-ggcylinder: A general cylinder in general direction

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-ggcylinder: A general cylinder in general direction

A ggcylinder is a general cylinder with a footprint described as a general polygon. This footprint is swept along an axis in a general direction, additionally, this footprint can shrink or expand along this axis, additionally, this footprint can be rotated along the axis, additionally, only parts of the ggcylinder that fulfill some additional condition will be filled.

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section -ggcylinder                                                        #
 ##############################################################################
 # material   =  1                                                            #
 # whichcells = all, taboo= none                                              #
 #     show   = off                     -- (off | all | later | now)          #
 #     name   = ggcyl-000000000                                               #
 #   fixpoints= no                      -- (yes|no)                           #
 #     inside = yes                     -- (yes|no)                           #
 # originprime    = ( 0.0, 0.0, 0.0 )                                         #
 # xprimedirection= ( 1.0, 0.0, 0.0 )                                         #
 # yprimedirection= ( 0.0, 1.0, 0.0 )                                         #
 #   zprimedirection= ( 0.0, 0.0, 1.0 )                                       #
 #   usezprimedirection= no             -- (yes|no)                           #
 # range      = ( undefined, undefined )                                      #
 # pitch      = 0.0                     -- [degs/m]                           #
 # xexpgrowth = 0.0                                                           #
 # yexpgrowth = 0.0                                                           #
 # xslope     = 0.0                     -- (x2/x1-1)/len [1/m]                #
 # yslope     = 0.0                     -- (y2/y1-1)/len [1/m]                #
 # xscaleprime= 1.0                                                           #
 # yscaleprime= 1.0                                                           #
 # zxscaletablefile= -none-
 # zyscaletablefile= -none-
 ##############################################################################
 ## syntax:                                                                   #
 #  point= (Xi, Yi)                                                           #
 #  arc, radius= RADIUS, type= [clockwise | counterclockwise]                 #
 #       size= [small | large ]                                               #
 #       deltaphi= 5                                                          #
 #  ellipse, center= (X0, Y0), size= [small | large ]                         #
 #       deltaphi= 5                                                          #
 ##############################################################################
 # doit, return, help, list, reset, clear                                     #
 ##############################################################################

