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$Id: README,v 1.1 2000-12-10 00:46:30 geuzaine Exp $
Here are the examples in the Gmsh tutorial. Feel free to send comments
about the tutorial to christophe.geuzaine@advalvas.be or
remacle@scorec.rpi.edu.
These examples are heavily commented (both C and C++-style comments
can be used in Gmsh input files) and should introduce new features
gradually, starting with t1.geo.
(The tutorial does not explain the mesh and post-processing file
formats. See the FORMATS file for this.)
There are two ways to actually run these examples with Gmsh. (The
operations to run Gmsh may vary depending on your operating system. In
the following, we will assume that you're working with a UNIX-like
shell.) The first working mode of Gmsh is the interactive graphical
mode. To launch Gmsh in interactive mode, just type
> gmsh
at the prompt on the command line. This will open two windows: the
graphic window (with a status bar at the bottom) and the menu window
(with a menu bar and some context dependent buttons). To open the
first tutorial file, you have to select the 'File->Open' menu, and
choose 't1.geo' in the input field. To perform the mesh generation,
you have to go to the mesh module (by selecting 'Module->Mesh' in the
menu bar) and choose the required dimension in the context-dependent
buttons ('1D' will mesh all the curves; '2D' will mesh all the
surfaces ---as well as all the curves if '1D' was not called before;
'3D' will mesh all the volumes ---and all the surfaces if '2D' was not
called before). To save the resulting mesh, select 'File->Save_Mesh'
in the menu bar. The default mesh file name is based on the name of
the first input file on the command line (or 'unnamed' if there wasn't
any input file given), with an appended extension depending on the
mesh format.
Note: nearly all the interactive commands have shortcuts. Select
'?->Short_Help' in the menu bar to learn about these shortcuts.
Instead of opening the tutorial with the 'File->Open' menu, it is
often more convenient to put the file name on the command line, here
for example with:
> gmsh t1.geo
(The '.geo' extension can also be omitted.)
Note: to define new geometries, if it is often handy to define the
variables and the points directly in the input files, it is almost
always simpler to define the curves, the surfaces and the volumes
interactively. To do so, just follow the context dependent buttons in
the Geometry module. For example, to create a line, select
'Module->Geometry' in the menu bar, and then select 'Elementary, Add,
Create, Line'. You will then be asked (in the status bar of the
graphic window) to select a list of points, and to click 'e' when
you're done. Once the interactive command is completed, a string is
automatically added at the end of the currently opened project file.
The second operating mode for Gmsh is the non-interactive mode. In
this mode, there is no graphical user interface, and all operations
are performed without any user interaction. To mesh the first tutorial
in non-interactive mode, just type:
> gmsh t1.geo -2
Several files can be loaded simultaneously in Gmsh. The first one
defines the project, while the others are appended ("merged") to this
project. You can merge such files with the 'File->Merge' menu, or by
directly specifying the names of the files on the command line. This
is most useful for post-processing purposes. For example, to merge the
post-processing views contained in the files 'view1.pos' and
'view2.pos' together with the first tutorial 't1.geo', you can type
the following line on the command line:
> gmsh t1.geo view1.pos view2.pos
In the Post-Processing module (select 'Module->Post_Processing'), two
view buttons will appear, respectively labeled "a scalar map" and "a
vector map". A left mouse click will toggle the visibility of the
selected view. A right mouse click provides access to the view's
options:
- Reload: reloads the file from which the view was loaded
- Remove: removes the view
- Duplicate: makes a copy of the view (without duplicating the data)
- Lighting: activates/deactivates lighting for the view
- Scale: gives access to the scale menu (range definition, iso-value
choice, ...)
- Color: defines the color map for the view
- Offset: permits to move the view around, and to make elevation
maps
- Vector display: changes vector attributes
- Time step: selects the displayed time step
- Export as background mesh: exports the map, considered as an
error map, as a background mesh, i.e. as a characteristic length map
- Apply as current bg mesh: applies the view as the current background
mesh.
If you want the modifications made to one view to affect also all other
views, select the 'Link all views' option in the
'Options->Post-Processing' menu.
Note: all the options specified interactively can also be directly
specified in the ascii input files. The current options can be saved
into a file by selecting 'File->Save_Options_as'. For UNIX versions,
all user interface options can be changed in a standard X resource file
('.gmshrc' in your home directory or app-defaults directory, or
'.Xdefaults'). Use 'editres' to get the full widget tree and
associated resources.
OK, that's all, folks. Enjoy the tutorial.
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/*********************************************************************
*
* Gmsh tutorial 1
*
* Variables, Elementary entities (Points, Lines, Surfaces), Physical
* entities (Points, Lines, Surfaces)
*
*********************************************************************/
// All geometry description in Gmsh is made by means of a special
// language (looking somewhat similar to C). The simplest construction
// of this language is the 'affectation'.
// The following command (all commands end with a semi colon) defines
// a variable called 'lc' and affects the value 0.007 to 'lc':
lc = 0.007 ;
// This newly created variable can be used to define the first Gmsh
// elementary entity, a 'Point'. A Point is defined by a list of four
// numbers: its three coordinates (x, y and z), and a characteristic
// length, which sets the target mesh size at the point:
Point(1) = {0, 0, 0, 9.e-1 * lc} ;
// As can be seen in this definition, more complex expressions can be
// constructed from variables on the fly. Here, the product of the
// variable 'lc' by the constant 9.e-1 is given as the fourth argument
// of the list defining the point.
//
// The following general syntax rule is applied for the definition of
// all geometrical entities:
//
// "If a number defines a new entity, it is enclosed between
// parentheses. If a number refers to a previously defined entity,
// it is enclosed between braces."
//
// Three additional points are then defined:
Point(2) = {.1, 0, 0, lc} ;
Point(3) = {.1, .3, 0, lc} ;
Point(4) = {0, .3, 0, lc} ;
// The second elementary geometrical entity in Gmsh is the
// curve. Amongst curves, straight lines are the simplest. A straight
// line is defined by a list of point numbers. For example, the line 1
// starts at point 1 and ends at point 2:
Line(1) = {1,2} ;
Line(2) = {3,2} ;
Line(3) = {3,4} ;
Line(4) = {4,1} ;
// The third elementary entity is the surface. In order to define a
// simple rectangular surface from the four lines defined above, a
// line loop has first to be defined. A line loop is a list of
// connected lines, each line being associated a sign, depending of
// its orientation.
Line Loop(5) = {4,1,-2,3} ;
// The surface is then defined as a list of line loops (only one
// here):
Plane Surface(6) = {5} ;
// At this level, Gmsh knows everything to display the rectangular
// surface 6 and to mesh it. But a supplementary step is needed in
// order for assign region numbers to the various elements in the mesh
// (the points, the lines and the triangles discretizing the points 1
// to 4, the lines 1 to 4 and the surface 6). This is achieved by the
// definition of Physical entities. Physical entities will group
// elements belonging to several elementary entities by giving them a
// common number (a region number), and specifying their orientation.
