Examples of ae.java.awt.geom.AffineTransform.preConcatenate()

ae.java.awt.geom.AffineTransform.preConcatenate()
Concatenates an AffineTransform Tx to this AffineTransform Cx in a less commonly used way such that Tx modifies the coordinate transformation relative to the absolute pixel space rather than relative to the existing user space. Cx is updated to perform the combined transformation. Transforming a point p by the updated transform Cx' is equivalent to first transforming p by the original transform Cx and then transforming the result by Tx like this: Cx'(p) = Tx(Cx(p)) In matrix notation, if this transform Cx is represented by the matrix [this] and Tx is represented by the matrix [Tx] then this method does the following:
```
 [this] = [Tx] x [this] 
```
@param Tx the AffineTransform object to beconcatenated with this AffineTransform object. @see #concatenate @since 1.2

        Color[] colors = paint.getColors();
        int numStops = colors.length;
        Point2D pt1 = paint.getStartPoint();
        Point2D pt2 = paint.getEndPoint();
        AffineTransform at = paint.getTransform();
        at.preConcatenate(sg2d.transform);


        if (!linear && numStops == 2 &&
            paint.getCycleMethod() != CycleMethod.REPEAT)
        {
            // delegate to the optimized two-color gradient codepath

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        double fx = focus.getX();
        double fy = focus.getY();


        // transform from gradient coords to device coords
        AffineTransform at = paint.getTransform();
        at.preConcatenate(sg2d.transform);
        focus = at.transform(focus, focus);


        // transform unit circle to gradient coords; we start with the
        // unit circle (center=(0,0), focus on positive x-axis, radius=1)
        // and then transform into gradient space

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            AffineTransform tx = sgv.ftx;
            if (!dtx.isIdentity() || gtx != null) {
                tx = new AffineTransform(sgv.ftx);
                if (gtx != null) {
                    tx.preConcatenate(gtx);
                    dx = (float)tx.getTranslateX(); // uses ftx then gtx to get translation
                    dy = (float)tx.getTranslateY();
                }
                if (!dtx.isIdentity()) {
                    tx.preConcatenate(dtx);

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                    tx.preConcatenate(gtx);
                    dx = (float)tx.getTranslateX(); // uses ftx then gtx to get translation
                    dy = (float)tx.getTranslateY();
                }
                if (!dtx.isIdentity()) {
                    tx.preConcatenate(dtx);
                }
            }


            int ptSize = 1; // only matters for 'gasp' case.
            Object aaHint = sgv.frc.getAntiAliasingHint();

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                    n = newn;
                }
                trans *= pointSize;
                double scale = Math.pow(2./3., n);


                at.preConcatenate(AffineTransform.getTranslateInstance(0, trans));
                at.scale(scale, scale);


                // note on placement and italics
                // We preconcatenate the transform because we don't want to translate along
                // the italic angle, but purely perpendicular to the baseline.  While this

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