assertEquals(0, RendererUtilities.findLiveItemsUpperBound(d, 3, 3.0, 
                4.0));
        
        // check a series with four items
        d.addSeries("S5", new double[][] {{4.0, 3.0, 2.0, 1.0}, {2.0, 2.0, 
                2.0, 2.0}});
        assertEquals(3, RendererUtilities.findLiveItemsUpperBound(d, 4, 0.1, 
                0.5));
        assertEquals(3, RendererUtilities.findLiveItemsUpperBound(d, 4, 0.1, 
                1.0));
        assertEquals(2, RendererUtilities.findLiveItemsUpperBound(d, 4, 1.1, 
                2.0));