//
// For example, the two points 1 and 2 can be grouped into the
// physical entity 1:
Physical Point(1) = {1,2} ;
// Consequently, two punctual elements will be saved in the output
// files, both with the region number 1. The mechanism is identical
// for line or surface elements:
Physical Line(10) = {1,2,4} ;
Physical Surface(100) = {6} ;
// All the line elements which will be created during the mesh of the
// lines 1, 2 and 4 will be saved in the output file with the
// associated region number 10; and all the triangular elements
// resulting from the discretization of the surface 6 will be
// associated the region number 100.
// It is important to notice that only those elements which belong to
// physical groups will be saved in the output file if the file format
// is the msh format (the native mesh file format for Gmsh). For a
// description of the mesh and post-processing formats, see the FORMATS
// file.
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/*********************************************************************
*
* Gmsh tutorial 2
*
* Includes, Geometrical transformations, Elementary entities
* (Volumes), Physical entities (Volumes)
*
*********************************************************************/
// The first tutorial file will serve as a basis to construct this
// one: it can be included like this:
Include "t1.geo" ;
// There are several possibilities to build a more complex geometry
// from the one previously defined in 't1.geo'.
//
// New points, lines and surfaces can first be directly defined in the
// same way as in 't1.geo':
Point(5) = {0, .4, 0, lc} ;
Line(5) = {4, 5} ;
// But Gmsh also provides geometrical transformation mechanisms to
// move (translate, rotate, ...), add (translate, rotate, ...) or
// extrude (translate, rotate) elementary geometrical entities. For
// example, the point 3 can be moved by 0.05 units on the left with:
Translate {-0.05,0,0} { Point{3} ; }
// The resulting point can also be duplicated and translated by 0.1
// along the y axis:
Translate {0,0.1,0} { Duplicata{ Point{3} ; } }
// Translation, rotation and extrusion commands of course not only
// apply to points, but also to lines and surfaces. The following
// command extrudes the surface 6 defined in 't1.geo', as well as a
// new surface 11, along the z axis by 'h':
h = 0.12 ;
Extrude Surface { 6, {0, 0, h} } ;
Line(7) = {3, 6} ; Line(8) = {6,5} ; Line Loop(10) = {5,-8,-7,3};
Plane Surface(11) = {10};
Extrude Surface { 11, {0, 0, h} } ;
// All these geometrical transformations generate automatically new
// elementary entities. The following commands permit to specify
// manually a characteristic length for some of the automatically
// created points:
Characteristic Length{6,22,2,3,16,12} = lc * 3 ;
// If the transformation tools are handy to create complex geometries,
// it is sometimes useful to be generate the flat geometry, consisting
// only of the explicit list elementary entities. This can be achieved
// by selecting the 'File->Print->Geo' menu or by typing
//
// > gmsh t2.geo -0
//
// on the command line.
// Volumes are the fourth type of elementary entities in Gmsh. In the
// same way one defines line loops to build surfaces, one has to
// define surface loops to build volumes. The following volumes are
// very simple, without holes (and thus consist of only one surface
// loop):
Surface Loop(145) = {121,11,131,135,139,144};
Volume(146) = {145};
Surface Loop(146) = {121,6,109,113,117,122};
Volume(147) = {146};
// To save all volumic (tetrahedral) elements of volume 146 and 147
// with the associate region number 1, a Physical Volume must be
// defined:
Physical Volume (1) = {146,147} ;
// Congratulations! You've created your first fully unstructured
// tetrahedral 3D mesh!
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/*********************************************************************
*
* Gmsh tutorial 3
*
* Extruded meshes, Options
*
*********************************************************************/
// Again, the first tutorial example is included:
Include "t1.geo" ;
// As in 't2.geo', an extrusion along the z axis will be performed:
h = 0.1 ;
// But contrary to 't2.geo', not only the geometry will be extruded,
// but we also the 2D mesh. This is done with the same Extrude
// command, but by specifying the number of layers (here, there will
// be two layers, of respectively 2 and 4 elements in depth), with
// volume numbers 9000 and 9001 and respective heights of 0.33*h and
// 0.67*h:
Extrude Surface { 6, {0,0,h} } { Layers { {2,4}, {9000,9001}, {0.33,1} } ; } ;
// The extrusion can also be combined with a rotation, and the
// extruded 3D mesh can be recombined into prisms (wedges). All
// rotations are specified by an axis direction ({0,1,0}), an axis
// point ({0,0,0}) and a rotation angle (Pi/2):
Extrude Surface { 122, {0,1,0} , {-0.1,0,0.1} , -Pi/2 } {
Recombine ; Layers { {7}, {9002}, {1} } ;
};
// All interactive options can also be set directly in the input file.
// For example, the following lines redefine the background color of
// the graphic window, the color of the points of the geometry,
// disable the display of the axes, and select an initial viewpoint in
// xyz mode (disabling the interactive trackball-like rotation mode):
General.Color.Background = Red;
Geometry.Color.Points = Orange;
General.Axes = 0;
General.Trackball = 0;
General.Rotation0 = 10;
General.Rotation1 = 70;
General.Translation0 = -0.1;
// Note: all colors can be defined literally or numerically, i.e.
// 'General.Color.Background = Red' is equivalent to
// 'General.Color.Background = {255,0,0}'. As with user-defined
// variables, the options can be used either as right hand or left
// hand sides, so that
Geometry.Color.Surfaces = Geometry.Color.Points;
// will set the color of the surfaces in the geometry to the same
// color as the points.
// For UNIX versions, a click on the '?' button in status bar of the
// graphic window will dump all current options to the terminal. To
// save the options to a file, use the 'File->Save_Options_as' menu.
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/*********************************************************************
*
* Gmsh tutorial 4
*
* Built-in functions, Holes
*
*********************************************************************/
cm = 1e-02 ;
e1 = 4.5*cm ; e2 = 6*cm / 2 ; e3 = 5*cm / 2 ;
h1 = 5*cm ; h2 = 10*cm ; h3 = 5*cm ; h4 = 2*cm ; h5 = 4.5*cm ;
R1 = 1*cm ; R2 = 1.5*cm ; r = 1*cm ;
ccos = ( -h5*R1 + e2 * Hypot(h5,Hypot(e2,R1)) ) / (h5^2 + e2^2) ;
ssin = Sqrt(1-ccos^2) ;
Lc1 = 0.01 ;
Lc2 = 0.003 ;
// A whole set of operators can be used, which can be combined in all
// the expressions. These operators are defined in a similar way to
// their C or C++ equivalents (with the exception of '^'):
//
// '-' (in both unary and binary versions, i.e. as in '-1' and '1-2')
// '!' (the negation)
// '+'
// '*'
// '/'
// '%' (the rest of the integer division)
// '<'
// '>'
// '<='
// '>='
// '=='
// '!='
// '&&' (and)
// '||' (or)
// '||' (or)
// '^' (power)
// '?' ':' (the ternary operator)
//
// Grouping is done, as usual, with parentheses.
