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SIMION v8.1.3.1-TEST posted - EA with new GEM features!
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GEM Geometry File

A SIMION geometry file (GEM) defines electrode geometries using constructive solid geometry (CSG) primitives. CSG operations define shapes using unions and intersections of other basic shapes (e.g. a rectangular slab with a cylinder hole cut through it), a bit similar in concept to machining. GEM files are text files and have the file name extension of ”.GEM”. SIMION can convert a GEM file to a PA file.

The GEM file appendix in the printed manual is perhaps the first place to start. See also SIMION Example: geometry for examples. “courses\advanced” also has some notes on GEM files. Additional tips are given on this page.

GEM Extensions in 8.2

SIMION 8.2 Early Access Mode makes major enhancements to the GEM syntax. Here is a summary of the new features described in more detail below.

  • New commands to define shapes easier or with fewer rotations:

    • cylinder3d() - easily defines a cylinder between two endpoints: cylinder3d(5,5,0, 5,5,10, 3). Use this rather than cylinder since it can be simpler and avoids locate rotations.
    • half_space() - defines a volume below an infinite plane defined by a point and normal vector. half_space(5,0,0, 1,1,1). Use this rather than than box3d since it is simpler and avoids rotations.
    • shape() - defines your own custom shapes from analytical equations or function. Example: e(1) { shape(function(x,y,z) return x^2 + y^2 > z end) . Complex surfaces can be defined directly in the GEM file. No need for doing this outside of a GEM file with the simion.pas pa:fill() API.
  • New transformations:

    • extrude_xy(), extrude_yz() and extrude_zx() - extrudes a 2D image drawn in the given plane. For example, polyline normally takes an XY plane drawing, which can then be wrapped in a rotation (locate) to another plane, but the rotation can be tricky. These commands make it more clear: extrude_yz() { polyline(0,0, 5,10, 10,0) } ; y,z points . Even XY extrusions can be specified more simply; for example to extrude from z=3 to z=5: extrude_xy(3,5) { polyline(0,0, 5,10, 10,0) } ; x,y points .
    • revolve_xy(), revolve_yz(), revolve_zx() - define volumes of rotation in any given plane. These are suggested instead of rotate_fill, which only operates in the XY plane without subsequent rotation. This command also defines a shape, so it can be used wherever shapes can be used, such as intersections, which is not possible with rotate_fill (except via the workaround of cutting away from a rotate_fill using a subsequent n(0) { } but that may cut more than the current shape).
    • rotate_x(), rotate_y(), rotate_z() - rotates contained objects. They rotate counter-clockwise (CCW) looking down the positive end of the given axis. These are recommended over locate commands for clarity. Many times you can omit rotate_x|y|z as well when the commands above are used.
  • Other command improvements:

    • pa_define() accepts named parameters. pa_define {101, 101, dx=0.1} is equivalent to pa_define(101,101,1, p, n, e,, 0.1,,,, auto). This is recommended. Please note that the {} syntax has different defaults than (), such as planar non-mirror symmetry and the newer surface='auto'. Another example: pa_define {101, 101, 1, 'planar xy', surface='fractional'}.
      • pa_define() can accept mm array sizes rather than grid point sizes. The above example can be rewritten as pa_define {10*mm, 10*mm, dx=0.1} . It defines a 10 * 10 mm^2 region. This recommended.
    • e(): and n() can accept a function parameter for defining gradient voltages over electrodes or analytic potentials in space.
    • fill and within can be omitted when not necessary, for shorter GEM code. Use e(1) { circle(0,0, 50) } rather than e(1) { fill { within { circle(0,0, 50) } } } . See omit fill/within commands.
    • intersect() is a synonym for within. The name intersect makes the meaning more clear and is recommended. e(1) { intersect { box(0,0, 10,10) circle(0,0, 10) } } .
    • include() supports improved ways to pass variables to/from included GEM files (see examples below).
    • inf to represent infinity rather than a large number (e.g. 1e6). box(-inf,0, inf, 2). This is more clear and recommended.
  • Simpler syntax:

    • $(...) and # can be omitted around Lua code. They are no longer necessary:

      local w = 2
      e(1) {
        for i=1,3 do
          box(i*10,0, i*10+w, 10)
    • Using a Lua style comment -- in the file will disable compatibility mode supporting older deprecated GEM syntax such as space-delimited argument lists, + before numbers, and unquoted strings. New syntax.

    • See New syntax for details on other language changes.

  • Upcomming features:

    • stl - include STL files in GEM file. stl("lens.gem").
  • Be sure to also utilize SIMION 8.1 features like surface='auto' or surface='fractional'. See surface=auto option in pa_define [].

Enable Early Access Mode to use the new features.

