Modeling A
==============


Characteristics of modeling
-----------------------------------

We place ourselves in a massive 3D frame. We will impose successively:


* a translation of vector :math:`(2.5;3.9;\mathrm{-}12.3)`,


* a rotation of an angle of 33 degrees and an axis passing through the points :math:`(10;0.5;3.8)` and :math:`(0;10;0)`,


* a second rotation with an angle :math:`\mathrm{-}161` degrees and an axis passing through :math:`(\mathrm{-}3.;0.5;3.8)` and with a direction :math:`(0;1;0)`,


* a scaling by a factor :math:`5`.

We thus test all the scenarios authorized by the syntax of the keywords TRANSLATION, ROTATION and ECHELLE.

Then, we start again from the initial mesh and we impose on it successively:


* a change in the base of vectors :math:`(1.23;0.23;0)` and :math:`(-2.3;12.3;0)`,


* a scaling by a factor :math:`5`.

In this way, we test the keywords MODI_BASE and ECHELLE together.


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

The mesh has a single element of type HEXA8.


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

For the first part, with TRANSLATION, ROTATION, and ECHELLE:


.. csv-table::

    "**Points observed**", "**Coordinates**", "**Reference**"
    ":math:`\mathit{P1}` "," :math:`X` ", "5.2501368890123E+00"
    "", ":math:`Y` ", "—2.1551486020681E+00"
    "", ":math:`Z` ", "7.8600118786924E+01"
    ":math:`\mathit{P7}` "," :math:`X` ", "—1.3714414455621E+01"
    "", ":math:`Y` ", "1.9199906921638E+01"
    "", ":math:`Z` ", "7.0898989267417E+01"
    ":math:`\mathit{P8}` "," :math:`X` ", "—9.9168576521849E+00"
    "", ":math:`Y` ", "2.0297577804345E+01"
    "", ":math:`Z` ", "6.783734242495183E+01"


For the second part, with MODI_BASE and ECHELLE:


.. csv-table::

    "**Points observed**", "**Coordinates**", "**Reference**"
    ":math:`P2` "," :math:`X` ", "4.9148126952461E+00"
    "", ":math:`Y` ", "—9.1903001618423E-01"
    "", ":math:`Z` ", "0.0000000000000E+00"
    ":math:`P7` "," :math:`X` ", "7.6719027437988E+00"
    "", ":math:`Y` ", "1.3825408069554E+01"
    "", ":math:`Z` ", "2.5000000000000E+01"
    ":math:`\mathit{P8}` "," :math:`X` ", "2.7570900485527E+00"
    "", ":math:`Y` ", "1.4744438085738E+01"
    "", ":math:`Z` ", "2.5000000000000E+01"