//
// In addition to these operators, all C mathematical functions can
// also be used (note the first capital letter):
//
// Exp(x)
// Log(x)
// Log10(x)
// Sqrt(x)
// Sin(x)
// Asin(x)
// Cos(x)
// Acos(x)
// Tan(x)
// Atan(x)
// Atan2(x,y)
// Sinh(x)
// Cosh(x)
// Tanh(x)
// Fabs(x)
// Floor(x)
// Ceil(x)
// Fmod(x,y)
// Hypot(x,y)
// An additional function 'Rand(x)' generates an random number in
// [0,x]
//
// Rand(x)
//
// The only predefined constant in Gmsh is Pi.
Point(1) = { -e1-e2, 0.0 , 0.0 , Lc1};
Point(2) = { -e1-e2, h1 , 0.0 , Lc1};
Point(3) = { -e3-r , h1 , 0.0 , Lc2};
Point(4) = { -e3-r , h1+r , 0.0 , Lc2};
Point(5) = { -e3 , h1+r , 0.0 , Lc2};
Point(6) = { -e3 , h1+h2, 0.0 , Lc1};
Point(7) = { e3 , h1+h2, 0.0 , Lc1};
Point(8) = { e3 , h1+r , 0.0 , Lc2};
Point(9) = { e3+r , h1+r , 0.0 , Lc2};
Point(10)= { e3+r , h1 , 0.0 , Lc2};
Point(11)= { e1+e2, h1 , 0.0 , Lc1};
Point(12)= { e1+e2, 0.0 , 0.0 , Lc1};
Point(13)= { e2 , 0.0 , 0.0 , Lc1};
Point(14)= { R1 / ssin , h5+R1*ccos, 0.0 , Lc2};
Point(15)= { 0.0 , h5 , 0.0 , Lc2};
Point(16)= { -R1 / ssin , h5+R1*ccos, 0.0 , Lc2};
Point(17)= { -e2 , 0.0 , 0.0 , Lc1};
Point(18)= { -R2 , h1+h3 , 0.0 , Lc2};
Point(19)= { -R2 , h1+h3+h4, 0.0 , Lc2};
Point(20)= { 0.0 , h1+h3+h4, 0.0 , Lc2};
Point(21)= { R2 , h1+h3+h4, 0.0 , Lc2};
Point(22)= { R2 , h1+h3 , 0.0 , Lc2};
Point(23)= { 0.0 , h1+h3 , 0.0 , Lc2};
Point(24)= { 0 , h1+h3+h4+R2, 0.0 , Lc2};
Point(25)= { 0 , h1+h3-R2, 0.0 , Lc2};
Line(1) = {1 ,17};
Line(2) = {17,16};
// All curves are not straight lines... Circles are defined by a list
// of three point numbers, which represent the starting point, the
// center and the end point, respectively. All circles have to be
// defined in the trigonometric (counter-clockwise) sense. Note that
// the 3 points should not be aligned (otherwise the plane in which
// the circle lies has to be defined, by 'Circle(num) =
// {start,center,end} Plane {nx,ny,nz}').
Circle(3) = {14,15,16};
Line(4) = {14,13};
Line(5) = {13,12};
Line(6) = {12,11};
Line(7) = {11,10};
Circle(8) = { 8, 9,10};
Line(9) = { 8, 7};
Line(10) = { 7, 6};
Line(11) = { 6, 5};
Circle(12) = { 3, 4, 5};
Line(13) = { 3, 2};
Line(14) = { 2, 1};
Line(15) = {18,19};
Circle(16) = {21,20,24};
Circle(17) = {24,20,19};
Circle(18) = {18,23,25};
Circle(19) = {25,23,22};
Line(20) = {21,22};
Line Loop(21) = {17,-15,18,19,-20,16};
Plane Surface(22) = {21};
// The surface is made of two line loops, i.e. it has one hole:
Line Loop(23) = {11,-12,13,14,1,2,-3,4,5,6,7,-8,9,10};
Plane Surface(24) = {23,21};
Physical Surface(1) = {22};
Physical Surface(2) = {24};
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/*********************************************************************
*
* Gmsh tutorial 5
*
* Characteristic lengths, Functions, Loops
*
*********************************************************************/
// This defines some characteristic lengths:
lcar1 = .1;
lcar2 = .0005;
lcar3 = .075;
// In order to change these lengths globally (without changing the
// file), a global scaling factor for all characteristic lengths can
// be specified on the command line with the option '-clscale'. For
// example, with:
//
// > gmsh t5 -clscale 1
//
// this example produces a mesh of approximately 2000 nodes and
// 10,000 tetrahedra (in 3 seconds on an alpha workstation running at
// 666MHz). With
//
// > gmsh t5 -clscale 0.2
//
// (i.e. with all characteristic lengths divided by 5), the mesh
// counts approximately 170,000 nodes and one million tetrahedra
// (and the computation takes 16 minutes on the same machine :-( So
// there is still a lot of work to do to achieve decent performance
// with Gmsh...)
Point(1) = {0.5,0.5,0.5,lcar2}; Point(2) = {0.5,0.5,0,lcar1};
Point(3) = {0,0.5,0.5,lcar1}; Point(4) = {0,0,0.5,lcar1};
Point(5) = {0.5,0,0.5,lcar1}; Point(6) = {0.5,0,0,lcar1};
Point(7) = {0,0.5,0,lcar1}; Point(8) = {0,1,0,lcar1};
Point(9) = {1,1,0,lcar1}; Point(10) = {0,0,1,lcar1};
Point(11) = {0,1,1,lcar1}; Point(12) = {1,1,1,lcar1};
Point(13) = {1,0,1,lcar1}; Point(14) = {1,0,0,lcar1};
Line(1) = {8,9}; Line(2) = {9,12}; Line(3) = {12,11};
Line(4) = {11,8}; Line(5) = {9,14}; Line(6) = {14,13};
Line(7) = {13,12}; Line(8) = {11,10}; Line(9) = {10,13};
Line(10) = {10,4}; Line(11) = {4,5}; Line(12) = {5,6};
Line(13) = {6,2}; Line(14) = {2,1}; Line(15) = {1,3};
Line(16) = {3,7}; Line(17) = {7,2}; Line(18) = {3,4};
Line(19) = {5,1}; Line(20) = {7,8}; Line(21) = {6,14};
Line Loop(22) = {11,19,15,18}; Plane Surface(23) = {22};
Line Loop(24) = {16,17,14,15}; Plane Surface(25) = {24};
Line Loop(26) = {-17,20,1,5,-21,13}; Plane Surface(27) = {26};
Line Loop(28) = {4,1,2,3}; Plane Surface(29) = {28};
Line Loop(30) = {7,-2,5,6}; Plane Surface(31) = {30};
Line Loop(32) = {6,-9,10,11,12,21}; Plane Surface(33) = {32};
Line Loop(34) = {7,3,8,9}; Plane Surface(35) = {34};
Line Loop(36) = {10,-18,16,20,-4,8}; Plane Surface(37) = {36};
Line Loop(38) = {-14,-13,-12,19}; Plane Surface(39) = {38};
// Instead of using included files, one can also define functions. In
// the following function, the reserved variable 'newp' is used, which
// automatically selects a new point number. This number is chosen as
// the highest current point number, plus one. Analogously to 'newp',
// there exists a variable 'newreg' which selects the highest number
// of all entities other than points, plus one.
