-gbor: A general body of revolution in general direction

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-gbor: A general body of revolution in general direction

A gbor is a body of revolution with a cross section described as a general polygon. This cross section is swept along an axis in a general direction, additionally, only cells that fulfill some additional condition will be filled.

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section -gbor                                                              #
 ##############################################################################
 # material       =  1                                                        #
 # whichcells     = all, taboo= none                                          #
 #     show       = off                 -- (off | all | later | now)          #
 #     name       = gbor-000000000                                            #
 # inside         = yes                 -- (yes|no)                           #
 # originprime    = ( 0.0, 0.0, 0.0 )                                         #
 # zprimedirection= ( 0.0, 0.0, 1.0 )                                         #
 # rprimedirection= ( 1.0, 0.0, 0.0 )                                         #
 # range          = ( 0.0, 360.0 )                                            #
 # xscaleprime    = 1.0                 -- elliptic coords.                   #
 # yscaleprime    = 1.0                 -- elliptic coords.                   #
 ##############################################################################
 ## syntax:                                                                   #
 #  point= (Zi, Ri)                                                           #
 #  arc, radius= RADIUS, type= [clockwise | counterclockwise]                 #
 #       size= [small | large ]                                               #
 #       deltaphi= 5                                                          #
 #  ellipse, center= (Z0, R0), 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 gbor.
zprimedirection:
The direction of the z'-axis of the gbor.
rprimedirection:
The direction of the r'-vector of the polygon. The r'-direction will internally be enforced to be perpendicular to the z'-direction.
range:
Start and end values (in degrees) of the phi-coordinate of the body of revolution.
xscaleprime, yscaleprime:
The x'-coordinates, resp. y'-coordinates of the footprint are multiplied by these factors.
inside:
Flag, specifying whether cells inside of the gbor 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 gbor should be displayed.
If show=off, no outline will be displayed.
If show=later, the outline will be shown later together with other specified gccylinders, ggcylinders and gbors.
If show=all, the outlines of all gccylinders, ggcylinders and gbors so far where show was not off will be displayed.
point= (XI, YI):
XI, YI are the coordinates of the i.th point in the polygon that describes the polygon of the gbor. There have to be minimum 3 points, or 2 points and an arc or 2 points and an ellipse.
arc:
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 body of revolution into the meshing database.

Example The following describes something like a tuning-plunger.

 # /usr/local/gd1/examples-from-the-manual/plunger0.gdf

 define(PlungerInnerRadius, 100e-3/2 )
 define(PlungerCurvature, 16e-3 )
 define(PlungerAngle, -67.5*@pi/180 )

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

    text()= A Plunger, modelled as a body of revolution.
    text()= Curvature     : PlungerCurvature
    text()= Radius        : PlungerInnerRadius
    text()= Angle of Axis : eval(PlungerAngle * 180 / @pi) Degrees

 -mesh
    spacing= 0.2e-2
    pxlow= -5e-2, pxhigh= 12e-2
    pylow= -18e-2, pyhigh= 3e-2
    pzlow= -6e-2, pzhigh= 6e-2

 -gbor
     material= 4
     originprime= ( 0, 0, 0 )
     zprimedirection= ( -cos(PlungerAngle), -sin(PlungerAngle), 0 )
     rprimedirection= ( 0, 0, 1 )
     range= ( 0, 360 )

     clear
        # point= ( z, r )
     point= ( 0, 0 )
     point= ( 0, PlungerInnerRadius-PlungerCurvature )
        arc, radius= PlungerCurvature, size= small, type= counterclockwise
     point= ( -PlungerCurvature, PlungerInnerRadius )
     point= ( -170e-3, PlungerInnerRadius )
     point= ( -170e-3, 0 )
     doit

 -volumeplot
     scale= 3
     doit

**Figure 1.9:** A simple gbor.
$\begin{figure}\centerline{ \psfig{figure=gbor-example0.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=760pt,bbury=552pt,clip=} }\end{figure}$

Example The following discretises the connection of two circular waveguides, meeting each other at an angle of 90 degrees.

 # /usr/local/gd1/examples-from-the-manual/gbor-example1.gdf
define(LargeNumber, 10000)       # some big number

define(MAXCELLS, 1e+5)

define(XLOW, 0) define(XHIGH, 5e-2)
define(YLOW, 0) define(YHIGH, 6e-2)
define(ZLOW, -1.1e-2) define(ZHIGH, 0)

define(STPSZE, ((XHIGH-XLOW)*(YHIGH-YLOW)*(ZHIGH-ZLOW)/MAXCELLS)**(1/3) )

 -mesh
    volume= ( XLOW, XHIGH, \
              YLOW, YHIGH, \
              ZLOW, ZHIGH )

    spacing= STPSZE

 -general
    outfile= /tmp/UserName/example
    scratch= /tmp/UserName/scratch
 define(R, 1.0e-2)
    text()= Intersection of two circular cylinders with radius R
    text()= generated as general cylinders
    text()= where 'taboo' is specified
    text()= stpsze= STPSZE, maxcells= MAXCELLS

