Is there a common technique for drawing a “stretched” line

I am trying to figure out how to draw a stretched / elastic line between two points in openGL / Cocos2d on an iPhone. Something like that

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Where the "group" gets thinner when the line gets longer. iOS uses the same technique that I aimed at Mail.app to update.

First of all, is there a name for this kind of thing?

My first thought was to draw a point on the radius of the start and end circles based on the angle between them and draw a quadratic Bezier curve using distance / 2 as a control point. But I'm not a mathematical whistle, so I'm struggling to figure out how to place a control point that will adjust the thickness of the path.

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