Remeshing using output frame field

[Gowrimv]

Is it not possible to define a frame field corresponding to the desired output mesh while remeshing? Not just anisotropy factor, but a new metric field at a point?

[BrunoLevy]

It is not impossible, but would require some work:

• 1: compute a high-dimensional isometric embedding defined from your metric, see this reference
• 2: remesh the high-dimensional surface using the Lloyd mesher in geogram. An example of curvature adaptation using 6D embedding is shown here. You will need a larger number of dimensions (I'd say 10 if you have full anisotropy tensor).

However, I confess that using a high D embedding is probably not the most efficient method for anisotropic surface meshing. You may also implement variants of Delaunay meshing, with an anisotropic definition of the cavity. There is a nice course on the topic by Frederic Alauzet, here.

[Gowrimv]

Thanks for the help. Just to clarify, geogram uses cvt in L2 norm with a specified anisotropy for the whole mesh, right?

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On Fri, Mar 15, 2024 at 9:00 PM Bruno Levy ***@***.***> wrote: It is not impossible, but would require some work: - 1: compute a high-dimensional isometric embedding defined from your metric, see this reference <https://dl.acm.org/doi/10.1145/3197517.3201369> - 2: remesh the high-dimensional surface using the Lloyd mesher in geogram. An example of curvature adaptation using 6D embedding is shown here <https://link.springer.com/chapter/10.1007/978-3-642-33573-0_21>. You will need a larger number of dimensions (I'd say 10 if you have full anisotropy tensor). — Reply to this email directly, view it on GitHub <#137 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AJDEWBKGBKDNJSSL7GVV6LTYYMHZXAVCNFSM6AAAAABETMRXICVHI2DSMVQWIX3LMV43SRDJONRXK43TNFXW4Q3PNVWWK3TUHM4DQMBTGY3DM> . You are receiving this because you authored the thread.Message ID: ***@***.***>

[BrunoLevy]

geogram's CVT can work in different modes:

• regular mode
• regular mode with a weight
• n-dimensional embedding + optional weight. Used by curvature-adapted meshing. Could be used to specify an anisotropy, but you need to implement the method in the article to compute the Nash embedding

[Gowrimv]

Ok. Thanks a lot!

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On Fri, 15 Mar 2024, 11:48 pm Bruno Levy, ***@***.***> wrote: geogram's CVT can work in different modes: - regular mode - regular mode with a weight - n-dimensional embedding + optional weight. Used by curvature-adapted meshing. Could be used to specify an anisotropy, but you need to implement the method in the article to compute the Nash embedding — Reply to this email directly, view it on GitHub <#137 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AJDEWBO5UYHHTQ5LOAYMWF3YYM3QXAVCNFSM6AAAAABETMRXICVHI2DSMVQWIX3LMV43SRDJONRXK43TNFXW4Q3PNVWWK3TUHM4DQMBWGEYTI> . You are receiving this because you authored the thread.Message ID: ***@***.***>

[Gowrimv]

Hello, I'm changing the energy function to be minimised to work in any p- norm as given in your paper, *"l* *p* centroidal voronoi tessellation and its applications", 2010. Can I make this change in geogram and use an n-d embedding of current mesh to implement metric based *l* *p *CVT meshing? Gowri On Fri, Mar 15, 2024 at 11:49 PM Gowri M V ***@***.***> wrote:

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Ok. Thanks a lot! On Fri, 15 Mar 2024, 11:48 pm Bruno Levy, ***@***.***> wrote: > geogram's CVT can work in different modes: > > - regular mode > - regular mode with a weight > - n-dimensional embedding + optional weight. Used by > curvature-adapted meshing. Could be used to specify an anisotropy, but you > need to implement the method in the article to compute the Nash embedding > > — > Reply to this email directly, view it on GitHub > <#137 (comment)>, > or unsubscribe > <https://github.com/notifications/unsubscribe-auth/AJDEWBO5UYHHTQ5LOAYMWF3YYM3QXAVCNFSM6AAAAABETMRXICVHI2DSMVQWIX3LMV43SRDJONRXK43TNFXW4Q3PNVWWK3TUHM4DQMBWGEYTI> > . > You are receiving this because you authored the thread.Message ID: > ***@***.***> >