New syntax

The GEM language has been significantly extended to merge GEM syntax, Lua syntax, and prepreprocessing syntax (# $()). Example:

-- new syntax
pa_define{wx=10, wy=10, wz=10, dx=0.5, surface='fractional'}
local function paraboloid(x0,y0,z0, a, b)
  shape(function(x,y,z) return ((x-x0)/a)^2 + ((y-y0)/b)^2 < (z-z0) end)
e(1) {
  for i=1, 3 do
    local y = i*2
    box(i*2, 0, i*2+1, y)
e(2) { paraboloid(5,5,5, 1, 1) }

Previously, something like that would require various preprocessing code:

; old SIMION 8.1 compatible GEM
# local function round(x) return math.floor(x+0.5) end
# local wx, wy, wz = 10, 10, 10
# local dx = 0.5
# local nx = round(wx/dx) + 1
# local ny = round(wy/dx) + 1
# local ny = round(wz/dx) + 1
pa_define($(nx), $(ny), $(nx), p, n, e,, 0.5, surface=fractional)
# function paraboloid(x0,y0,z0, a)
  locate($(x0),$(y0),$(z0), 1, -90) {
    rotate_fill() {
      locate(,,, 1, 0,-90) {
        within { parabola(0, 0, $(a^2/4)) }
# end
e(1) {
  # for i=1, 3 do
    # local y = i*2
    fill { within { box($(i*2), 0, $(i*2+1), $(y)) } }
  # end
e(2) { $(paraboloid(5,5,5, 1)) }

A more prominent change seen above is that variables and code used in GEM commands need not be escaped anymore with # and $(...), as as these are built into the language now.

Most Lua syntax is now available in GEM, including

  • Lua style comments: single line -- and multiline --[[...]]:

    -- this is line comment.
      This is a
      multi-line comment.
    e(1) { box() }  -- another line comment

    These are similar to ; style comments, and the two comments styles must not be mixed in the same file.

    Added in also.

  • Named parameters can be used with { style function calls. This is primary used for the pa_define() command:

    pa_define {wx=10, wy=10, dx=0.1, surface='fractional'}
  • Arbitrary Lua code, outside of commands braces:

    local x = 1
    for i=1,10 do
      x = x + i
    print('hello world', x)
    e(1) { box(x,x, x+1, x+1) }
  • if, for and local statements within command brackets:

    e(1) {
      for i=1,4 do
        local j = i*2
        if i % 2 == 0 then
        for i=1,3 do
          i, i*2

    This is convenient for geometric constructions. It is an extension to Lua syntax (normally statements cannot exist inside expressions such as inside braces, but this syntax extension allows it).

    Note: Commas may be placed around statements but also can be omitted:

    {local i=1, -i, if i > 0 then 3, 4 end, 5} ; these are equivalent
    {local i=1  -i  if i > 0 then 3, 4 end  5}
    {-1, 3, 4, 5}

    It is recommended to omit commas around statements in most cases. local can be confusing in a few cases without commas, such as local i=1 - i (space before i is interpreted as a subtraction).

  • No maximum line length. Prior to, more than 200 characters in a line were ignored.

The following GEM syntax is retained for compatibility:

  • Adjacent commas are interpreted as a nil value, consistent with traditional GEM syntax. These are equivalent:

    box(,, 10, 10)
    box(,, 10, 10,)
    box(nil, nil, 10, 10)
    box{,, 10, 10}
    box{,, 10, 10,}
    box{nil, nil, 10, 10}

    Note that , before an end brace does not pass another nil value.

  • Commas may be omitted between end braces }} or end parenthesis ) and an identifier, consistent with traditional GEM syntax. Example:

    e(1) {
      circle(0,0, 20)
      notin { box(0,0, 10,10) }
      circle(30,30, 10)

    rather than:

    e(1) {
      circle(0,0, 20),
      notin { box(0,0, 10,10) },
      circle(30,30, 10)

    Omitting commas is recommended.

  • Using a Lua style style comment -- in the file will disable “compatibility mode.” With compatibility mode enabled, the following traditional GEM syntax is supported:

    • ; is interpreted as GEM line comment. (In regular mode, ; is interpreted as a Lua statement or Lua table field separator):

      ; first example
      t = {1, 2, 3}  v = {4, 5}    ; do this
      t = {1; 2; 3}; v = {4, 5};   ; can't do this
      -- second example, this line disables compatibility mode
      t = {1, 2, 3}  v = {4, 5}    -- do this
      t = {1; 2; 3}; v = {4, 5};   -- ok do to this
    • Numbers may be preceeded by an optional +, consistent with traditional GEM syntax:

      box(-10, -10,  10,  10)  ; these are the same
      box(-10, -10, +10, +10)

      The + is not recommended.

    • Commas may be omitted between numbers in function arguments lists and table field lists, consistent with traditional GEM syntax:

      circle(0 +20  -20)      ; these are the same
      circle(0, 20, -20)
      circle{0 +20  -20}
      circle{0, 20, -20}

      However, use of commas is strongly recommended to avoid ambiguity. Compare:

      circle(0  -5  +20)    ; means circle(0, -5, 20)
      circle(0 - 5+  20)    ; means circle(15)
      circle(0, (-5 +20))   ; means circle(0, 15)
      circle(0  f (5))      ; means circle(0, f(5))
    • pa_define and include commands can accept unquoted strings, consistent with traditional GEM syntax, though only in compatibility mode. These are equivalent:

      include(example.gem)      ; ok in compatibility mode
      include("example.gem")    ; ok in compatibility mode; required in non-compatibility mode
      pa_define(11, 11, 1, planar)
      pa_define(11, 11, 1, "planar")
      pa_define(11, 11, 1, n, p, surface=fractional)
      pa_define{11, 11, 1, surface='fractional'}
      pa_define(101,101,101,"planar","xyz", "electrostatic",, 0.05,,,"gu", "fractional") ; new
      pa_define(101,101,101,planar,xyz, electrostatic,, 0.05,,,gu,fractional)  ; old style

      Quotes are recommended. Quotes are required when using the new {...} syntax:

      pa_define{101,101,101,"planar","xyz", "electrostatic",, 0.05,,,"gu", "fractional"}


  • The preprocessing syntax $(...) is still supported for compatibility. But some semantics of preprocessing have changed because it is now part of the language rather than as a separate preprocessing step that operatings on strings. If the old $(...) syntax is used, it is now more strict and may break some existing code in obscure cases.