material=MAT:
The material index that will be assigned to cells inside the volume.
whichcells
Possible values are all, or a material-index.
If whichcells=all, all volume inside the ggcylinder is assigned the material-index, provided the former material is not taboo. If whichcells is a material-index, only the parts of the ggcylinder that are currently filled with the given index are assigned the new material-index.
taboo
Possible values are none, or a material-index.
If taboo=none, all volume inside the ggcylinder is assigned the material-index. If taboo is a material-index, only the parts of the ggcylinder that are currently filled with another index than the given index are assigned the new material-index.
originprime:
The coordinates of the origin of the ggcylinder.
xprimedirection:
The direction of the x'-axis of the polygon that describes the footprint.
yprimedirection:
The direction of the y'-axis of the polygon that describes the footprint. The y'-direction will internally be enforced to be perpendicular to the x'-direction.
usezprimedirection= [yes|no]:
If usezprimedirection= yes, the axis of the cylinder is not computed from the cross product of xprimedirection and yprimedirection, but is taken to be the direction given by zprimedirection= ( XZ, YZ, ZZ ).
zprimedirection= ( XZ, YZ, ZZ ):
If usezprimedirection= yes, the axis of the cylinder has the direction given by zprimedirection= ( XZ, YZ, ZZ ). If usezprimedirection= no, the given values are not used and the direction is given by the cross product of xprimedirection and yprimedirection.
range:
Start and end values of the z'-coordinate of the cylinder in the coordinate system of xprimedirection,yprimedirection,(xprime $\times$ yprime), relative to originprime.
pitch:
Phase in degrees/m. The footprint will be rotated along the axis.
xexpgrowth, yexpgrowth
Alpha of the exponential growth of the x-coordinates, resp. y-coordinates of the footprint along the axis in 1/m.
xslope, yslope:
Factor of the linear growth of the x-coordinates, res. y-coordinates of the footprint along the axis in 1/m.
xscaleprime, yscaleprime:
The x'-coordinates, resp. y'-coordinates of the footprint are multiplied by these factors.
zxscaletablefile, zyscaletablefile:
The x'-coordinates, resp. y'-coordinates of the footprint are multiplied by these factors. The factors are given as tables in external files. The format is: first colume z-coordinate, second column the scaling.
inside:
Flag, specifying whether cells inside of the ggcylinder should be assigned material index MAT, or whether the cells outside of it should be changed.
show:
Flag, specifying whether an outline of the specified ggcylinder should be displayed.
If show=off, no outline will be displayed.
If show=later, the outline will be shown later together with other specified bricks, gccylinders, ggcylinders and gbors.
If show=all, the outlines of all bricks, gccylinders, ggcylinders and gbors so far where show was not off will be displayed.
fixpoints
Enshure meshplanes at the points of the footprint, both at the beginning and the end of the extrusion range.
point= (XI, YI):
XI, YI are the coordinates of the i.th point in the polygon that describes the footprint of the ggcylinder. There have to be minimum 3 points, or 2 points and an arc or 2 points and an ellipse.
arc:
(optional):
Indication, that there should be a circular arc from the point that was specified before to the point that will be specified as next point.
In order to determine the arc between two points, three parameters are necessary: The radius of the arc, whether the connection is clockwise or counterclockwise, and whether the connection should take the large path or the small path.
- radius= RADIUS:
  The points are to be connected by an arc with radius=RADIUS
- size= [small | large] (optional):
  Indication, whether the the connection between the two points should be on the smaller or the larger side of the arc.
- type= [clockwise | counterclockwise]:
  Indication, whether the connection between the two points should proceed clockwise or counterclockwise along the arc.
clear:
Clears the current polygon path.
doit:
Puts the current data as the data of a general cylinder into the meshing database.

Example The following decribes a cavity with rounded corners.

 # /usr/local/gd1/examples-from-the-manual/ggcylinder-example.gdf

 -general
    outfile= /tmp/UserName/example
    scratch= /tmp/UserName/scratch

    text()= We use 'fixpoints= yes'
    text()= to enshure meshplanes at the points of the polygon.
    text()=
    text()= We use a graded mesh.

 -mesh
    spacing= 100.0e-06
    graded= yes, dmaxgraded= 263.3e-06
    pxlow= -5e-03, pxhigh= 5e-03
    pylow= -4.34e-03, pyhigh= 0
    pzlow= -1.6665e-03, pzhigh= 1.6665e-03

    cxlow= ele, cxhigh= mag
    cylow= ele, cyhigh= mag
    czlow= ele, czhigh= ele

 -ggcylinder

    material= 7
    originprime= ( 0, 0, 0 )
    xprimedirection= ( 1, 0, 0 )
    yprimedirection= ( 0, 0, 1 )
    range= ( -4.2e-03, 4.2e-03 )

    clear  # clear the polygon-list, if any
    point= ( -3.3405e-03, -816.5e-06 )
       arc, radius= 500.0e-06, type= counterclockwise, size= small
    point= ( -2.8405e-03, -1.3165e-03 )
    point= (  2.8405e-03, -1.3165e-03 )
       arc
    point= (  3.3405e-03, -816.5e-06 )
    point= (  3.3405e-03,  816.5e-06 )
       arc
    point= (  2.8405e-03, 1.3165e-03 )
    point= ( -2.8405e-03, 1.3165e-03 )
       arc
    point= ( -3.3405e-03,  816.5e-06 )

    fixpoints= yes # enshure mesh-planes at the points of the polygon
    doit

 -volumeplot
    scale= 4
    doit

**Figure 1.4:** A simple ggcylinder
$\begin{figure}\centerline{ \psfig{figure=ggcylinder-example.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=760pt,bbury=552pt,clip=} } \end{figure}$

Example The following decribes a twisted rectangular waveguide.