// Note: there are no local variables. This will be changed in a
// future version of Gmsh.
Function CheeseHole
p1 = newp; Point(p1) = {x, y, z, lcar3} ;
p2 = newp; Point(p2) = {x+r,y, z, lcar3} ;
p3 = newp; Point(p3) = {x, y+r,z, lcar3} ;
p4 = newp; Point(p4) = {x, y, z+r,lcar3} ;
p5 = newp; Point(p5) = {x-r,y, z, lcar3} ;
p6 = newp; Point(p6) = {x, y-r,z, lcar3} ;
p7 = newp; Point(p7) = {x, y, z-r,lcar3} ;
c1 = newreg; Circle(c1) = {p2,p1,p7};
c2 = newreg; Circle(c2) = {p7,p1,p5};
c3 = newreg; Circle(c3) = {p5,p1,p4};
c4 = newreg; Circle(c4) = {p4,p1,p2};
c5 = newreg; Circle(c5) = {p2,p1,p3};
c6 = newreg; Circle(c6) = {p3,p1,p5};
c7 = newreg; Circle(c7) = {p5,p1,p6};
c8 = newreg; Circle(c8) = {p6,p1,p2};
c9 = newreg; Circle(c9) = {p7,p1,p3};
c10 = newreg; Circle(c10) = {p3,p1,p4};
c11 = newreg; Circle(c11) = {p4,p1,p6};
c12 = newreg; Circle(c12) = {p6,p1,p7};
// All surfaces are not plane... Here is the way to define ruled
// surfaces (which have 3 or 4 borders):
l1 = newreg; Line Loop(l1) = {c5,c10,c4}; Ruled Surface(newreg) = {l1};
l2 = newreg; Line Loop(l2) = {c9,-c5,c1}; Ruled Surface(newreg) = {l2};
l3 = newreg; Line Loop(l3) = {-c12,c8,c1}; Ruled Surface(newreg) = {l3};
l4 = newreg; Line Loop(l4) = {c8,-c4,c11}; Ruled Surface(newreg) = {l4};
l5 = newreg; Line Loop(l5) = {-c10,c6,c3}; Ruled Surface(newreg) = {l5};
l6 = newreg; Line Loop(l6) = {-c11,-c3,c7}; Ruled Surface(newreg) = {l6};
l7 = newreg; Line Loop(l7) = {c2,c7,c12}; Ruled Surface(newreg) = {l7};
l8 = newreg; Line Loop(l8) = {-c6,-c9,c2}; Ruled Surface(newreg) = {l8};
l9 = newreg; Surface Loop(l9) = {l8+1, l5+1, l1+1, l2+1, -(l3+1), -(l7+1), l6+1, l4+1};
thehole = newreg; Volume(thehole) = {l9};
Return
x = 0; y = 0.75; z = 0; r = 0.09;
// A For loop is used to generate five holes in the cube:
For t In {1:5}
x += 0.166 ;
z += 0.166 ;
// This command calls the function CheeseHole. Note that, instead of
// defining a function, we could have define a file containing the
// same code, and used the Include command to include this file.
Call CheeseHole;
// A physical volume is defined for each cheese hole
Physical Volume (t) = thehole ;
// The Printf function permits to print the value of variables on the
// terminal:
Printf("The cheese hole has number %g!", thehole);
EndFor
// This is the surface loop for the exterior surface of the cube:
Surface Loop(185) = {35,31,29,37,33,23,39,25,27};
// The volume of the cube, without the 5 cheese holes, is defined by 6
// surface loops (the exterior surface and the five interior loops):
Volume(186) = {185,184,155,126,97,68};
// This physical volume assigns the region number 10 to the tetrahedra
// paving the cube (but not the holes, whose elements were tagged from
// 1 to 5 in the 'For' loop)
Physical Volume (10) = 186 ;
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/*********************************************************************
*
* Gmsh tutorial 6
*
* Transfinite meshes
*
*********************************************************************/
r_int = 0.05 ;
r_ext = 0.051 ;
r_far = 0.125 ;
r_inf = 0.4 ;
phi1 = 30. * (Pi/180.) ;
angl = 45. * (Pi/180.) ;
nbpt_phi = 5 ; nbpt_int = 20 ;
nbpt_arc1 = 10 ; nbpt_arc2 = 10 ;
nbpt_shell = 10 ; nbpt_far = 25 ; nbpt_inf = 15 ;
lc0 = 0.1 ; lc1 = 0.1 ; lc2 = 0.3 ;
Point(1) = {0, 0, 0, lc0} ;
Point(2) = {r_int, 0, 0, lc0} ;
Point(3) = {r_ext, 0, 0, lc1} ;
Point(4) = {r_far, 0, 0, lc2} ;
Point(5) = {r_inf, 0, 0, lc2} ;
Point(6) = {0, 0, r_int, lc0} ;
Point(7) = {0, 0, r_ext, lc1} ;
Point(8) = {0, 0, r_far, lc2} ;
Point(9) = {0, 0, r_inf, lc2} ;
Point(10) = {r_int*Cos(phi1), r_int*Sin(phi1), 0, lc0} ;
Point(11) = {r_ext*Cos(phi1), r_ext*Sin(phi1), 0, lc1} ;
Point(12) = {r_far*Cos(phi1), r_far*Sin(phi1), 0, lc2} ;
Point(13) = {r_inf*Cos(phi1), r_inf*Sin(phi1), 0, lc2} ;
Point(14) = {r_int/2, 0, 0, lc2} ;
Point(15) = {r_int/2*Cos(phi1), r_int/2*Sin(phi1), 0, lc2} ;
Point(16) = {r_int/2, 0, r_int/2, lc2} ;
Point(17) = {r_int/2*Cos(phi1), r_int/2*Sin(phi1), r_int/2, lc2} ;
Point(18) = {0, 0, r_int/2, lc2} ;
Point(19) = {r_int*Cos(angl), 0, r_int*Sin(angl), lc2} ;
Point(20) = {r_int*Cos(angl)*Cos(phi1), r_int*Cos(angl)*Sin(phi1), r_int*Sin(angl), lc2} ;
Point(21) = {r_ext*Cos(angl), 0, r_ext*Sin(angl), lc2} ;
Point(22) = {r_ext*Cos(angl)*Cos(phi1), r_ext*Cos(angl)*Sin(phi1), r_ext*Sin(angl), lc2} ;
Point(23) = {r_far*Cos(angl), 0, r_far*Sin(angl), lc2} ;