    This used to be valid but is no longer valid because the if and { are not properly nested:

    #if x then
    locate(10) {
    #if x then

    Do this instead:

    function f()
    if x then
      locate(10) { f() }

    Keep in mind $(...) can now only be used in the context of a command or parameter, and $(x) is usually equivalent to x except when x is a string, where it is interpreted as GEM code to be compiled. So $("box(0,0,10,10)") is equivalent to box(0,0,10,10) . One obscure behavior:

    local function f() return "" end
    local function g() return "2,3" end
    box3d($(f()), $(g()), $(g()))

    will be interpreted as box3d(2, 3, 2, 3).

omit fill/within commands

The fill and within statements can now be omitted, to give simpler syntax. Also intersect is now a synonym for within but more clearly indicates its purpose.

The following examples are equivalent (original followed by simpler syntax):

e(1) { circle(0,0, 10) }  ; new
e(1) { fill { within { circle(0,0, 10) } } }  ; old

e(1) { box(0,0, 10,10) notin { box(2,2, 8, 8) } }  ; new
e(1) { fill { within { box(0,0, 10,10) } notin { box(2,2, 8, 8) } } }  ; old

e(1) { intersect { box(0,0, 10,10) circle(0,0, 10) } }  ; new
e(1) { fill { within { box(0,0, 10,10) circle(0,0, 10) } } } ; old

e(1) { box(0,0, 10,10) circle(0,0, 10) }  ; new
e(1) { fill { within { box(0,0, 10,10) } within { circle(0,0, 10) } } } ; old

e(1) { box(0,0, 10,10) notin{box(1,1, 9, 9)} box(3,3, 7,7) notin{box(4,4, 6,6)} } ; new
e(1) { fill { within { box(0,0, 10,10) } notin { box(1,1, 9,9) } }
       fill { within { box(3,3, 7,7)   } notin { box(3,3, 7,7) } } }  ; old


  • within/intersect is still required if you need to take the intersection (AND) of two shapes rather than union (OR), as shown above.
  • Inside a fill the order of notin‘s and within‘s is not important, but multiple fill‘s are applied in order, and if fill is omitted, then each within that follows a notin creates a new fill. Therefore, order can be important when fill is omitted. This is seen in the example above: e(1) { box(0,0, 10,10) notin{box(1,1, 9, 9)} box(3,3, 7,7) notin{box(4,4, 6,6)} } - the notin‘s only cuts from the immediately prior within‘(s), not the following ones, nor ones before previous notin‘s.

Compatibility: Added in 8.2EA-20170324 (Early Access Mode).



pa_define can now accept named parameters:

pa_define{nx=nx,ny=ny,nz=nz, gx=gx,gy=gy,gz=gz, wx=wx,wy=wy,wz=wz,
          symmetry=symmetry,mirror=mirror, type=type, ng=ng,
          dx=dx,dy=dy,dz=dz, unit=unit, surface=surface, refinable=refinable}
           -- new syntax


pa_define{11, 12, 3, 'planar x', dx=1,dy=2,dz=0.5, surface='auto') -- new syntax
pa_define(11, 12, 3, planar, x, e,, 1, 2, 0.5,, auto) ; old syntax

Common examples:

-- 2D planar array
pa_define{11, 11}

-- 2D cylindrical array
pa_define{11, 11, 1, 'cylindrical'}

-- 2D cylindrical array with x mirroring
pa_define{11, 11, 1, 'cylindrical x'}

-- 3D array with yz mirroring
pa_define{11, 11, 11, 'planar yz'}

-- 3D magnetic array
pa_define{11, 11, 11, type='magnetic'}

-- 2D planar array with 0.5 mm per grid unit and fractional surface enhancement
pa_define{11, 11, dx=0.5, surface='fractional'}

-- 2D planar array of 5 mm * 5 mm region with 0.5 mm per grid unit.
-- Each dimension will have 5/0.5 + 1 = 11 grid points.
pa_define{5*mm, 5*mm, 1, dx=0.5}

Named parameters require using {...} not (...). When using named parameters or when compatibility mode is disabled (using Lua -- comments), string values must be quoted (single or double quotation marks), like 'planar' and surface='auto'.

When using the {...} syntax, there are a few differences:

  • values are checked more strictly:
    • symmetry must be ‘planar’ (or ‘p’) or ‘cylindrical’ (or ‘c’). Other abbreviations or capitalization like ‘Plan’ are not allowed.
    • mirror must be ‘’ (none), ‘x’, ‘y’, ‘z’, ‘xy’, ‘xz’, ‘yz’, or ‘xyz’.
    • type must be ‘electric’ (or ‘e’) or ‘magnetic’ (or ‘m’).
  • default values differ:
    • symmetry defaults to 'planar' (not 'cylindrical').
    • mirror defaults to ‘’none’` (not “y”). So, pa_define(11,11,1,p,n) can now be written pa_define{11,11,1}, and pa_define(11,11,1) can now be written pa_define{11,11,1,'c'}.
    • surface defaults to 'auto'.