 # /usr/local/gd1/examples-from-the-manual/ggcylinder-twisted.gdf

 define(LargeNumber, 10000)

 define(LENGTH, 10e-3)
 define(WGW, 2.54e-3 )
 define(WGH, WGW/2 )

 -general
    outfile= /tmp/UserName/example
    scratch= /tmp/UserName/scratch

    text()= A waveguide-twist
    text()= Waveguide-Width : WGW
    text()= Waveguide-Height: WGH

 -mesh
    spacing= WGW/40
    pxlow= -1e-3, pxhigh= LENGTH+1e-3
    pylow= -WGW*0.6, pyhigh= 0.6*WGW
    pzlow= -WGW*0.6, pzhigh= 0.6*WGW


 define(EL, 10)
 -material, material= EL, type= electric 
 -brick
    #
    # Fill the universe with metal:
    #
    material= EL
       volume= ( -LargeNumber, LargeNumber, \
                 -LargeNumber, LargeNumber, \
                 -LargeNumber, LargeNumber )
    doit

 -ggcylinder
    #
    # The twisted waveguide.
    # We use a rectangular footprint,
    # and specify a pitch.
    # The footprint shall rotate by -90 degrees, over a length of LENGTH.
    #


    material= 0
    originprime= ( 0, 0, 0 )
    xprimedirection= ( 0, 1, 0 )
    yprimedirection= ( 0, 0, 1 )
    range= ( 0, LENGTH )
    pitch= -90/LENGTH

    clear  # clear the previous polygon-list, if any
    point= ( -WGW/2, -WGH/2 )
    point= (  WGW/2, -WGH/2 )
    point= (  WGW/2,  WGH/2 )
    point= ( -WGW/2,  WGH/2 )
    doit

 -volumeplot
    eyeposition= ( 1, 2, 1.3 )
    scale= 4.5
    doit

**Figure 1.5:** A simple ggcylinder, with a pitch.
$\begin{figure}\centerline{ \psfig{figure=ggcylinder-twisted.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=760pt,bbury=552pt,clip=} } \end{figure}$

Example The following decribes a transition from a circular waveguide to an elliptical waveguide.

 # /usr/local/gd1/examples-from-the-manual/ggcylinder-circular-to-elliptic.gdf

 define(LargeNumber, 10000)

 define(LENGTH, 10e-3)
 define(RADIUS1, 2.54e-3 ) define(RADIUS2, 5.0e-3  )
 -general
    outfile= /tmp/UserName/example
    scratch= /tmp/UserName/scratch

    text()= A transition from a circular waveguide to an elliptical one.
    text()= The bounding box is specified such,
    text()= that only the part below the plane z=0 is discretised.

 -mesh
    spacing= RADIUS1/20
    pxlow= -1e-3, pxhigh= LENGTH+1e-3
    pylow= -RADIUS2*1.0, pyhigh= RADIUS2*1.0
    pzlow= -RADIUS1*1.1, pzhigh= 0


 define(EL, 10)
 -material, material= EL, type= electric 
 -brick
    #
    # Fill the universe with metal:
    #
    material= EL
       volume= ( -LargeNumber, LargeNumber, \
                 -LargeNumber, LargeNumber, \
                 -LargeNumber, LargeNumber )
    doit

 -ggcylinder
    #
    # The waveguide.
    # We use a circular footprint,
    # and specify a slope, different in x- and y
    #
    material= 0
    originprime= ( 0, 0, 0 )
    xprimedirection= ( 0, 1, 0 )
    yprimedirection= ( 0, 0, 1 )
    range= ( 0, LENGTH )
# xlingro 1+(RADIUS2/RADIUS1-1)/LENGTH
    xslope= (RADIUS2/RADIUS1-1)/LENGTH
    yslope= 0

    clear  # clear the previous polygon-list, if any
    point= ( -RADIUS1, 0 )
      arc, radius= RADIUS1, size= large, type= counterclockwise
    point= (  RADIUS1, 0 )
      arc
    point= ( -RADIUS1, 0 )
    doit

 -volumeplot
    eyeposition= ( 2, 1, 1.8 )
    scale= 3
    doit

**Figure 1.6:** A simple ggcylinder, with different growthfactors for x and y.
$\begin{figure}\centerline{ \psfig{figure=ggcylinder-circular-to-elliptic.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=760pt,bbury=552pt,clip=} } \end{figure}$

Example The following decribes a elliptical wedge where the axis of the ggcylinder is in the z-direction, while the plane normal of the wedge is titled.

