmentCollection tranformPolygon=new Polygon()as ISegmentCollection;
    IEnvelope envelope=new EnvelopeClass();
    envelope.PutCoords(0, 0, 10, 10);
    tranformPolygon.SetRectangle(envelope);

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

    // 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[length];
    for (int i=0; i < length; i++)
    {
        fromPoints[i]=(i + 1) * 2;
    }
    double[] toPoints=new double[length];

    affineTransformation2D.TransformPointsFF
        (esriTransformDirection.esriTransformForward, ref fromPoints, ref toPoints);

    // Print results.
    String report="";
    for (int i=0; i < length; i++)
    {
        report=report + "Coordinate before=" + fromPoints[i] + 
            " and after transformation=" + toPoints[i] + "\n";
    }
    System.Windows.Forms.MessageBox.Show(report);

}

Private Sub AffineTransformation2D_Example()
    ' Define control points: Source points.
    Dim controlFromPoints(4) As IPoint
    
    ' Target points.
    Dim controlToPoints(4) As IPoint
    For i As Integer=0 To 4
        controlFromPoints(i)=New PointClass()
        controlToPoints(i)=New PointClass()
    Next i
    
    ' 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 IAffineTransformation2D3GEN because DefineFromControlPoints
    ' uses C-Style Arrays in IAffineTransformation2D, which are not usable in .NET.
    Dim affineTransformation2D As IAffineTransformation2D3GEN=New AffineTransformation2DClass()
    affineTransformation2D.DefineFromControlPoints(controlFromPoints, controlToPoints)
    Dim fromError As Double=0
    Dim toError As Double=0
    AffineTransformation2D.GetRMSError(fromError, toError)
    
    If fromError > 0.05 Then
        System.Windows.Forms.MessageBox.Show("RMS error is too large; please redigitize control points")
    End If
    
    ' Create a polygon.
    Dim tranformPolygon As ISegmentCollection=New Polygon()
    Dim envelope As IEnvelope=New EnvelopeClass()
    envelope.PutCoords(0, 0, 10, 10)
    tranformPolygon.SetRectangle(envelope)
    Dim transformee As ITransform2D=CType(tranformPolygon, ITransform2D)
    transformee.Transform(esriTransformDirection.esriTransformForward, 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.
    Dim Length As Integer=50
    Dim fromPoints(Length) As Double
    For i As Integer=0 To Length Step 1
        fromPoints(i)=((i + 1) * 2)
    Next i
    
    Dim toPoints(Length) As Double
    AffineTransformation2D.TransformPointsFF(esriTransformDirection.esriTransformForward, fromPoints, toPoints)
    
    ' Print results.
    Dim report As String=""
    For i As Integer=0 To Length -1 Step 1
        report=report & "Coordinate before=" & fromPoints(i) & " and after transformation=" & toPoints(i) & ControlChars.NewLine
    Next i
    System.Windows.Forms.MessageBox.Show(report)
End Sub

• ESRI.ArcGIS.Geometry