Visually apealing holologous transformation of a given contour

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There is this problem which roughly says:

You want to put a framed picture onto the wall with a cord to the picture frame. The cord is a single one, and both ends are attached to the frame. How do you need to put the cord around $n$ nails, so that the picture can be taken down by taking out any of the nails?

For my page about the picture frame problem, I would like to create another section about four nails.

The problem is that the path I have drawn is really complex and hard to see, even with colors:

http://chaos.stw-bonn.de/users/mu/uploads/2013-09-19/four.png

The important part is just the windings, not the actual path. Is there some way or program to move the path in a way that makes it the most visually appealing and easy to follow?