When using the older (...) syntax, the following enhancements were also made:

  • symmetry now defaults to planar when nz > 1, rather than raising an error, so you can now do pa_define(11,11,11), and mirroring will be none in that case.

The following parameters were added in 8.2EA:

  • gx, gy, gz - number of grid units. These are one less than the number of grid points. These are requivalent:

    pa_define{gx=10, gy=20, gz=0} ; new style
    pa_define(11,21,1,p,n)        ; old style
  • wx, wy, wz - distance in mm. These are equivalent:

    pa_define{wx=5, wy=10, dx=0.1}   ; new style
    pa_define{5*mm, 10*mm, dx=0.1}   ; new style #2
    pa_define(51,101,1, p,n,e,, 0.1) ; old style

    If the distance converted to grid units is a fractional amount, the distance is rounded up to the nearest grid unit.

    As a convenience, you can pass mm lengths in the first three positional parameters if you multiply the numbers by the unit object mm as shown above.

  • refinable - true or false - whether PA is allowed to be refined (default true). This is useful for PAs that store some type of special field that should not be automatically refined in the usual manner (e.g. magnetic vector potential, space-charge, dielectric constants, permeability, gas flow, etc.). It is used extensively in SIMION Example: magnetic_potential and SIMION Example: dielectric (Magnetic Potential and Dielectrics).

The following parameters were addded in 8.1:

  • dx, dy, dz - Grid cell sizes in mm in x, y, and z directions. If dx omitted, it defaults to 1. If dy omitted, it defaults to dx. If dz omitted, it detaults to dy.
  • unit - 'gu' or nil (default) If 'gu', then coordinates in the GEM file are in grid units rather than mm. Normally, coordinates are in mm. However, if dx, dy, dz are all 1, then mm and gu are the same.
  • surface - 'none' (default - old SIMION 7.0/8.0), 'auto' (automatic) or 'fractional' (automatic with surface enhancement). See surface=auto option in pa_define [].

Compatibility: Changes added in 8.2EA-20170324.



When compatibility mode is disabled (using Lua -- comments), the file name string must be quoted, like include("example.gem").

You can now pass additional parameters via the include() statement, which are accessible via the expression ... in the included GEM file:

; 1.gem
pa_define(11,11,1, p)
include("2.gem", 5,6)

; 2.gem
local a, b = ...
box(a, b, a+5, b+5)

You can now also use global variables defined in a GEM file in an included GEM file:

; 1.gem
pa_define(11,11,1, p)
# x = 5
e(1) { include("2.gem") }

; 2.gem
circle(x,x, 5)

Note: for this to work you must do x = 5 not local x = 5 (the latter defined a local variable only within the scope of the current file).

You can also define variables (as well as functions in the included GEM and for use in the main GEM file:

; myshapes.gem
function xplane(x0)
  return function(x,y,z) return x == x0 end
function myobject(r)
e(2) { circle(5,5, r) }

; 1.gem
pa_define(11,11,1, p)
e(1) { xplane(3) }

Compatibility: Added in 8.2EA-20170324 (Early Access Mode).



Defines a custom GEM shape from a Lua function. The given function must return another function that given the coordinates (x,y,z) returns true or false whether that points is inside the shape.


-- defining a paraboloid
pa_define{21,21,21, 'planar', 'xy'}
e(1) {
  shape(function(x,y,z) return (x/5)^2 + (y/5)^2 < z end)

It’s convenient to wrap these in a named function for reuse:

local function paraboloid(x0,y0,z0, a, b)
  shape(function(x,y,z) return ((x-x0)/a)^2 + ((y-y0)/b)^2 > (z-z0) end)
e(1) { paraboloid(0,0,0, 1, 1) }

Other examples:

pa_define(101,101,1, p, surface=fractional)

local function yplane(y0)
  shape(function(x,y,z) return y==y0 end)
local function rbox(x0,y0, r)
    return (x-x0)^4 + (y-y0)^4 <= r^3

e(1) {
e(0) {
  rbox(50,50, 40)
  notin { circle(50,50, 10) }

Compatibility: Added in 8.2EA-20170324 (Early Access Mode).


intersect { ... }

This is now a synonym of within but provided for improved readability. intersect (or within) defines a volume that is inside the all the listed shapes (i.e. their “intersected” or boolean “and” volume).


e(1) {
  intersect {
    circle(0,0, 10)
    polyline(0,0, 20,0, 20,5)
  notin { circle(0,0, 5) }

Compatibility: Added in 8.2EA-20170324 (Early Access Mode).


revolve_xy(angle) { ... }

Forms a volume of revolution with the given angle (defaults to 360 degrees) of the XY plane around the X-axis (CCW facing down positive X axis). This is similar to rotate_fill but can be used in shape context. The contents inside the brackets can be within’s and notin’s.


pa_define(21,21,21, p, surface=fractional)
e(1) {
  fill {
    within { revolve_xy() { within { box(0,1, 7,8) } } }
    notin { points(5,5) }

The above is the same as this:

pa_define(21,21,21, p, surface=fractional)
e(1) {
  rotate_fill(360) { within { box(0,1, 7,8) } }
n(0) {
  fill { within { points(5,5) } }

Furthermore, within can be omitted (see omit fill/within commands), so these two are equivalent (standard and simpler syntax):

revolve_xy() { within { box(0,1, 7,8) } }
revolve_xy() { box(0,1, 7,8) }

The revolve_xy can be more natural and powerful than rotate_fill.

