Rendered Rectangles missing in a huge WPF Control

Question

I need a WPF Control with 300000000 Width and Height, on which I will draw Rectangles, based on some input. I am drawing the Rectangle on the OnRender of the control. For testing purpose I have put the control inside a ScrollViewer and am drawing Rectangles on each pixels from (0,0) to (1000,1000). If the Width & Height is 1000000, the Rectangles are drawn properly, shown below, (the Rectangles are plotted on all the pixels from (0,0) to (1000,1000), so it looks like the on in the below link)

https://social.msdn.microsoft.com/Forums/getfile/950012

But If I increase the size to 3000000, few lines are missing in the drawing like below, https://social.msdn.microsoft.com/Forums/getfile/950018

My Xaml:

<ScrollViewer x:Name="MainScrollViewer"
              Grid.Row="2"
              Grid.ColumnSpan="2"
              HorizontalScrollBarVisibility="Auto"
              VerticalScrollBarVisibility="Auto">
  <waferControl:WaferMapControl x:Name="WaferControl"
                                Grid.Row="2"
                                Grid.ColumnSpan="2"
                                Width="30000000"
                                Height="30000000"
                                Margin="10"
                                ColumnCount="{Binding WaferInfo.ColumnCount}"
                                RowCount="{Binding WaferInfo.RowCount}"
                                SelectedCells="{Binding SelectedCellCollection}"
                                Visibility="Collapsed" />
</ScrollViewer>

I am using the following code in OnRender of WaferMapControl.

private void RenderBackgroud(IEnumerable lists`enter code here`)
{
    using (DrawingContext dc = _backgroundDv.RenderOpen())
    {
        SolidColorBrush brush = Brushes.Black;

        if (brush.CanFreeze)
            brush.Freeze();

        foreach (GridCellInfo cellInfo in lists)
        {
            double length = cellInfo.GridRange;

            var point = new Point(
                cellInfo.RowIndex + 1,
                ActualHeight - cellInfo.ColumnIndex  - length);

            RenderBackgroud(dc, point, brush, length);
        }
    }
}

private void RenderBackgroud(DrawingContext dc, Point point, Brush brush, double length)
{
   var rect = new Rect(point, new Size(length, length));

   dc.DrawRectangle(brush, null, rect);
} 

The cellInfo contains the x,y coordinates. The point calculation is done to draw from the bottom left. The length is 1 in my sample.

Can someone help me out, what is the issue here. Let me know if you require anything from my side.