Drawing line with border - qt

I've faced a problem in Qt where I need to draw lines with borders (I have coordinates for nodes and I am just drawing simple thick line from node to node). Just like this: http://img23.imageshack.us/img23/3596/askej.jpg
At first I tried to draw thicker red line and after that black line, but I got inappropriate connecting as you can see at the image above.
Moreover the idea in which we draw all red lines and after that all black lines won't work as well. The lines can be crossed so with this idea we won't have borders over the crossing another line.
Could somebody help me with this problem, please?
Thanks.
// feel free to show me mistakes in my english too

I have exactly this situation in a GIS app (Merkaartor)
You need to work by layers, where all paths on the same layer will first be drawn red then black.
For instance, layer -1 would be tunnels, you draw them first, red then black, then layer 0 are surface roads, you draw them red then black, then layer 1 are bridges, etc...
This properly render a "map" feeling.

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Marking overlapping paths with off-color borders

Say I have an image of a rose which I want to trace:
I construct a few curvature shapes with it's stroke weight set to 5 like so:
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Say my bottom layered stroke crosses a top layered stroke, it then might draw two little lines across the stroke like so:
Is there any way to set up such functionality? Or mimic it? It would help work like this a ton.
The program could get the order of overlap right by looking at the layer orders, which you would of course have to manually order yourself. But having a feature that enables me to see which shape is on top of which when they're overlapping would be great.

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I added a red circle to show the interlacing I'm having issues with.
Screenshot

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I am new to RRDtool. I generated a graph with grid(--grid-dash 1:0), a LINE(LINE1:rt#4e9a06) and I also have the area between the line and the x-axis coloured (AREA:rt#4e9a06 ). I notice the grid still shows up in the colored-area. I am wondering if there is any way to cover the grid with the colored-area.
Also, I am also wondering if there is any good-looking rrdtool samples/examples available online? Thanks.
I have no way of testing this currently, but here's what the documentation says (emphasis mine) :
[-c|--color COLORTAG#rrggbb[aa]]
Override the default colors for the standard elements of the graph.
The COLORTAG is one of BACK background, CANVAS for the background of
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-c MGRID#<hex triplet>7F -c GRID#<hex triplet>7F
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Note that this answer from the developer of RRDTool says that the grid is always painted after the graph, so in the end you'll always have it in the foreground, your only solution is to either totally disable it or tinker with color/transparency parameters to make it invisible when covered by the graphed data.

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There used to be (probably still is) a great AS 2/3 library for this but I can't find it.
This looks pretty promising:
http://blog.alegitimatebusiness.com/2007/11/07/as2-as3-draw-a-dotted-rounded-corner-box/

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