# [Gmsh] How are set up U and V vectors for elements ?

Christophe Geuzaine cgeuzaine at uliege.be
Tue Oct 6 19:43:33 CEST 2020

```
> On 5 Oct 2020, at 07:05, bilou at netc.it wrote:
>
> Hello. I'm trying to parse a mesh.msh generated by gmsh.
>
> I work with 9-quad elements. I see in documentation that inside of the elements, nodes are ordered like this :
>
>            v
>            ^
>            |
> 3-------6-------2
> |          |         |
> |          |         |
> 7        8-------5 --> u
> |                    |
> |                    |
> 0-------4-------1
>
> I made a 2D mesh (all surfaces normals are oriented in the same direction)
>
> When i look at my 2D mesh (in plan XY) the element 265 :
> 265 2 44 1047 533 49 1102 1103 544 1104
>
> is oriented like this related to the golbal X and Y axis
>
> ie, when looking at the screen i see:
>   44-------49-------2
>      |           |         |     Y
>      |           |         |     ^
> 1102   1104    544    |
>      |           |         |     |
>     |           |         |     |
> 1047--1103----533    x------> X
>
> it seems that u anv v vectors are oriented like this :
>         1-----4-----0
>         |        |       |
>         |        |       |
> u <---5-----8      7
>         |        |       |
>         |        |       |
>         2-----6-----3
>                  |
>                 V
>                 v
>
>
> How are V and U vectors defined for each element ?

It depends on the definition of the surface and the meshing algorithm.

>  Is there a way to orient them along the natural X and Y axis ?

With the transfinite algorithm you could force the elements to be generated in a certain order by specifying the interpolation corners. But in general you won't know the correspondance - Gmsh produces unstructured meshes! So you would use the (u,v,w) -> (x,y,z) mapping (through e.g. Lagrange basis functions) to make the connection.

Christophe

>
> Thanks
>
>
>
>
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—
Prof. Christophe Geuzaine
University of Liege, Electrical Engineering and Computer Science
http://www.montefiore.ulg.ac.be/~geuzaine

```