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May 30 at 22:07 comment added Henrik Schumacher Hi @Greg, of course I do not mind. I think that is an accelent idea. =) And the code is in the public domain anyways, so how could I object?
May 30 at 21:28 comment added Greg Hurst @HenrikSchumacher Do you mind if I integrate some of this functionality into my UTCG library? Giving credit of course :)
Jan 25, 2021 at 8:20 comment added Henrik Schumacher It works fine when I insert "Multicells" -> True back into the code where it belongs...
Jan 25, 2021 at 6:33 comment added ap21 Dear @HenrikSchumacher, I tried using your GraphDiffusionFlow code to perform Laplacian smoothing on a mesh of mine, and it gave me a long string of errors I couldn't comprehend. Could you possibly take a look? It's at the bottom of the file: file.io/mWGiV4CZ5ejh
Mar 28, 2020 at 19:56 history edited Henrik Schumacher CC BY-SA 4.0
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Dec 7, 2019 at 7:34 history edited Henrik Schumacher CC BY-SA 4.0
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Mar 26, 2019 at 19:39 history edited Henrik Schumacher CC BY-SA 4.0
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Jan 28, 2019 at 23:25 history edited Henrik Schumacher CC BY-SA 4.0
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Jan 28, 2019 at 23:19 comment added Henrik Schumacher Thanks, @ChipHurst, indeed the code did not make sense. I fixed that and some performance degradation caused by Position. Hopefully, I did not introduce any new bugs. It is always good to hear that my code is useful!
Jan 28, 2019 at 23:16 history edited Henrik Schumacher CC BY-SA 4.0
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Jan 28, 2019 at 23:11 history edited Henrik Schumacher CC BY-SA 4.0
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Jan 28, 2019 at 23:02 comment added Greg Hurst @HenrikSchumacher I wish I could upvote this twice. I believe there is a typo in GraphDiffusionFlow. If[Length[belist] > 0, belist = blah; ...] should be belist = blah; If[Length[belist] > 0, ...], right?
Sep 7, 2018 at 21:46 history edited Henrik Schumacher CC BY-SA 4.0
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May 20, 2018 at 22:22 history edited Henrik Schumacher CC BY-SA 4.0
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May 6, 2018 at 9:58 history edited Henrik Schumacher CC BY-SA 4.0
Fixed some issues in GraphDiffusionFlow.
May 6, 2018 at 9:35 history edited Henrik Schumacher CC BY-SA 4.0
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May 6, 2018 at 9:05 comment added Henrik Schumacher Yes, these things may happen. ^^ I added paragraph "Usage Notes" a explains a bit why and how to deal with it.
May 6, 2018 at 8:59 history edited Henrik Schumacher CC BY-SA 4.0
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May 6, 2018 at 8:54 history edited Henrik Schumacher CC BY-SA 4.0
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May 5, 2018 at 19:00 comment added Henrik Schumacher Fixed a $\LaTeX$ typo. Thanks for the hint!
May 5, 2018 at 18:58 history edited Henrik Schumacher CC BY-SA 4.0
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May 5, 2018 at 13:51 vote accept chris
May 5, 2018 at 12:01 history edited Henrik Schumacher CC BY-SA 4.0
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May 5, 2018 at 11:33 comment added Henrik Schumacher I am not exactly sure what you mean? Mean curvature flow can contract triangles to points or lines, so there might always occur numerical problems. I tried to make the code more robust by introducing several Checks. I would expect that the flow smoothes the boundaries a bit better than the generic averaging procedure.
May 5, 2018 at 10:25 history edited Henrik Schumacher CC BY-SA 4.0
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May 5, 2018 at 10:14 history edited Henrik Schumacher CC BY-SA 4.0
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May 5, 2018 at 10:02 comment added Henrik Schumacher The second fundamental form at point $x$ is in general a bilinear map $I\!I_x \colon T_x\varSigma \times T_x\varSigma \to \mathbb{R}^m$. Usually, it gets contracted with the surface normal $\nu(x)$ in order to get a biliear form $ \colon T_x\varSigma \times T_x\varSigma \to \mathbb{R}$. Note that $\Delta_f f$ is also vector valued for $f$ is vector valued. So the PDE governing mean curvature flow is actually a nonlinear system of PDEs.
May 5, 2018 at 10:01 comment added Henrik Schumacher Well, that's a question of nomenclatur. Scalar mean curvature only exists for oriented surfaces of codimension 1 (a $n$-dimensional surface in $m=n+1$-dimensional Euclidean space - or any other oriented Riemannian manifold of dimension $n+1$; that means, only when the surface normal is well-defined), while the mean curvature vector is defined for arbitrary codimension and orientability as the trace of the second fundamental form $I\!I$ (usually divided by $n$).
May 5, 2018 at 9:54 comment added chris Out of curiosity why is the mean curvature called a vector. It seems to be a scalar?
May 5, 2018 at 9:51 comment added Henrik Schumacher Thank you, chris!
May 5, 2018 at 9:23 history edited Henrik Schumacher CC BY-SA 4.0
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May 5, 2018 at 8:56 history edited Henrik Schumacher CC BY-SA 4.0
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May 5, 2018 at 8:26 history edited Henrik Schumacher CC BY-SA 4.0
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May 5, 2018 at 7:34 history edited Henrik Schumacher CC BY-SA 4.0
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May 4, 2018 at 21:18 history answered Henrik Schumacher CC BY-SA 4.0