 # /usr/local/gd1/examples-from-the-manual/ggcylinder-usezprimedirection.gdf

 #
 # Some helpful symbols:
 #
 define(EL, 1) define(MAG, 2)
 define(INF, 1000)

 define(STPSZE, 0.5e-3)       # define the transverse mesh step size, 0.5 mm
 
 #
 # description of the flange geometry
 #
# define(FlangeGap, 2e-3 )     # gap of the flange joint
 define(FlangeGap, 10e-3 )     # gap of the flange joint
 define(FlangeD0, 80e-3)      # diameter of gasket seal
 define(Width, FlangeGap/2 )  # 1/2 width of flange gap in z-axis
 define(FlangeRadius, FlangeD0/2 )
 define(AxisA  , 70e-3/2 )    # 1/2 *major diameter of interior ellipse
 define(AxisB  , 32e-3/2 )    # 1/2 *minor diameter of interior ellipse

  #--- parameters related to a tilted flange joint ---
 define(ZW, 10e-3)                      # z-deviation from the y-axis 
 define(Theta, atan(ZW/FlangeRadius) )  # angle between y-axis and y'-axis
 define(RR, FlangeRadius/cos(Theta) )   # radius of tilted cylinder
 define(LL, Width/cos(Theta) )          # half length of tilted cylinder


 ###
 ### We enter the section "-general"
 ### Here we define the name of the database where the
 ### results of the computation shall be written to.
 ###    (outfile= )
 ### We also define what names shall be used for scratchfiles.
 ###    (scratchbase= )
 ###
 -general
    outfile= /tmp/UserName/bla
    scratch= /tmp/UserName/scratch-

    text()= flange gap= FlangeGap
    text()= mesh= STPSZE m
    text()= tilt angle of flange= eval(Theta*180/@pi) [degrees]

 ###
 ### We define the default mesh-spacing,
 ### we define the borders of the computational volume.
 ###
 define(Zmin, -4e-2)
 define(Zmax,  4e-2)
 -mesh
   spacing= STPSZE
   pxlow= -5e-2, pxhigh= 0
   pylow= -4e-2, pyhigh= 4e-2
   pzlow= Zmin, pzhigh= Zmax

 #####
 # Specify that the material index '3'
 # describes a perfect conducting material.
 -material
   material= 3
   type= electric

## 
## fill the universe with metal
##
 -brick
   material= 3
     xlow= -INF, xhigh= INF
     ylow= -INF, yhigh= INF
     zlow= -INF, zhigh= INF
   doit


 ##
 ## Step 1: carve out a tilted circular box
 ##
  -ggcylinder         # a parallelogram gap with a tilt angle
     material= 0
     origin= (0,0,0)
     xprimedirection= (1,0,0)
     yprimedirection= (0, cos(Theta), sin(Theta) )
 zprimedirection= ( 0, 0, 1 )
 usezprimedirection= yes
     range= ( -LL, LL )

     clear
     point= ( -RR, 0 )
       arc, radius= RR,type= counterclockwise, size= small
     point= (  RR, 0 )
       arc, radius= RR,type= counterclockwise, size= smal 
     point= ( -RR, 0 )
     show= later
     doit
 usezprimedirection= no # Switch back to the default, 'no'

