C modeling
==============

Here we test the 3D changes on a 2D mesh. Always starting from the initial grid, we will impose separately:


* a deformation with a field (1, 2, 3) applied to all the nodes


* a vector translation (1, 2, 3)


* a rotation of 45 degrees along the X axis (rotation out of plane)


* a base change of vectors :math:`(1;0;0)`, :math:`(0;1;1)` and their orthogonal


* symmetry with respect to the plane constituted by the point (0,0,0) and the vectors :math:`(1;0;0)`, :math:`(0;1;1)`

A three-dimensional displacement is thus tested for an initially two-dimensional mesh.


Characteristics of the mesh
----------------------------

The mesh has a single element of type QUAD4.


Tested sizes and results
------------------------------

With a deformation of the type 'TRAN' according to the vector (1, 2, 3)

DEFORME =_F (OPTION =' TRAN '...)


.. csv-table::

    "**Points observed**", "**Coordinates**", "**Reference**"
    ":math:`\mathit{P1}` "," :math:`X` ", "1"
    "", ":math:`Y` ", "2"
    "", ":math:`Z` ", "3"


     With a translation according to the vector (1, 2, 3)


.. csv-table::

    "**Points observed**", "**Coordinates**", "**Reference**"
    ":math:`P1` "," :math:`X` ", "1"
    "", ":math:`Y` ", "2"
    "", ":math:`Z` ", "3"


     With a rotation of 45 degrees along the X axis (rotation out of plane)


.. csv-table::

    "**Points observed**", "**Coordinates**", "**Reference**"
    ":math:`P3` "," :math:`X` ", "1"
    "", ":math:`Y` ", "2.1213203436"
    "", ":math:`Z` ", "2.1213203436"


With a base change of vectors :math:`(1;0;0)`, :math:`(-0;1;1)`

.. csv-table::

    "**Points observed**", "**Coordinates**", "**Reference**"
    ":math:`P3` "," :math:`X` ", "1"
    "", ":math:`Y` ", "2.1213203436"
    "", ":math:`Z` ", "-2.1213203436"


With symmetry with respect to the plane constituted by the point (0,0,0) and the vectors :math:`(1;0;0)`, :math:`(0;1;1)`


.. csv-table::

    "**Points observed**", "**Coordinates**", "**Reference**"
    ":math:`P3` "," :math:`X` ", "1"
    "", ":math:`Y` ", "0"
    "", ":math:`Z` ", "3"