요소 절점 순서 (element node odering)

출처: https://gmsh.info/doc/texinfo/gmsh.html#Node-ordering

 

아래는 요소 절점 순서...

Line:                  Line3:           Line4:

      v
      ^
      |
      |
0-----+-----1 --> u    0----2----1      0---2---3---1

Triangle:               Triangle6:          Triangle9/10:

v
^
|
2                       2                    2
|`\                     |`\                  | \
|  `\                   |  `\                7   6
|    `\                 5    `4              |     \
|      `\               |      `\            8  (9)  5
|        `\             |        `\          |         \
0----------1--> u       0-----3----1         0---3---4---1

Triangle12/15:

 v
 ^
 |
 2
 | \
 9   8
 |     \
10 (14)  7
 |         \
11 (12) (13) 6
 |             \
 0---3---4---5---1--> u

Quadrangle:            Quadrangle8:            Quadrangle9:

      v
      ^
      |
3-----------2          3-----6-----2           3-----6-----2
|     |     |          |           |           |           |
|     |     |          |           |           |           |
|     +---- | --> u    7           5           7     8     5
|           |          |           |           |           |
|           |          |           |           |           |
0-----------1          0-----4-----1           0-----4-----1

Tetrahedron:                          Tetrahedron10:

                   v
                 .
               ,/
              /
           2                                     2
         ,/|`\                                 ,/|`\
       ,/  |  `\                             ,/  |  `\
     ,/    '.   `\                         ,6    '.   `5
   ,/       |     `\                     ,/       8     `\
 ,/         |       `\                 ,/         |       `\
0-----------'.--------1 --> u         0--------4--'.--------1
 `\.         |      ,/                 `\.         |      ,/
    `\.      |    ,/                      `\.      |    ,9
       `\.   '. ,/                           `7.   '. ,/
          `\. |/                                `\. |/
             `3                                    `3
                `\.
                   ` w

Hexahedron:             Hexahedron20:          Hexahedron27:

       v
3----------2            3----13----2           3----13----2
|\     ^   |\           |\         |\          |\         |\
| \    |   | \          | 15       | 14        |15    24  | 14
|  \   |   |  \         9  \       11 \        9  \ 20    11 \
|   7------+---6        |   7----19+---6       |   7----19+---6
|   |  +-- |-- | -> u   |   |      |   |       |22 |  26  | 23|
0---+---\--1   |        0---+-8----1   |       0---+-8----1   |
 \  |    \  \  |         \  17      \  18       \ 17    25 \  18
  \ |     \  \ |         10 |        12|        10 |  21    12|
   \|      w  \|           \|         \|          \|         \|
    4----------5            4----16----5           4----16----5

Prism:                      Prism15:               Prism18:

           w
           ^
           |
           3                       3                      3
         ,/|`\                   ,/|`\                  ,/|`\
       ,/  |  `\               12  |  13              12  |  13
     ,/    |    `\           ,/    |    `\          ,/    |    `\
    4------+------5         4------14-----5        4------14-----5
    |      |      |         |      8      |        |      8      |
    |    ,/|`\    |         |      |      |        |    ,/|`\    |
    |  ,/  |  `\  |         |      |      |        |  15  |  16  |
    |,/    |    `\|         |      |      |        |,/    |    `\|
   ,|      |      |\        10     |      11       10-----17-----11
 ,/ |      0      | `\      |      0      |        |      0      |
u   |    ,/ `\    |    v    |    ,/ `\    |        |    ,/ `\    |
    |  ,/     `\  |         |  ,6     `7  |        |  ,6     `7  |
    |,/         `\|         |,/         `\|        |,/         `\|
    1-------------2         1------9------2        1------9------2

Pyramid:                     Pyramid13:

               4                            4
             ,/|\                         ,/|\
           ,/ .'|\                      ,/ .'|\
         ,/   | | \                   ,/   | | \
       ,/    .' | `.                ,/    .' | `.
     ,/      |  '.  \             ,7      |  12  \
   ,/       .' w |   \          ,/       .'   |   \
 ,/         |  ^ |    \       ,/         9    |    11
0----------.'--|-3    `.     0--------6-.'----3    `.
 `\        |   |  `\    \      `\        |      `\    \
   `\     .'   +----`\ - \ -> v  `5     .'        10   \
     `\   |    `\     `\  \        `\   |           `\  \
       `\.'      `\     `\`          `\.'             `\`
          1----------------2            1--------8-------2
                    `\
                       u

Pyramid14:

               4
             ,/|\
           ,/ .'|\
         ,/   | | \
       ,/    .' | `.
     ,7      |  12  \
   ,/       .'   |   \
 ,/         9    |    11
0--------6-.'----3    `.
  `\        |      `\    \
    `5     .' 13     10   \
      `\   |           `\  \
        `\.'             `\`
           1--------8-------2
                    `\
                       u