I would like to alternate between gray and white as background from one line of my JTextPane to the next. I tried to do this by overloading the paintComponent() method and drawing the background manually according to component height an Font size but I did not succeed.
Any hints?
You can use the line highlighter (here or here), written by @VonC, in response to this question.
In order to highlight alternate lines you can use it as follows:
public static void main(String[] args)  {
    JTextPane t = new JTextPane();
    t.setSelectionColor(new Color(1.0f, 1.0f, 1.0f, 0.0f));
    Highlighter hilite = new MyHighlighter();
    t.setHighlighter(hilite);
    t.setText("Line1\nLine2\nLine3\nLine4\nLine5\n");
    DefaultHighlightPainter whitePainter = new DefaultHighlighter.DefaultHighlightPainter(Color.WHITE);
    DefaultHighlightPainter grayPainter = new DefaultHighlighter.DefaultHighlightPainter(Color.GRAY);
    try {
        Document doc = t.getDocument();
        String text = doc.getText(0, doc.getLength());
        int start = 0;
        int end = 0 ;
        boolean even = true;
        //look for newline char, and then toggle between white and gray painters.
        while ((end = text.indexOf('\n', start)) >= 0) {
            even = !even;
            DefaultHighlightPainter painter = even ? grayPainter : whitePainter;
            hilite.addHighlight(start, end+1, painter);
            start = end+1;
        }
    } catch (BadLocationException e) {
        e.printStackTrace();
    }
    JPanel p = new JPanel(new BorderLayout());      
    p.add(t, BorderLayout.CENTER);
    JFrame f = new JFrame();
    f.add(p);
    f.setSize(100, 100);
    f.setVisible(true);
}
Here is VonC's MyHighlighter:
class MyHighlighter extends DefaultHighlighter
{
    private JTextComponent component;
    /**
     * @see javax.swing.text.DefaultHighlighter#install(javax.swing.text.JTextComponent)
     */
    @Override
    public final void install(final JTextComponent c)
    {
        super.install(c);
        this.component = c;
    }
    /**
     * @see javax.swing.text.DefaultHighlighter#deinstall(javax.swing.text.JTextComponent)
     */
    @Override
    public final void deinstall(final JTextComponent c)
    {
        super.deinstall(c);
        this.component = null;
    }
    /**
     * Same algo, except width is not modified with the insets.
     * 
     * @see javax.swing.text.DefaultHighlighter#paint(java.awt.Graphics)
     */
    @Override
    public final void paint(final Graphics g)
    {
        final Highlighter.Highlight[] highlights = getHighlights();
        final int len = highlights.length;
        for (int i = 0; i < len; i++)
        {
            Highlighter.Highlight info = highlights[i];
            if (info.getClass().getName().indexOf("LayeredHighlightInfo") > -1)
            {
                // Avoid allocing unless we need it.
                final Rectangle a = this.component.getBounds();
                final Insets insets = this.component.getInsets();
                a.x = insets.left;
                a.y = insets.top;
                // a.width -= insets.left + insets.right + 100;
                a.height -= insets.top + insets.bottom;
                for (; i < len; i++)
                {
                    info = highlights[i];
                    if (info.getClass().getName().indexOf(
                            "LayeredHighlightInfo") > -1)
                    {
                        final Highlighter.HighlightPainter p = info
                                .getPainter();
                        p.paint(g, info.getStartOffset(), info
                                .getEndOffset(), a, this.component);
                    }
                }
            }
        }
    }
}
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