(feature) add anisotropic meshing to LearnerND

[basnijholt]

(original issue on GitLab)

opened by Jorn Hoofwijk (@Jorn) at 2018-07-07T16:35:34.237Z

like this:

from this source

Still need to figure out whether de stretching should depend on the derivative or the second derivative

[basnijholt]

originally posted by Joseph Weston (@jbweston) at 2018-07-07T17:08:30.027Z on GitLab

Nice idea!

I think its the derivative: imagine plotting a flat plane at an angle. To get the same triangles at different tilt angles we need to stretch differently, but in all cases the second derivative is 0

[basnijholt]

originally posted by Anton Akhmerov (@anton-akhmerov) at 2018-07-07T20:05:51.668Z on GitLab

Nice reference. I have thought about particle-based methods, but decided in favor of triangulation because I thought it is simpler when we don't have a luxury of being able to query the function at will.

With having the triangulation we should be able to do just that using the transform argument to the triangulation.

[basnijholt]

originally posted by Jorn Hoofwijk (@Jorn) at 2018-07-08T11:03:01.973Z on GitLab

I agree that particle based solutions are not very useful for adaptive. I just figured this image to be a perfect example of what we want to achieve.

[krokosik]

I am interested in implementing that. Do you have any materials to get started or some concept in mind? Should it work in a similiar way to the deviations calculation in Learner2D?

[basnijholt]

There is #141 however it's been 7 years and I don't quite remember the details 😅
Something with it didn't work well, @akhmerov or @jhoofwijk might know more?

[akhmerov]

It's complicated: we ran into problems with both stability (the tesselations generated were invalid for strongly anisotropic functions) and performance. I believe to be a viable alternative to scipy, the triangulation would also likely need to be optimized to be in a compiled language.

I'm happy to chat in more detail to provide more info.

[krokosik]

I am researching this on my own now, would be more than happy to chat about it! Would you like to move to some nicer medium than Github Issues?