Compatibility: Added in 8.2EA-20170324.


revolve_yz(angle) { ... }

This is similar to revolve_xy but revolves the YZ plane figure around the Y axis (CCW facing down positive Y axis).

It is equivalent to rotate_y(90) { rotate_z(90) { revolve_xy(angle) { ... } } }.

Compatibility: Added in 8.2EA-20170324.


revolve_zx(angle) { ... }

This is similar to revolve_xy but revolves the ZX plane figure around the Z axis (CCW facing down positive Z axis).

It is equivalent to rotate_z(-90) { rotate_y(-90) { revolve_xy(angle) { ... } } }.

Compatibility: Added in 8.2EA-20170324.


extrude_xy(z1, z2) { ... }

Extrudes the figure drawn in the XY plane in the Z direction from Z=z1 to Z=z2.


e(1) {
  extrude_xy(2, 8) {
    polyline(1,1, 10,19, 19,1)
    notin { circle(10,8, 2) }

The above is equivalent to:

e(1) {
  within { polyline(1,1, 10,19, 19,1) box3d(-100,-100,2, 100,100,8) }
  notin  { circle(10,8, 2) }

The extrude_xy can provide a cleaner approach and can also be intersected with other shapes like within { extrude() { ... } sphere(...) }.

If both z1 and z2 are omitted, then the extrusion is infinite in the +-Z directions. If only one is omitted, then the omitted one is assumed to be 0. The order of z1 and z2 (swapped) doesn’t matter.


e(1) {
  extrude_xy() {  ; infinite extrusion in Z
    polyline(1,1, 10,19, 19,1)
    notin { circle(10,8, 2) }

Note that e(1) { fill { within { extrude_xy(z2,z2) { fill { within { box() } } } } } } can be written more simply as e(1) { extrude_xy(z2,z2) { box() } }.

Compatibility: Added in 8.2EA-20170324.


extrude_yz(x1, x2) { ... }

This is similar to extrude_xy but extrudes a YZ plane figure in the X direction.

It is equivalent to rotate_y(0) { rotate_z(90) { extrude_xy(x1, x2) { ... } } }.

Compatibility: Added in 8.2EA-20170324.


extrude_zx(y1, y2) { ... }

This is similar to extrude_xy but extrudes a ZX plane figure in the Y direction.

It is equivalent to rotate_z(-90) { rotate_y(-90) { extrude_xy(y1, y2) { ... } } }.

Compatibility: Added in 8.2EA-20170324.


scale(sx) { ... }

scale(sx, sy, sz) { ... }

Scales in the x, y, and z directions by the given factors. If sy or sz is omitted it defaults to sx.

This is identical to:

locate(0,0,0, sx, 0,0,0, sx,sy,sz) { ... }

Compatibility: Added in 8.2EA-20170324.


rotate_x(anglex) { ... }

Rotate counter-clockwise looking down positive x-axis.

This is identical to locate(,,,,,, anglex) (rot rotation).

Compatibility: Added in 8.2EA-20170324.


rotate_y(angley) { ... }

Rotate counter-clockwise looking down positive y-axis.

This is identical to locate(,,,, angley) (azimuth rotation).

Compatibility: Added in 8.2EA-20170324.


rotate_z(anglez) { ... }

Rotate counter-clockwise looking down positive z-axis.

This is identical to locate(,,,,, anglez) (elevation rotation).

Compatibility: Added in 8.2EA-20170324.


cylinder3d(x1,y1,z1, x2,y2,z2, r) { ... }

Defines a cylinder volume of radius r whose circular bases have centers (x1,y1,z1) and (x2,y2,z2).

This is identical to locate(x1,y1,z1,1,?,0,?) { cylinder(0,0,?, r,r,?) } for appropriate values of ? but is more convenient.

Compatibility: Added in 8.2EA-20170324.


half_space(x1,y1,z1, ux,uy,uz)

half_space(axis, val)

Defines the volume below the given plane. The plane is defined by the point (x1,y1,z1) and surface normal vector (ux,uy,uz) on that plane. The fill is in the direction opposite the normal vector. The normal vector length is not important (need not be normalized).

For example, the region x <= 2 is defined by half_space(2,0,0, 1,0,0). The region x + y <= 4 is defined by half_space(2,2,0, 1,1,0).

There is also a short syntax:

half_space('+x')     -- same as half_space( 0,0,0,  1,0,0)
half_space('-x')     -- same as half_space( 0,0,0, -1,0,0)
half_space('+y')     -- same as half_space( 0,0,0,  0,1,0)
half_space('-y')     -- same as half_space( 0,0,0,  0,-1,0)
half_space('+z')     -- same as half_space( 0,0,0,  0,0,1)
half_space('-z')     -- same as half_space( 0,0,0,  0,0,-1)

half_space('+x', x)  -- same as half_space( x,0,0,  1,0,0)
half_space('-x', x)  -- same as half_space( x,0,0, -1,0,0)
half_space('+y', y)  -- same as half_space( 0,y,0,  0,1,0)
half_space('-y', y)  -- same as half_space( 0,y,0,  0,-1,0)
half_space('+z', z)  -- same as half_space( 0,0,z,  0,0,1)
half_space('-z', z)  -- same as half_space( 0,0,z,  0,0,-1)

This is useful for cutting another shape in half, like to define a half-sphere:

e(1) { intersect { sphere(10,10,10, 5) half_space('+x', 10) } }

Compatibility: Added in 8.2EA-20170324.

e, n

e(f) { ... }
n(f) { ... }

The electrode and non-electrode commands now accept a function as the parameter, which will be queried to determine the potential at the current point. This allows things like defining gradient voltages over electrode surface or analytical potentials in space.