#
# Fill everything with metal
#
 -brick
    material= 1
    volume= ( -LargeNumber, LargeNumber, \
              -LargeNumber, LargeNumber, \
              -LargeNumber, LargeNumber )
    doit

#
# First step,
# fill cells above the diagonal with material 3
# these cells will not be filled by the first circular cylinder,
# since we will specify 'taboo= 3'
#
#
 -ggcylinder
    material= 3,
    origin= ( 0, 0, 0 ), xprime= ( 1, 0, 0 ), yprime= ( 0, 1, 0 ),
    range= ( ZLOW, ZHIGH ),

    clear
    point= ( XLOW, YLOW ), point= ( XLOW, YHIGH ),
    point= ( XLOW+(YHIGH-YLOW), YLOW )

    doit

#
# Second step:
# fill a circular cylinder in x-direction,
# but NOT cells with material index 3 (taboo=3)
#
 -ggcylinder
    material= 0, taboo= 3,
    xprime= ( 0, 1, 0 ), yprime= ( 0, 0, 1 ),  # so the axis will be in +x
    origin= ( 0, 4e-2, 0 ),                    # shift of origin
    range= ( XLOW, XHIGH ),

    clear
       point= ( -R, 0 ),
         arc, radius= R, type= counterclockwise,
       point= ( 0, -R ),
         arc, radius= R,
       point= ( R, 0 ),
    doit

#
# Third step:
# fill a circular cylinder in y-direction,
# but ONLY cells with material index 3 (whichcells=3),
#
 -ggcylinder
    material= 0, whichcells= 3, taboo= none
    xprime= ( 1, 0, 0 ), yprime= ( 0, 0, -1 ),  # so the axis will be in +y
    origin= ( 2.e-2, 0, 0 ),                    # shift of origin
    range= ( YLOW, YHIGH ),

    clear
       point= ( -R, 0 ),
          arc, radius= R, type= clockwise,
       point= ( 0, R ),
          arc, radius= R,
       point= ( R, 0 ),
    doit

 -volumeplot
    eyeposition= ( 1, 2, 1 )
    scale= 3.5
    doit

**Figure 1.10:** The intersection of two circular cylinders, where **whichcells** and **taboo** were specified.
$\begin{figure}\centerline{ \psfig{figure=gbor-example1.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=760pt,bbury=552pt,clip=} }\end{figure}$

Example The following describes a reentrant cavity.

 # /usr/local/gd1/examples-from-the-manual/gbor-example.gdf
 define(MaxCells, 2e+6)

 #
 # define the geometry parameters
 #
 define(RBeamTube, 4.7625e-2)
 define(RCurve,  1.0e-2)
 define(ZGapNose, 10.9e-2)
 define(RLarge, 25.0e-2)  define(RSmall, 15.0e-2)  define(RCenter, 10.0e-2)

 define(INF, 10000) define(EL, 1) define(MAG, 2)

 define(XLOW, -0.250) define(XHIGH, 0.250)
 define(YLOW, -0.250) define(YHIGH, 0.250)
 define(ZLOW, -0.200) define(ZHIGH, 0.200)

 define(STPSZE, ((XHIGH-XLOW)*(YHIGH-YLOW)*(ZHIGH-ZLOW)/MaxCells)**(1/3) )

 #
 # gdfidl can evaluate sin(), cos(), atan() and X**Y
 # definition of functions degsin() and degcos()
 #
 sdefine(degsin, [sin((@arg1)*@pi/180)])
 sdefine(degcos, [cos((@arg1)*@pi/180)])
 sdefine(degtan, [sin((@arg1)*@pi/180)/cos((@arg1)*@pi/180)])

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

   text(3)= A quarter of a reentrant cavity
   text()= The cavity is described as a body of revolution,
   text()=
   text()= maxcells= MaxCells, stpsze= STPSZE

-mesh
   pxlow= 0*XLOW, pxhigh= 1*XHIGH
   pylow= 0*YLOW, pyhigh= 1*YHIGH
   pzlow= 1*ZLOW, pzhigh= 1*ZHIGH

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

   spacing= 1*STPSZE

 -material
   material= 3, type= electric

 -brick
    #
    # we fill the universe with metal
    #
    material= 3
       volume= ( -INF,INF, -INF,INF, -INF,INF )
    doit

