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About photograph transform


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At first, I have to say sorry about my English. English is not my native language. Hopefully, you could understand what I'm trying to say .

I'm running a project about 
photograph transformation with Html5. I've known the formula of "Liquify effect",but I don't know how to calculate it. I've been stuck at this for days, please help!


Here is what formula looks like: http://www.gson.org/thesis/warping-thesis.pdf (page thirty eighth)

I don't exactly understand what U and X are. Can anyone explain it for me? thanks

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