Point(24) = {r_far*Cos(angl)*Cos(phi1), r_far*Cos(angl)*Sin(phi1), r_far*Sin(angl), lc2} ;
Point(25) = {r_inf, 0, r_inf, lc2} ;
Point(26) = {r_inf*Cos(phi1), r_inf*Sin(phi1), r_inf, lc2} ;
Circle(1) = {2,1,19}; Circle(2) = {19,1,6}; Circle(3) = {3,1,21};
Circle(4) = {21,1,7}; Circle(5) = {4,1,23}; Circle(6) = {23,1,8};
Line(7) = {5,25}; Line(8) = {25,9};
Circle(9) = {10,1,20}; Circle(10) = {20,1,6}; Circle(11) = {11,1,22};
Circle(12) = {22,1,7}; Circle(13) = {12,1,24}; Circle(14) = {24,1,8};
Line(15) = {13,26}; Line(16) = {26,9};
Circle(17) = {19,1,20}; Circle(18) = {21,1,22}; Circle(19) = {23,1,24};
Circle(20) = {25,1,26}; Circle(21) = {2,1,10}; Circle(22) = {3,1,11};
Circle(23) = {4,1,12}; Circle(24) = {5,1,13};
Line(25) = {1,14}; Line(26) = {14,2}; Line(27) = {2,3}; Line(28) = {3,4};
Line(29) = {4,5}; Line(30) = {1,15}; Line(31) = {15,10}; Line(32) = {10,11};
Line(33) = {11,12}; Line(34) = {12,13}; Line(35) = {14,15}; Line(36) = {14,16};
Line(37) = {15,17}; Line(38) = {16,17}; Line(39) = {18,16}; Line(40) = {18,17};
Line(41) = {1,18}; Line(42) = {18,6}; Line(43) = {6,7}; Line(44) = {16,19};
Line(45) = {19,21}; Line(46) = {21,23}; Line(47) = {23,25}; Line(48) = {17,20};
Line(49) = {20,22}; Line(50) = {22,24}; Line(51) = {24,26}; Line(52) = {7,8};
Line(53) = {8,9};
Line Loop(54) = {39,-36,-25,41}; Ruled Surface(55) = {54};
Line Loop(56) = {44,-1,-26,36}; Ruled Surface(57) = {56};
Line Loop(58) = {3,-45,-1,27}; Ruled Surface(59) = {58};
Line Loop(60) = {5,-46,-3,28}; Ruled Surface(61) = {60};
Line Loop(62) = {7,-47,-5,29}; Ruled Surface(63) = {62};
Line Loop(64) = {-2,-44,-39,42}; Ruled Surface(65) = {64};
Line Loop(66) = {-4,-45,2,43}; Ruled Surface(67) = {66};
Line Loop(68) = {-6,-46,4,52}; Ruled Surface(69) = {68};
Line Loop(70) = {-8,-47,6,53}; Ruled Surface(71) = {70};
Line Loop(72) = {-40,-41,30,37}; Ruled Surface(73) = {72};
Line Loop(74) = {48,-9,-31,37}; Ruled Surface(75) = {74};
Line Loop(76) = {49,-11,-32,9}; Ruled Surface(77) = {76};
Line Loop(78) = {-50,-11,33,13}; Ruled Surface(79) = {78};
Line Loop(80) = {-51,-13,34,15}; Ruled Surface(81) = {80};
Line Loop(82) = {10,-42,40,48}; Ruled Surface(83) = {82};
Line Loop(84) = {12,-43,-10,49}; Ruled Surface(85) = {84};
Line Loop(86) = {14,-52,-12,50}; Ruled Surface(87) = {86};
Line Loop(88) = {16,-53,-14,51}; Ruled Surface(89) = {88};
Line Loop(90) = {-30,25,35}; Ruled Surface(91) = {90};
Line Loop(92) = {-40,39,38}; Ruled Surface(93) = {92};
Line Loop(94) = {37,-38,-36,35}; Ruled Surface(95) = {94};
Line Loop(96) = {-48,-38,44,17}; Ruled Surface(97) = {96};
Line Loop(98) = {18,-49,-17,45}; Ruled Surface(99) = {98};
Line Loop(100) = {19,-50,-18,46}; Ruled Surface(101) = {100};
Line Loop(102) = {20,-51,-19,47}; Ruled Surface(103) = {102};
Line Loop(104) = {-2,17,10}; Ruled Surface(105) = {104};
Line Loop(106) = {-9,-21,1,17}; Ruled Surface(107) = {106};
Line Loop(108) = {-4,18,12}; Ruled Surface(109) = {108};
Line Loop(110) = {-11,-22,3,18}; Ruled Surface(111) = {110};
Line Loop(112) = {-13,-23,5,19}; Ruled Surface(113) = {112};
Line Loop(114) = {-6,19,14}; Ruled Surface(115) = {114};
Line Loop(116) = {-15,-24,7,20}; Ruled Surface(117) = {116};
Line Loop(118) = {-8,20,16}; Ruled Surface(119) = {118};
Line Loop(120) = {-31,-35,26,21}; Ruled Surface(121) = {120};
Line Loop(122) = {32,-22,-27,21}; Ruled Surface(123) = {122};
Line Loop(124) = {33,-23,-28,22}; Ruled Surface(125) = {124};
Line Loop(126) = {34,-24,-29,23}; Ruled Surface(127) = {126};
Surface Loop(128) = {93,-73,-55,95,-91}; Volume(129) = {128}; // int
Surface Loop(130) = {107,-75,-97,95,57,121}; Volume(131) = {130}; // int b
Surface Loop(132) = {105,-65,-97,-83,-93}; Volume(133) = {132}; // int h
Surface Loop(134) = {99,-111,77,123,59,107}; Volume(135) = {134}; // shell b
Surface Loop(136) = {99,-109,67,105,85}; Volume(137) = {136}; // shell h
Surface Loop(138) = {113,79,-101,-111,-125,-61}; Volume(139) = {138}; // ext b
Surface Loop(140) = {115,-69,-101,-87,-109}; Volume(141) = {140}; // ext h
Surface Loop(142) = {103,-117,-81,113,127,63}; Volume(143) = {142}; // inf b
Surface Loop(144) = {89,-119,71,103,115}; Volume(145) = {144}; // inf h
// Transfinite line commands explicitly specify the number of points
// and their distribution. A minus sign in the argument list of the
// transfinite command will produce the reversed mesh.
