What use of having double precision in java.awt.geom?

Hi,
I am trying to draw a line using Line2D with this param:
g2d.draw( new Line2D.Double( 1.1d, 1.5d, 1.9d, 1.5d ) );
in my own JPanel paint method.
However, the result is that the panel does not display a line nor a dot at all. Only when i change it to:
g2d.draw( new Line2D.Double( 1.0d, 1.5d, 2.0d, 1.5d ) );
that it draws a dot in the panel's first pixel.
Can someone please guide or tell me why is this so? And what is the purpose of providing a double value for a geom ( such as Rentagle2D, Line2D, etc )?
The actual case is that I have created a graph with x and y axis. I set the graph to be 400pixel * 400 pixels. And the scale for the graph is 1 million unit * 1 million unit which means a pixel would have contain (1000000/400) units, or 0.004 pixels represent 1 unit. The problem occurs when i try to draw a line that is only 10 unit.(which nothing is draw on the panel). I try to use all 2D geom with double precision, yet i could not get the result that I wanted. Isn't that java 2D will handle the double precision for graphing or drawing?
Your help and reply is very much appreciated.
Thank you.

have in mind that you always have to fill 1 pixel to see anything as the panel has a 1 pixel grid.
i guess the thing about double precision is in the contains(...) or crosses(...) methods of the geom.* objects.
its nothing about drawing. how can you draw finer than the 1 pixel grid.
even the antialias has to fill more pixel to make you thing the line is smooth. (BTW: antialias makes fonts widt less than 10px look terrible :))

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