hi I also had the same problem , I overcome it by using *XOR *mode in java
awt
here is a code segment
to move a rect shape without fliker

Rectangle regionRect = new Rectangle();

public void moveRectanglePreview(MapMouseEvent e, GeoRect geoRect) {
        x = e.getX();
        y = e.getY();

/*
 geoRect is the user defined one which has the rectagle info 

calculate pixel width & height of the shape
*/

        *height *= (int) (Math.abs(geoRect.getY2() - geoRect.getY1()) *   
getMapPane().getWorldToScreenTransform().getScaleX());

        *width *= (int) (Math.abs(geoRect.getX2() - geoRect.getX1()) *
getMapPane().getWorldToScreenTransform().getScaleX());

        Graphics2D graphic = (Graphics2D) getMapPane().getGraphics();
        graphic.setColor(geoRect.getColor());
        
graphic.setXORMode(Color.WHITE);

        if (dragging) { /*
to avoid initial draw
*/
            graphic.drawRect(regionRect.x, regionRect.y, regionRect.width,
regionRect.height);
        }
        regionRect.setFrame(x - width / 2, y - height / 2, width, height);
/* *to set the mouse cursor with the centre of the rect, while moving **/
        graphic.drawRect(regionRect.x, regionRect.y, regionRect.width,
regionRect.height);
        dragging = true;

    }

I simply call this method on jmappane's mouse dragged method

on mouse released I call the original /move(destX, destY) ;/  method to move
the original shape
so no map flickering while moving.
I 've also implemented the move, resize methods for CIRCLE, RECT, POLYGON.

hope this is helpful :)



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