Editing Input syntax manual (section)

=== trans (transformations)<span id="trans"></span> ===

 '''trans''' ''TYPE'' ''UNIT'' [ ''IDX'' ] ''LVL''

 '''trans''' ''TYPE'' ''UNIT'' [ ''IDX'' ] ''X'' ''Y'' ''Z''

 '''trans''' ''TYPE'' ''UNIT'' [ ''IDX'' ] ''X'' ''Y'' ''Z'' ''&theta;<sub>x</sub>'' ''&theta;<sub>y</sub>'' ''&theta;<sub>z</sub>'' ''ORD''

 '''trans''' ''TYPE'' ''UNIT'' [ ''IDX'' ] ''X'' ''Y'' ''Z'' ''&alpha;<sub>1</sub>'' ''&alpha;<sub>2</sub>'' ''&alpha;<sub>3</sub>'' ''&alpha;<sub>4</sub>'' ''&alpha;<sub>5</sub>'' ''&alpha;<sub>6</sub>'' ''&alpha;<sub>7</sub>'' ''&alpha;<sub>8</sub>'' ''&alpha;<sub>9</sub>'' ''ORD''

 '''trans''' ''TYPE'' ''UNIT'' [ ''IDX'' ] '''rot''' ''X<sub>0</sub>'' ''Y<sub>0</sub>'' ''Z<sub>0</sub>'' ''I'' ''J'' ''K'' ''&beta;''

Defines surface, universe, fill, lattice, detector mesh or source transformation. Input values:

{|
| <tt>''TYPE''</tt>
| : type of transformation (S = surface, F = fill, U = universe, L = lattice, D = detector mesh, SR = source)
|-
| <tt>''UNIT''</tt>
| : surface, cell, universe, lattice, detector mesh or source name to which the transformation is applied
|-
| <tt>''IDX''</tt>
| : index number of lattice position to which the lattice transformation (type L) is applied
|-
| <tt>''LVL''</tt>
| : level number in universe level transformation
|-
| <tt>''X'',''Y'',''Z''</tt>
| : translation vector [in cm]
|-
| <tt>''&theta;<sub>x</sub>'' ''&theta;<sub>y</sub>'' ''&theta;<sub>z</sub>''</tt>
| : rotation angles with respect to x-, y- and z-axes [in degrees]
|-
| <tt>''&alpha;<sub>1</sub>'' ... ''&alpha;<sub>9</sub>''</tt>
| : coefficients of the rotation matrix
|-
| <tt>''ORD''</tt>
| : order in which translations and rotations are applied (1 = rotations first, 2 = translations first)
|-
| <tt>''X<sub>0</sub>'',''Y<sub>0</sub>'',''Z<sub>0</sub>''</tt>
| : origin of vector defining rotation axis [in cm]
|-
| <tt>''I'',''J'',''K''</tt>
| : components of vector defining rotation axis.
|-
| <tt>''&beta;''</tt>
| : angle around rotation axis defined by a vector [in degrees].
|-
|}

The possible transformation types are:
::{| class="wikitable" style="text-align: left;"
! Type
! Description
! Notes
|-
| <tt>s</tt>
| surface
|
|-
| <tt>f</tt>
| fill
| It is applied in the universe filling the given cell.
|-
| <tt>u</tt>
| universe
| ''Special type'': <u>level</u> transformation,  in which the coordinates in the given universe are obtained relative to geometry level <tt>''LVL''</tt>.
|-
| <tt>l</tt>
| lattice
| It requires to provide the index number <tt>''IDX''</tt> of lattice position to which the transformation is applied.
|-
| <tt>d</tt>
| mesh detector
| It is associated to mesh detectors (such as '''dx''', '''dy''', '''dz''', '''dh''', '''dn''' or '''dmesh''', see [[#det|det card]])
|-
| <tt>sr</tt>
| source
| It is inverted compared to how surface, universe, etc. are handled
|-
|}

<u>Notes:</u>
*Translations: by providing the translation vector.
**By default translations are applied before rotations, and the order can be switched using the <tt>''ORD''</tt> parameter.
*Rotations:
**With respect x-/y-/z-axes:  either by providing the three angles with respect to the three coordinate axes, or by defining the rotation matrix.
***In the second case Serpent applies vector multiplication: <math>\vec{r'} = \bold{A} \vec{r}</math>
:::where <math>\vec{r}</math> and <math>\vec{r'}</math> are the position vectors before and after the operation and coefficients <tt>''&alpha;<sub>1</sub>'' ... ''&alpha;<sub>9</sub>''</tt> define the 3 by 3 matrix <math>\bold{A}</math>.
:*With respect a general axes: using the '''rot''' keyword and associated syntax.
:**In Serpent 2.1.29, a positive value of ''&beta;'' corresponds to rotation to the negative mathematical direction and vice versa.
*Backwards compatibility:
**To preserve backwards compatibility, input parameters "<tt>strans</tt>", "<tt>utrans</tt>", "<tt>ftrans</tt>" and "<tt>dtrans</tt>" without the following type identifier are also accepted for defining surface, universe, fill and detector mesh transformations, respectively. 
**To preserve compatibility with Serpent 1, parameter "<tt>trans</tt>" without type identifier defines a universe transformation.