; sphere with gradient voltage over surface
pa_define {21,21,21}
local function f(x,y,z)
  return x+y
e(f) { sphere(10,10,10, 10) }

Only the coordinate transformations (locate) outside the e move the potential function. In the following case, the potential at grid points (x,y,z) inside the circle will be f(x-1, y+2, z):

locate(1,-2,0) {
  e(f) {
    locate(0,2,0) {
      sphere(10,10,10, 10)

Normally PA’s don’t assign potentials of non-electrode points, allowing Refine to assign their values, but you can use n to do this:

; generate theoretical field plus electrodes.
pa_define {21,21,1}
local function f(x,y,z)  return (x-10)^2 - (y-10)^2 end
local function g1(x,y,z) return f(x,y,z) >  5^2 end
local function g2(x,y,z) return f(x,y,z) < -5^2 end
n(f) { box(-inf,-inf, inf,inf) }  ; assign first (subsequent elecrodes overwrite)
e(f(15,10,0)) { shape(g1) }
e(f(10,15,0)) { shape(g2) }

Another example:

-- circular electrode with linear gradient potential
pa_define {30,30,1, symmetry='planar', mirror='xy'}
local function linear(x1,v1, x2,v2)
  return function(x,y,z)
    local f = (x - x1) / (x2 - x1)
    return (1 - f) * v1 + f * v2
e(linear(5,100, 10,200)) {
  circle(0,0, 20)



Imports an STL file.


e(1) {
e(2) {




This constant represents infinity. Previously a large number like 1e6 was used.


box(-inf,0, inf, 2)

Compatibility: Added in 8.2EA-20170324.

Extensions in 8.1

Macro Support (e.g. variable expansion and preprocessing) - 8.0.4

As of SIMION 8.0.4, the GEM processor incorporates a preprocessor that allows things like variable expansion and loops (Issue-I296). which allows GEM files to be more maintainable and easily modified. (This new feature is not described in the 8.0.4 manual except in a footnote.)

A new example GEM file (examples\geometry\macro.gem) illustrates the use of this new feature:

; Example SIMION GEM file using preprocessing to expand Lua variables
; and macros.
; Preprocessing is a new feature SIMION 8.0.4.
; Lines starting with '#' or text inside $() are interpreted as Lua
; code and evaluated.  If $() contains an expression (rather than a
; statement), the result is outputted.  All other text is outputted
; verbatim.

; These variables are intended to be adjusted by the user.
; Note: both # and $ syntax are shown for demonstration.
# local ro = 45     -- outer radius, gu
# local ri = 40     -- inner radius, gi
$(local nshells = 4) ; number of shells

; Now do some calculations on those variables.  Note: math.ceil(x) is
; the ceiling function: it returns the integer closest to but no
; greater than x.
# local hw = math.ceil(ro * 1.1) -- half width, gu
# local nx = hw * 2 + 1          -- num array points in x

; Define array size.
pa_define($(nx),$(nx),$(nx), planar, non-mirrored)

; Declare a function to be used later.
; This returns the voltage for electrode number n.
$( local function volts(n)
     return n^2 * 10 + n + 1
   end )

; This locate centers the shells in the array.
locate($(hw),$(hw),$(hw), 1, 0,0,0) {
; Now define a loop that creates each shell.
# for n=1,nshells do
#   local rop = ro * n / nshells
#   local rip = ri * n / nshells
    electrode($(volts(n))) {  ; example calling a function
      fill {
        within{sphere(0,0,0, $(rop))}
        notin {sphere(0,0,0, $(rip - 1))}
# end

; Note: the following two lines are equivalent:
fill { within { box3d(0,0,0, $(nx),0,$(nx)) }}
# _put("fill { within { box3d(0,0,0, " .. nx .. ",0," .. nx .. ") }}")

; Print output to the log window.  This can be
; useful for debugging.
# print("Hello from GEM file. nx=" .. nx)

The example examples\geometry\polygon_regular.gem illustrates subroutines in GEM files, allowing you to in effect create your own reusable shapes:

# -- builds regular polygon in XY plane
# -- with center (x0,y0), radius r, and n sides.
# function regular_polygon(x0,y0, r,n)
    # for i=1,n do
    #   local theta = math.rad(i/n*360)
        $(x0+r*math.cos(theta)), $(y0+r*math.sin(theta))
    # end
# end

e(1) { fill {
  within { $(regular_polygon(50,50, 40,6)) }
  notin  { $(regular_polygon(50,50, 20,6)) }
} }

When SIMION loads a GEM file containing macros (e.g. macro.gem), it processes those macros, writes the result to temporary file (e.g. macro.processed.gem), and loads that temporary file.