 #
 # carve out the cavity itself
 #
 -gbor
     material= 0, range= ( 0, 360 )
     origin= ( 0, 0, 0 )
     show= later,      # don't show now, but show later
#

     clear   # clear a possible previous polygon list

        point= (     0          , 0 ),
        point= ( ZHIGH+2*STPSZE , 0 ),
        point= ( ZHIGH+2*STPSZE , RBeamTube ),
        point= ( ZGapNose+RCurve, RBeamTube ),
           arc, radius= RCurve, size= small, type= clockwise,
           deltaphi= 10
define(rdum, RBeamTube+(1+degcos(30))*RCurve)
define(zdum, ZGapNose +(1-degsin(30))*RCurve)
        point= ( zdum, rdum )
define(deltaz, RSmall-zdum)
define(deltar, deltaz*degtan(30))
 define(ffac, 0.85)   ## adjust this for a smooth transition
define(zdum2, zdum+ffac*deltaz)
define(rdum2, rdum+ffac*deltar)
        point= ( zdum2, rdum2 )
          arc, radius= RCurve, size= small, type= counterclockwise,
          deltaphi 10
        point= ( RSmall, RCenter-0.8*RCurve ),
        point= ( RSmall, RCenter ),
           arc, radius= RSmall, size= small, type= counterclockwise,
           delta= 3
        point= ( -RSmall, RCenter ),
        point= ( -RSmall, RCenter-0.8*RCurve ),
           arc, radius= RCurve, size= small, type= counterclockwise,
           deltaphi= 10
        point= ( -zdum2, rdum2 )
        point= ( -zdum, rdum )
           arc, radius= RCurve, size= small, type= clockwise, delta 10
        point= ( -(ZGapNose+RCurve), RBeamTube ),

        point= ( ZLOW-2*STPSZE, RBeamTube ),
        point= ( ZLOW-2*STPSZE, 0 )
     list
     doit
#
# enforce some meshplanes:
#
-mesh
   zfixed( 2, -(ZGapNose+RCurve), -ZGapNose ) # at the noses
   zfixed( 2,  (ZGapNose+RCurve),  ZGapNose ) # at the noses

   zfixed( 2, -RSmall, RSmall)                # at the z-borders of the cavity

-volumeplot
   scale= 3
   doit

**Figure 1.11:** A complicated gbor
$\begin{figure}\centerline{ \psfig{figure=gbor-example.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=760pt,bbury=552pt,clip=} }\end{figure}$

Example The following describes two bodies of revolution that look similiar to glasses. The shape is only specified once, but two different glasses are generated by varying 'zprime' and 'rprime'

 # /usr/local/gd1/examples-from-the-manual/gbor-glasses.gdf

define(MAXCELLS,1e+6)

define(XLOW,-5e-2) define(XHIGH,18e-2)
define(YLOW,-0e-2) define(YHIGH,17e-2)
define(ZLOW,-3e-2) define(ZHIGH,18e-2)

define(STPSZE, ((XHIGH-XLOW)*(YHIGH-YLOW)*(ZHIGH-ZLOW)/MAXCELLS)**(1/3) )


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

 -mesh
    spacing= STPSZE
    volume= ( XLOW, XHIGH, \
              YLOW, YHIGH, \
              ZLOW, ZHIGH )

# Fill the universe with vacuum
 define(LargeNumber,10000)
 -brick
     material= 0
        volume= ( -LargeNumber, LargeNumber, \
                  -LargeNumber, LargeNumber, \
                  -LargeNumber, LargeNumber )
     doit

 #
 # The glasses:
 #
  -gbor

     #
     # Definition of the cross-section:
     #
     clear
     point= (  0.7e-2,      0 ),
     point= (       0, 4.0e-2 ),
       arc, radius=0.25e-2, size= large, type= clockwise
     point= (  0.3e-2, 4.0e-2 ),
     point= (  1.0e-2, 1.0e-2 ),
     point= (  8.0e-2, 0.8e-2 ),
     point= ( 10.0e-2, 1.4e-2 ),
     point= ( 15.0e-2, 6.0e-2 ),
       arc, radius= 0.4e-2, type= clockwise
     point= ( 15.2e-2, 5.4e-2 ),
     point= ( 10.0e-2,      0 )

     #
     # That cross-section is used twice,
     # with different parameters for origin, zprime etc..
     #

     material= 1,
     origin= ( -2e-2, 0, 4e-2 ),
     zprimedir= ( 1, 0, 0 ),
     rprimedir= ( 0, 1, 0 ),
     range= ( -90, 90 ),
     show= now
     doit                 # this 'doit' generates the first 'glass'


     material= 3
     origin= ( 0, 12e-2, 4e-2 ),
     zprimedir= ( 1, -0.5, 0.7 ),
     rprimedir= ( 0, 1, 0 ),
     range= ( 0, 360 ),
     show= all
     doit                 # this 'doit' generates the second 'glass'

 -volumeplot
     eyeposition= ( 0.7, 1, 0.5 )
     scale= 4
    doit

**Figure 1.12:** Two complicated gbors (glasses).
$\begin{figure}\centerline{ \psfig{figure=gbor-glasses.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=760pt,bbury=552pt,clip=} }\end{figure}$

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