Thanks for the helpful comments. I think I didn't pose my question clearly enough; yes, when creating text and pictures, rotation is fairly easy, and I have mastered this aspect of it. However, after the object in question has been bitmapped into the picture, it can be devilishly hard to go back and select some parts of it, especially, for example, slanted text that sits within a few pixels of a line or some other object. The lasso tool is not quite up to this task. My original idea was to implement some form of rotation for the selection tool itself, so as to match a selection rectangle to some rotated part of the picture. However, an easier technique might be to have another selection tool which is similar to the standard line-drawing tools in which you click once to locate a starting point, and then, perhaps while holding down the shift key, click on successive points until you have the object in question surrounded (by a series of straight lines), and then release the shift key, at which point the tool completes the selection back to the starting point. This would make it relatively easy to create a selection line that navigates through long, narrow gaps between parts of the diagram. (An example of this might be a bar code printed at an angle, where you want to splice out one or more lines for some reason.)
Well, I'm outta here. My map is completed, and I couldn't have done it with Microsoft Paint. Thanks a lot for Paint.net, and for all the help! I'll make a contribution, if I can find out how to pay by check.