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(feature) add anisotropic meshing to LearnerND #65

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@basnijholt

(original issue on GitLab)

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

like this:

image

from this source

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

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  1. basnijholt commented on Dec 19, 2018

    @basnijholt
    MemberAuthor

    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

  2. basnijholt commented on Dec 19, 2018

    @basnijholt
    MemberAuthor

    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.

  3. basnijholt commented on Dec 19, 2018

    @basnijholt
    MemberAuthor

    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.

  4. krokosik commented on Aug 20, 2025

    @krokosik
    Contributor

    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?

  5. basnijholt commented on Aug 20, 2025

    @basnijholt
    MemberAuthor

    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?

  6. akhmerov commented on Sep 5, 2025

    @akhmerov
    Contributor

    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.

  7. krokosik commented on Sep 5, 2025

    @krokosik
    Contributor

    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?

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