Transfinite Line{35,21,22,23,24,38,17,18,19,20} = nbpt_phi ;
Transfinite Line{31,26,48,44,42} = nbpt_int Using Progression 0.95;
Transfinite Line{41,37,36,9,11,1,3,13,5,15,7} = nbpt_arc1 ;
Transfinite Line{30,25,40,39,10,2,12,4,14,6,16,8} = nbpt_arc2 ;
Transfinite Line{32,27,49,45,43} = nbpt_shell ;
Transfinite Line{33,28,46,50,52} = nbpt_far Using Progression 1.05 ;
Transfinite Line{34,29,51,47,53} = nbpt_inf Using Progression 0.01;
// *All* 2D and 3D transfinite entities are defined in respect to
// points. The ordering of the points defines the ordering of the mesh
// elements.
Transfinite Surface{55} = {1,14,16,18};
Transfinite Surface{57} = {14,2,19,16};
Transfinite Surface{59} = {2,3,21,19};
Transfinite Surface{61} = {3,4,23,21};
Transfinite Surface{63} = {4,5,25,23};
Transfinite Surface{73} = {1,15,17,18};
Transfinite Surface{75} = {15,10,20,17};
Transfinite Surface{77} = {10,11,22,20};
Transfinite Surface{79} = {11,12,24,22};
Transfinite Surface{81} = {12,13,26,24};
Transfinite Surface{65} = {18,16,19,6};
Transfinite Surface{67} = {6,19,21,7};
Transfinite Surface{69} = {7,21,23,8};
Transfinite Surface{71} = {8,23,25,9};
Transfinite Surface{83} = {17,18,6,20};
Transfinite Surface{85} = {20,6,7,22};
Transfinite Surface{87} = {22,7,8,24};
Transfinite Surface{89} = {24,8,9,26};
Transfinite Surface{91} = {1,14,15};
Transfinite Surface{95} = {15,14,16,17};
Transfinite Surface{93} = {18,16,17};
Transfinite Surface{121} = {15,14,2,10};
Transfinite Surface{97} = {17,16,19,20};
Transfinite Surface{123} = {10,2,3,11};
Transfinite Surface{99} = {20,19,21,22};
Transfinite Surface{107} = {10,2,19,20};
Transfinite Surface{105} = {6,20,19};
Transfinite Surface{109} = {7,22,21};
Transfinite Surface{111} = {11,3,21,22};
Transfinite Surface{101} = {22,21,23,24};
Transfinite Surface{125} = {11,3,4,12};
Transfinite Surface{115} = {8,24,23};
Transfinite Surface{113} = {24,12,4,23};
Transfinite Surface{127} = {12,13,5,4};
Transfinite Surface{103} = {24,23,25,26};
Transfinite Surface{119} = {9,26,25};
Transfinite Surface{117} = {13,5,25,26};
// As with Extruded meshes, the Recombine command tells Gmsh to
// recombine the simplices into quadrangles, prisms or hexahedra when
// possible. A colon in a list acts as in the 'For' loop: all surfaces
// having numbers between 55 and 127 are considered.
Recombine Surface {55:127};
// *All* 2D and 3D transfinite entities are defined in respect to
// points. The ordering of the points defines the ordering of the mesh
// elements.
Transfinite Volume{129} = {1,14,15,18,16,17};
Transfinite Volume{131} = {17,16,14,15,20,19,2,10};
Transfinite Volume{133} = {18,17,16,6,20,19};
Transfinite Volume{135} = {10,2,19,20,11,3,21,22};
Transfinite Volume{137} = {6,20,19,7,22,21};
Transfinite Volume{139} = {11,3,4,12,22,21,23,24};
Transfinite Volume{141} = {7,22,21,8,24,23};
Transfinite Volume{143} = {12,4,5,13,24,23,25,26};
Transfinite Volume{145} = {8,24,23,9,26,25};
VolInt = 1000 ;
SurfIntPhi0 = 1001 ;
SurfIntPhi1 = 1002 ;
SurfIntZ0 = 1003 ;
VolShell = 2000 ;
SurfShellInt = 2001 ;
SurfShellExt = 2002 ;
SurfShellPhi0 = 2003 ;
SurfShellPhi1 = 2004 ;
SurfShellZ0 = 2005 ;
LineShellIntPhi0 = 2006 ;
LineShellIntPhi1 = 2007 ;
LineShellIntZ0 = 2008 ;
PointShellInt = 2009 ;
VolExt = 3000 ;
VolInf = 3001 ;
SurfInf = 3002 ;
SurfExtInfPhi0 = 3003 ;
SurfExtInfPhi1 = 3004 ;
SurfExtInfZ0 = 3005 ;
SurfInfRight = 3006 ;
SurfInfTop = 3007 ;
Physical Volume (VolInt) = {129,131,133} ;
Physical Surface (SurfIntPhi0) = {55,57,65} ;
Physical Surface (SurfIntPhi1) = {73,75,83} ;
Physical Surface (SurfIntZ0) = {91,121} ;
Physical Volume (VolShell) = {135,137} ;
Physical Surface (SurfShellInt) = {105,107} ;
Physical Surface (SurfShellExt) = {109,111} ;
Physical Surface (SurfShellPhi0) = {59,67} ;
Physical Surface (SurfShellPhi1) = {77,85} ;
Physical Surface (SurfShellZ0) = {123} ;
Physical Line (LineShellIntPhi0) = {1,2} ;
Physical Line (LineShellIntPhi1) = {9,10} ;
Physical Line (LineShellIntZ0) = 21 ;
Physical Point (PointShellInt) = 6 ;
Physical Volume (VolExt) = {139,141} ;
Physical Volume (VolInf) = {143,145} ;
Physical Surface (SurfExtInfPhi0) = {61,63,69,71} ;
Physical Surface (SurfExtInfPhi1) = {79,87,81,89} ;
Physical Surface (SurfExtInfZ0) = {125,127} ;
Physical Surface (SurfInfRight) = {117} ;
Physical Surface (SurfInfTop) = {119} ;
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/*********************************************************************
*
* Gmsh tutorial 7
*
* Anisotropic meshes, Attractors
*
*********************************************************************/
// The new anisotropic 2D mesh generator can be selected with:
Mesh.Algorithm = 2 ;
// One can force a 4 step Laplacian smoothing of the mesh with:
Mesh.Smoothing = 4 ;
lc = .1;
Point(1) = {0.0,0.0,0,lc};
Point(2) = {1,0.0,0,lc};
Point(3) = {1,1,0,lc};
Point(4) = {0,1,0,lc};
Line(1) = {3,2};
Line(2) = {2,1};
Line(3) = {1,4};
Line(4) = {4,3};
Line Loop(5) = {1,2,3,4};
Plane Surface(6) = {5};
Point(5) = {0.1,0.2,0,lc};
Point(11) = {0.5,0.5,-1,lc};
Point(22) = {0.6,0.6,1,lc};
Line(5) = {11,22};
// Anisotropic attractors can be defined on points and lines:
Attractor Line{5} = {1, 0.1, 7};
Attractor Point{5} = {0.1, 0.5, 3};
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/*********************************************************************
*
* Gmsh tutorial 8
*
* Post-Processing, Scripting, Animations, Options
*
*********************************************************************/
// The first example is included, as well as two post-processing maps
// (for the format of the post-processing maps, see the FORMATS file):
Include "t1.geo" ;
Include "view1.pos" ;
Include "view1.pos" ;
// Some general options are set (all the options specified
// interactively can be directly specified in the ascii input
// files. The current options can be saved into a file by selecting
// 'File->Save_Options_as')...