It also possible to do your own GEM file preprocessing outside of SIMION with your own programming tools. This was more popular prior to the introduction of the above feature but can still be useful in some cases.


This page is abridged from the full SIMION 8.1.1 “Supplemental Documentation” (Help file). The following additional sections can be found in the full version of this page accessible via the “Help > Supplemental Documentation” menu in SIMION 8.1.1:
  • Helpful Tips for Authoring GEM Files

surface=auto option in pa_define []

Obtaining optimal field accuracy of curved surfaces had been tricky prior to the addition of the Electrode Surface Enhancement / Fractional Grid Units feature in SIMION 8.1.1. Electrode surfaces that did not exactly align to PA grid points had to be placed instead on nearby grid points, and certain ways of making this placement were more accurate than others. Cutout volumes (e.g. notin GEM commands) were also prone to error (Intersecting within and notin_inside). Consider the example of defining the field between concentric spheres of radii 40 and 80 mm. We can now accurately and simply define this in a GEM file using the (“fractional”) surface enhancement option like this:

pa_define(101,101,1, cylindrical,xy, surface=fractional)
e(1) { fill { within { circle(0,0, 40) } } }
e(2) { fill { notin  { circle(0,0, 80) } } }

However, perhaps there are still cases where you prefer not to use surface enhancement. For whatever the reason (see below), SIMION supports a new surface=auto option in the pa_define statement of GEM files to achieve a more accurate alignment of surfaces in a simple manner when not using surface enhancement. It can be used simply like this:

pa_define(101,101,1, cylindrical,xy, surface=auto)
e(1) { fill { within { circle(0,0, 40) } } }
e(2) { fill { notin  { circle(0,0, 80) } } }

To understand this feature, let’s consider the way this used to be done in SIMION 7.0/8.0....

You might naively define the concentric spheres like this:

pa_define(101,101,1, cylindrical,xy)
e(1) { fill { within { circle(0,0, 40) } } }
e(2) { fill { notin  { circle(0,0, 80) } } }

However, without care, surfaces could be off effectively by about 0.5-1.0 grid unit (gu), thereby distorting fields by the same amount as if the electrodes were misaligned by this distance in the real physical system (e.g. machining or assembly error). The above is nearly equivalent to this:

pa_define(101,101,1, cylindrical,xy)
e(1) { fill { within_inside_or_on { circle(0,0, 40.5) } } }
e(2) { fill { notin_inside_or_on  { circle(0,0, 80.5) } } }

The within and notin commands apply a +0.5 grid unit (gu) adjustment to the radius of the fill, which improves field accuracy for the within, but for the notin we actually want more like a -0.5 gu adjustment. In fact, electrode #2 in the above two examples is visibily off slightly when measured in the View screen. We have typically recommended using notin_inside rather than notin:

pa_define(101,101,1, cylindrical,xy)
e(1) { fill { within        { circle(0,0, 40) } } }
e(2) { fill { notin_inside  { circle(0,0, 80) } } }

Visually that looks about right if you examine the PA on the View screen, and the calculated field is reasonably good. However, the notin_inside (as with within_inside) actually applies a nearly 0 gu not -0.5 gu adjustment, so fields are slightly biased. But even this is not ideal in the case of spheres. In fact, the optimal adjustment is often not 0.5 gu but about 0.35 gu, as has been observed for spherical capacitor studies ref and other internal studies on flat and curved shapes rasterized to PA’s.

In SIMION, a new surface=auto option has been added that automatically applies the best adjustment to within and notin fill types. It can be used simply like this:

pa_define(101,101,1, cylindrical,xy, surface=auto)
e(1) { fill { within { circle(0,0, 40) } } }
e(2) { fill { notin  { circle(0,0, 80) } } }

and it’s nearly identical to this:

pa_define(101,101,1, cylindrical,xy)
e(1) { fill { within_inside { circle(0,0, 40.35) } } }
e(2) { fill { notin_inside  { circle(0,0, 79.65) } } }

surface=auto also affects other shape types like box, parabola, hyperbola, and polyline by applying approximately 0.35 gu offsets in the appropriate directions.

surface=auto is even useful when electrodes do exactly align to PA grid points (like surfaces that are flat, orthogonal to the axes, and have coordinates that are integral multiples of grid units) because it will automatically get the surfaces boundary points right. Consider defining a 4x4 mm box with a 2x2 mm hole inside, which obviously easily aligns to points on a 1 mm/gu grid. You might naively try to do it like this:

pa_define(11,11,1, planar,n)
e(1) { fill {
  within { box(1,1,  5,5) }
  notin  { box(2,2,  4,4) }
} }

However, the notin { box(2,2, 4,4) } (as is also true when using notin_inside_or_on) excludes from the cut the PA grid points on both the inside and border of the 2x2 box. You want to instead use a notin_inside to only exclude the grid points on the “inside” (not border) of the 2x2 box:

pa_define(11,11,1, planar,n)
e(1) { fill {
  within       { box(1,1,  5,5) }
  notin_inside { box(2,2,  4,4) }
} }

That’s pretty simple once you know about it, but it’s easier to do this right just by enabling surface=auto like this:

pa_define(11,11,1, planar,n, surface=auto)
e(1) { fill {
  within { box(1,1,  5,5) }
  notin  { box(2,2,  4,4) }
} }

or even (if you prefer) expressing it like this:

pa_define(11,11,1, planar,n, surface=auto)
e(1) { fill { within { box(1,1,  5,5) } } }
n(0) { fill { within { box(2,2,  4,4) } } }

