deformation question...

I read this article and it's very interesting.

https://www.google.it/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CDYQFjAA&url=http%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fdownload%3Fdoi%3D10.1.1.124.3856%26rep%3Drep1%26type%3Dpdf&ei=xB1IUYqQIMiR7Aav04HQDQ&usg=AFQjCNFp2S9gAcCMX8vOKnuTC-rM5WKmEA&sig2=CDlXQWYcOxdUOx6bTML3cw

I would implement an animation tool following this article. I saw the video of the article and the tool developed its very user-friendly.

But I am confused and I trying understand how deformation graph should be modified.

and how could be the mainloop about minimization.

I think the weight of vertex should be precalculated and I should understand how deformation graph should be modified to calculate the final vertex. Someone can help me?