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Error of T-Map does not converge #2

Open foamliu opened 3 years ago

foamliu commented 3 years ago

Thanks for the great work, it is extremely helpful!

My problem is it seems the error cannot converge to 1e-6: image

Is this expected?

cbutakoff commented 3 years ago

Uff... I haven't had a look at it for a long time. I'm not sure. I programmed it a long time ago for fun. :) Depending on the deformation it may not converge, I assume. I think that group has newer algorithms published, that might work better.

foamliu commented 3 years ago

Hi Constantine, Teichmuller space and mapping are qutie tough math concepts, many people read them from math book but have no idea how to use them somewhere/someday. The algorithm is cool, but not easy to implement. You've laid some sound code framework. It is sad to know you don't work on this any longer. I found three difference between your implementation and the paper, are you still interested? :)

cbutakoff commented 3 years ago

Sure, if you find any bug, just post it here. It might be useful for anyone who tries to download the code. What I remember is that in the papers there was an error with the sign of some derivatives, that I had to go equation by equation and re-derive everything.

ps. I found these ideas much simpler than Ricci flows. :D

foamliu commented 3 years ago

The following are three differences, I am still struggling with the equations. 1.There is normalization in formula (5.2), but not in CalculateBC function (confirmed no normalization is right). 2.In formula(5.7), the denominator in one area(of triangle), but in CalculateAB function, it is two. 3.In formula(5.12) and (5.13), it multiply alphas with aT,bT,cT and dT, but in CalculateVerticesFromBC function, Ai and Bi is used.

I agree Ricci flow is really tough, however the author delivered a online summer course this year. With his guidance I managed to implement one which embeds the high genus surface into poincare disk.

You can find the course link here. The hyperbolic Ricci flow mentioned above is homework 8.