When surface=auto is enabled (and this is also true of surface=fractional as of, any PA grid points that precisely align to an edge of a within or notin fill volume are made to be electrode points, which is usually what you want. In other words, a notin inside an e or a within inside an n (both of which remove electrode material) will be treated as an “inside” fill to avoid removing the electrode points from the border. This largely avoids fiddling with within_inside/within_inside_or_on/notin_inside/notin_inside_or_on fill variants since within and notin will now just do the right thing. In fact, with surface=auto, it’s not usually needed nor recommended to use fill types other than within and notin; for example, the following is not correct but behaves similar to the “naive” approach mentioned earlier:

pa_define(11,11,1, planar,n, surface=auto)
e(1) { fill { within{box(1,1, 5,5)}  notin_inside_or_on{box(2,2, 4,4)} } }

In fact, the following four GEM files are all correct and generate exactly the same PA:

pa_define(11,11,1, planar,n)
e(1) { fill { within{box(1,1, 5,5)}  notin_inside{box(2,2, 4,4)} } }

pa_define(11,11,1, planar,n, surface=auto)
e(1) { fill { within{box(1,1, 5,5)}  notin{box(2,2, 4,4)} } }

pa_define(11,11,1, planar,n, surface=fractional)
e(1) { fill { within{box(1,1, 5,5)}  notin{box(2,2, 4,4)} } }

pa_define(11,11,1, planar,n, surface=auto)
e(1) { fill { within_inside_or_on{box(1,1, 5,5)}
                     notin_inside{box(2,2, 4,4)} } }

Please note, however, that although surface=auto is generally preferred over surface=none (i.e. the default old behavior in SIMION 7.0/8.0) for ease and accuracy reasons, surface=fractional (see Electrode Surface Enhancement / Fractional Grid Units) is still preferred over both of these. So, there’s not really a reason to use surface=auto unless for some reason you don’t want to use surface enhancement. It’s not really clear what that reason would be except maybe to generate PA’s that are refinable under SIMION 8.0 or to compare accuracy differences with/without surface enhancement. A GEM file using surface=fractional can be quickly switched to surface=auto without any changes, but switching to surface=none may cause 1 gu errors unless additional changes are made to within/notin fill types due to the semantic difference these have under surface=none. surface=auto is somewhat of an anachronism that behaves between surface=none and surface=fractional but happened to be implemented after both for completeness.


  • 8.2EA-20170324: Major enhancements. See GEM Extensions in 8.2.
  • Some changes consistent with 8.2EA-20170324.
  • Macro lines beginning with ‘#’ can now be indented with tabs and spaces. This allows cleaner indenting of GEM code.
  • A GEM: New surface=auto parameter in pa_define. This provides a simple way to more accurately position curved surfaces and cutout (notin) volumes when not using surface enhancement (surface=fractional). This particularly applies to circle/sphere/cylinder, hyperbola (Issue-I371), parabola, polyline, notin, and others. Surface enhancement is still better, but if you don’t want to use surface enhancement for some reason, then this is better than nothing. See surface=auto option in pa_define [].
  • C GEM: within_inside_or_on/notin_inside_or_on now shift the electrode surface outward by a small 0.0001 gu offset. (within_inside and notin_inside already apply this offset but in the reverse redirection.) This more reliably ensures points “on” the shape boundary are filled even when small numerical round-off occurs in operations like polyline and scaling. Example: fill{within_inside_or_on{box(1,1,5,5)}} and fill{within_inside_or_on{polyline(1,1, 5,1, 5,5, 1,5)}} behave identically now, as expected. [*]
  • x GEM/polyline: polyline GEM command accuracy has been improved. Previously, the points on the polygon edge might not be optimally filled with the desired electrode/non-electrode point type. This particularly affected within_inside/notin_inside/within_inside_or_on/notin_inside_or_on rather than within. However, under surface=fractional, it also affected within/notin (but is somewhat cosmetic since electrode point types on the surface are not critical for field accuracy under surface=fractional). Example: polyline(10,5 15,5 15,10 20,10 20,15 15,15 15,20 10,20 10,15 5,15 5,10 10,10) (cross).
  • C GEM/Surface: PA grid points that precisely align to an edge of a within/notin fill volume are made to be electrode points if surface=fractional or surface=auto is enabled. In other words, a notin inside an e or a within inside an n (both of which remove electrode material) will be treated as an “inside” fill to avoid removing the electrode points from the border. This largely avoids fiddling with within_inside/within_inside_or_on/notin_inside/notin_inside_or_on fill variants since within and notin will now just do the right thing. The default option (surface=none) retains the old behavior for compatibility though. Example: e(1){fill{within{box(1,1,5,5)} notin{box(1,1,5,5)}}} and e(1){fill{within{box(1,1,5,5)}}} n(0){fill{notin{box(1,1,5,5)}}} both create a 4x4 hollow box with infinitesimally thin walls under surface=auto or surface=fractional. See surface=auto option in pa_define [].
  • c GEM: polyline, points, and points3d commands can now accept an arbitrary number of points. Previously these were limited to 100, 100, and 65 points.
  • x GEM: Fix polyline problems when using exactly 100 points. [*sf-t1338]
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