General.Trackball = 0 ;
General.Rotation0 = 0 ;
General.Rotation1 = 0 ;
General.Rotation2 = 0 ;
General.Color.Background = White ;
General.Color.Text = Black ;
General.Orthographic = 0 ;
General.Axes = 0 ;
// ...as well as some options for each post-processing view...
PostProcessing.View[0].Name = "This is a very stupid demonstration..." ;
PostProcessing.View[0].IntervalsType = 2 ;
PostProcessing.View[0].Offset = {0,0,0.05} ;
PostProcessing.View[0].Raise = {0,0,0} ;
PostProcessing.View[0].Light = 1 ;
PostProcessing.View[1].Name = "...of Gmsh's scripting capabilities" ;
PostProcessing.View[1].IntervalsType = 1 ;
PostProcessing.View[1].Color = { Green, Blue } ;
PostProcessing.View[1].NbIso = 10 ;
// ...and loop from 1 to 255 with a step of 1 is performed (to use a
// step different from 1, just add a third argument in the list,
// e.g. 'For num In {0.5:1.5:0.1}' increments num from 0.5 to 1.5 with
// a step of 0.1):
t = 0 ;
For num In {1:255}
PostProcessing.View[0].TimeStep = t ;
PostProcessing.View[1].TimeStep = t ;
t = (PostProcessing.View[0].TimeStep < PostProcessing.View[0].NbTimeStep-1) ? t+1 : 0 ;
PostProcessing.View[0].Raise += {0,0,0.001*t} ;
// It is possible to nest loops:
For num2 In {1:10}
General.Rotation0 += 10 ;
General.Rotation1 = General.Rotation0 / 3 ;
General.Rotation2 += 0.1 ;
Sleep 0.01; // sleep for 0.01 second
Draw; // draw the scene
EndFor
// It is also possible make tests
If (!(num % 20))
Print Sprintf("t8-%g.gif", num); // print the scene in a gif file
EndIf
EndFor
// Here is the list of available scripting commands:
//
// Merge string; (to merge a file)
// Draw; (to draw the scene)
// Mesh int; (to perform the mesh generation; 'int' = 0, 1, 2 or 3)
// Save string; (to save the mesh)
// Print string; (to print the graphic window)
// Sleep expr; (to sleep during expr seconds)
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<!DOCTYPE html PUBLIC "-//IETF//DTD HTML 2.0//EN">
<HTML>
<HEAD>
<TITLE>Enscript Output</TITLE>
</HEAD>
<BODY BGCOLOR="#FFFFFF" TEXT="#000000" LINK="#1F00FF" ALINK="#FF0000" VLINK="#9900DD">
<A NAME="top">
<H1>Contents</H1>
<OL>
<LI><A HREF="#file1">README</A>
<LI><A HREF="#file2">t1.geo</A>
<LI><A HREF="#file3">t2.geo</A>
<LI><A HREF="#file4">t3.geo</A>
<LI><A HREF="#file5">t4.geo</A>
<LI><A HREF="#file6">t5.geo</A>
<LI><A HREF="#file7">t6.geo</A>
<LI><A HREF="#file8">t7.geo</A>
<LI><A HREF="#file9">t8.geo</A>
</OL>
<HR>
<A NAME="file1">
<H1>README 1/9</H1>
[<A HREF="#top">top</A>][prev][<A HREF="#file2">next</A>]
<PRE>
$Id: tutorial.html,v 1.1 2000-12-10 00:46:30 geuzaine Exp $
Here are the examples in the Gmsh tutorial. Feel free to send comments
about the tutorial to christophe.geuzaine@advalvas.be or
remacle@scorec.rpi.edu.
These examples are heavily commented (both C and C++-style comments
can be used in Gmsh input files) and should introduce new features
gradually, starting with t1.geo.
(The tutorial does not explain the mesh and post-processing file
formats. See the FORMATS file for this.)
There are two ways to actually run these examples with Gmsh. (The
operations to run Gmsh may vary depending on your operating system. In
the following, we will assume that you're working with a UNIX-like
shell.) The first working mode of Gmsh is the interactive graphical
mode. To launch Gmsh in interactive mode, just type
&gt; gmsh
at the prompt on the command line. This will open two windows: the
graphic window (with a status bar at the bottom) and the menu window
(with a menu bar and some context dependent buttons). To open the
first tutorial file, you have to select the 'File-&gt;Open' menu, and
choose 't1.geo' in the input field. To perform the mesh generation,
you have to go to the mesh module (by selecting 'Module-&gt;Mesh' in the
menu bar) and choose the required dimension in the context-dependent
buttons ('1D' will mesh all the curves; '2D' will mesh all the
surfaces ---as well as all the curves if '1D' was not called before;
'3D' will mesh all the volumes ---and all the surfaces if '2D' was not
called before). To save the resulting mesh, select 'File-&gt;Save_Mesh'
in the menu bar. The default mesh file name is based on the name of
the first input file on the command line (or 'unnamed' if there wasn't
any input file given), with an appended extension depending on the
mesh format.
Note: nearly all the interactive commands have shortcuts. Select
'?-&gt;Short_Help' in the menu bar to learn about these shortcuts.
Instead of opening the tutorial with the 'File-&gt;Open' menu, it is
often more convenient to put the file name on the command line, here
for example with:
&gt; gmsh t1.geo
(The '.geo' extension can also be omitted.)
