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Simulating a line flow

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Hi All,


I would like to simulate a simple line flow.  Suppose that I have a line that is drawn like that ----------------   and it has a texture. 


I would like to give the feel that the line flows from left to right.  In case having also different line styles like -/\/\-- , the flow also should go from left to right considering the ripples.


I'm using stage3D, Flash, Actionscript, and plan to do that using shaders.   


My idea is just to tween the alpha of the texture, but how do I tween it so that it feels like the there is a flow in the line ?



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