##
## Step 2: Creating the interior footprint of elliptic beampipe(hollow)
##
-ggcylinder
   material= 0
   origin= (0, 0, 0)
   xprimedirection= (1, 0, 0)
   yprimedirection= (0, 1, 0)
   range= (Zmin-2*STPSZE, Zmax+STPSZE)
   xslope= 0, yslope= 0

   clear  # clear any old polygon-description of the footprint
    # point= (x', y')
   point= (0, -AxisB),
     ellipse, center= (0,0),
   point= (AxisA, 0),
     ellipse,
   point= (0, AxisB),
     ellipse,
   point= (-AxisA, 0),
     ellipse,
   point= (0, -AxisB),
# show= all
   doit

 ############

 -volumeplot
    eyeposition= ( 1, -0.5, 0.5 )
    scale= 3
    doit

**Figure 1.7:** A simple ggcylinder, with zprimedirection different from the footprints plane normal.
$\begin{figure}\centerline{ \psfig{figure=ggcylinder-usezprimedirection.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=760pt,bbury=552pt,clip=} } \end{figure}$

Example The following decribes a corrugated waveguide. The cross-section is specified as a ggcylinder, the cross section is circular. The xscale and yscale is specified via tables.

 # /usr/local/gd1/examples-from-the-manual/zxscale-example.gdf


## beginning of structure modeling
##
define(FFAC, 1)
 define(BunchLength, 2e-2)              # rms bunch length of Gaussian beam 
 define(Radius, eval(240.03e-3/2) )     # Radius of circle
 define(TaperLength, 374.93e-3)         # Length of the taper
 define(AxisA, eval(80e-3/2) )          # Radius a of the ellipse
 define(AxisB, eval(38e-3/2) )          # Radius b of the ellipse
 define(PipeLength, 6e-2)               # Length of elliptic beampipe
 define(CircularPipe, 20e-2)            # Half length of circular beampipe
 define(STPSZE, eval(BunchLength/5/FFAC) )  # Mesh size
 define(FMAX, 2e9)                      # Max. frequency of interest in [Hz]
 define(MAXSPACING, eval(3e8/FMAX/20) )


 -general
    outfile= /tmp/UserName/bla
    scratch= /tmp/UserName/scratch-


 -mesh
    spacing= 2*STPSZE
    pxlow = -Radius, pxhigh= 0
    pylow = -Radius, pyhigh= 0
    pzlow=  -0.5, pzhigh= 0.5
    zfixed( 2, -(TaperLength+CircularPipe), -CircularPipe )
    zfixed( 2, CircularPipe, CircularPipe+TaperLength )

    #
    # The conditions to use at the borders of the computational volume:
    #
    cxlow= electric, cxhigh= magnetic
    cylow= electric, cyhigh= magnetic
    czlow= electric, czhigh= electric


 define(CircularPipe, 200e-2)            # Half length of circular beampipe

 # Fill the universe with metal.
 -brick
    material= 1
    volume= ( -INF,INF, -INF,INF, -INF,INF )
    doit


##
## Create the circular beampipe, with corrugation.
##
 -ggcylinder
    material= 0
    origin= (0,0, -0.4 )
    xprimedirection= (1,0,0)
    yprimedirection= (0,1,0)
    range= (0, 0.8 )
    xslope= 0
    yslope= 0
 zxscale= zxscale-sinus
 zyscale= zxscale-sinus

    clear  # clear any old polygon-description of the footprint
     # point= (x', y')
    point= (0, -Radius)
      arc, radius= Radius, type= clockwise, size= small
    point= (0,  Radius)
      arc
    point= (0, -Radius)
#    show= now
    doit

 -gccylinder
    material= 0, radius= Radius, length= INF
    origin= ( 0, 0, 0.4 ), direction= ( 0, 0, 1 ), doit
    origin= ( 0, 0, -0.4 ), direction= ( 0, 0, -1 ), doit

 -volumeplot, doit

**Figure 1.8:** The discretisation of a corrugated circular waveguide, specified as a ggcylinder with zxscale.
$\begin{figure}\centerline{ \psfig{figure=zxscale-example.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=760pt,bbury=552pt,clip=} }\end{figure}$

Next: -gbor: A general body Up: Geometric primitives Previous: -gccylinder: A circular cylinder Contents