[Gmsh] Local referential for the hexahedron and prism element family

[Geordie McBain]

 On Mon, Feb 15, 2010 at 11:57 PM, Rui Maciel <rui.maciel at gmail.com> wrote:
> This isn't a node ordering problem per se.  My only issue is that according to
> Gmsh's manual it appears there is an inconsistency regarding the local
> coordinate system for the prism family of elements.  In fact it appears that,
> at least on the ASCII art representation presented in the manual, the
> tetrahedron and hexahedron element family follow a "right-hand" coordinate
> system while the prism and pyramid follow a "left-hand" one.

Yes, I see what you mean.  The ASCII representations are a little
ambiguous.  For the tet and hex I had thought the u-axis was behind
and to the right of the vw-plane, while for the prism the u- and
v-axes were forward and for the pyramid the u-axis was forward with
the vw-plane in the plane of the page.  With those interpretations,
all four systems are right-handed, but I think there are other valid
interpretations; e.g. for the prism the u- and v-axes could be into
the page which would give a left-handed system.

Perhaps the figures would be clearer if where one edge crossed
another, the closer edge symbol was used, rather than using a
plus-symbol?

(Hoping these are rendered in monospace.)

 Prism (base forward):
      		
                w
                ^
                |
                3
              ,/|`\
            ,/  |  `\
          ,/    |    `\
         4-------------5
         |      |      |
         |    ,/|`\    |
         |  ,/  |  `\  |
         |,/    |    `\|
        ,|      |      |\
      ,/ |      0      | `\
     u   |    ,/ `\    |    v
         |  ,/     `\  |
         |,/         `\|
         1-------------2
      		
 Prism (ridge forward):
      		
                w
                ^
                |
                3
              ,/|`\
            ,/  |  `\
          ,/    |    `\
         4------|------5
         |      |      |
         |    ,/|`\    |
         |  ,/  |  `\  |
         |,/    |    `\|
        ,/      |      `\
      ,/ |      0      | `\
     u   |    ,/ `\    |    v
         |  ,/     `\  |
         |,/         `\|
         1-------------2