Note: to define new geometries, if it is often handy to define the
variables and the points directly in the input files, it is almost
always simpler to define the curves, the surfaces and the volumes
interactively. To do so, just follow the context dependent buttons in
the Geometry module. For example, to create a line, select
'Module-&gt;Geometry' in the menu bar, and then select 'Elementary, Add,
Create, Line'. You will then be asked (in the status bar of the
graphic window) to select a list of points, and to click 'e' when
you're done. Once the interactive command is completed, a string is
automatically added at the end of the currently opened project file.
The second operating mode for Gmsh is the non-interactive mode. In
this mode, there is no graphical user interface, and all operations
are performed without any user interaction. To mesh the first tutorial
in non-interactive mode, just type:
&gt; gmsh t1.geo -2
Several files can be loaded simultaneously in Gmsh. The first one
defines the project, while the others are appended (&quot;merged&quot;) to this
project. You can merge such files with the 'File-&gt;Merge' menu, or by
directly specifying the names of the files on the command line. This
is most useful for post-processing purposes. For example, to merge the
post-processing views contained in the files 'view1.pos' and
'view2.pos' together with the first tutorial 't1.geo', you can type
the following line on the command line:
&gt; gmsh t1.geo view1.pos view2.pos
In the Post-Processing module (select 'Module-&gt;Post_Processing'), two
view buttons will appear, respectively labeled &quot;a scalar map&quot; and &quot;a
vector map&quot;. A left mouse click will toggle the visibility of the
selected view. A right mouse click provides access to the view's
options:
- Reload: reloads the file from which the view was loaded
- Remove: removes the view
- Duplicate: makes a copy of the view (without duplicating the data)
- Lighting: activates/deactivates lighting for the view
- Scale: gives access to the scale menu (range definition, iso-value
choice, ...)
- Color: defines the color map for the view
- Offset: permits to move the view around, and to make elevation
maps
- Vector display: changes vector attributes
- Time step: selects the displayed time step
- Export as background mesh: exports the map, considered as an
error map, as a background mesh, i.e. as a characteristic length map
- Apply as current bg mesh: applies the view as the current background
mesh.
If you want the modifications made to one view to affect also all other
views, select the 'Link all views' option in the
'Options-&gt;Post-Processing' menu.
Note: all the options specified interactively can also be directly
specified in the ascii input files. The current options can be saved
into a file by selecting 'File-&gt;Save_Options_as'. For UNIX versions,
all user interface options can be changed in a standard X resource file
('.gmshrc' in your home directory or app-defaults directory, or
'.Xdefaults'). Use 'editres' to get the full widget tree and
associated resources.
OK, that's all, folks. Enjoy the tutorial.
</PRE>
<HR>
<A NAME="file2">
<H1>t1.geo 2/9</H1>
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<PRE>
<I><FONT COLOR="#B22222">/*********************************************************************
*
* Gmsh tutorial 1
*
* Variables, Elementary entities (Points, Lines, Surfaces), Physical
* entities (Points, Lines, Surfaces)
*
*********************************************************************/</FONT></I>
<I><FONT COLOR="#B22222">// All geometry description in Gmsh is made by means of a special
</FONT></I><I><FONT COLOR="#B22222">// language (looking somewhat similar to C). The simplest construction
</FONT></I><I><FONT COLOR="#B22222">// of this language is the 'affectation'.
</FONT></I>
<I><FONT COLOR="#B22222">// The following command (all commands end with a semi colon) defines
</FONT></I><I><FONT COLOR="#B22222">// a variable called 'lc' and affects the value 0.007 to 'lc':
</FONT></I>
lc = 0.007 ;
<I><FONT COLOR="#B22222">// This newly created variable can be used to define the first Gmsh
</FONT></I><I><FONT COLOR="#B22222">// elementary entity, a 'Point'. A Point is defined by a list of four
</FONT></I><I><FONT COLOR="#B22222">// numbers: its three coordinates (x, y and z), and a characteristic
</FONT></I><I><FONT COLOR="#B22222">// length, which sets the target mesh size at the point:
</FONT></I>
Point(1) = {0, 0, 0, 9.e-1 * lc} ;
<I><FONT COLOR="#B22222">// As can be seen in this definition, more complex expressions can be
</FONT></I><I><FONT COLOR="#B22222">// constructed from variables on the fly. Here, the product of the
</FONT></I><I><FONT COLOR="#B22222">// variable 'lc' by the constant 9.e-1 is given as the fourth argument
</FONT></I><I><FONT COLOR="#B22222">// of the list defining the point.
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// The following general syntax rule is applied for the definition of
</FONT></I><I><FONT COLOR="#B22222">// all geometrical entities:
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// &quot;If a number defines a new entity, it is enclosed between
</FONT></I><I><FONT COLOR="#B22222">// parentheses. If a number refers to a previously defined entity,
</FONT></I><I><FONT COLOR="#B22222">// it is enclosed between braces.&quot;
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// Three additional points are then defined:
</FONT></I>
Point(2) = {.1, 0, 0, lc} ;
Point(3) = {.1, .3, 0, lc} ;
Point(4) = {0, .3, 0, lc} ;
<I><FONT COLOR="#B22222">// The second elementary geometrical entity in Gmsh is the
</FONT></I><I><FONT COLOR="#B22222">// curve. Amongst curves, straight lines are the simplest. A straight
</FONT></I><I><FONT COLOR="#B22222">// line is defined by a list of point numbers. For example, the line 1
</FONT></I><I><FONT COLOR="#B22222">// starts at point 1 and ends at point 2:
</FONT></I>
Line(1) = {1,2} ;
Line(2) = {3,2} ;
Line(3) = {3,4} ;
Line(4) = {4,1} ;
<I><FONT COLOR="#B22222">// The third elementary entity is the surface. In order to define a
</FONT></I><I><FONT COLOR="#B22222">// simple rectangular surface from the four lines defined above, a
</FONT></I><I><FONT COLOR="#B22222">// line loop has first to be defined. A line loop is a list of
</FONT></I><I><FONT COLOR="#B22222">// connected lines, each line being associated a sign, depending of
</FONT></I><I><FONT COLOR="#B22222">// its orientation.
</FONT></I>
Line Loop(5) = {4,1,-2,3} ;
<I><FONT COLOR="#B22222">// The surface is then defined as a list of line loops (only one
</FONT></I><I><FONT COLOR="#B22222">// here):
</FONT></I>
Plane Surface(6) = {5} ;
<I><FONT COLOR="#B22222">// At this level, Gmsh knows everything to display the rectangular
</FONT></I><I><FONT COLOR="#B22222">// surface 6 and to mesh it. But a supplementary step is needed in
</FONT></I><I><FONT COLOR="#B22222">// order for assign region numbers to the various elements in the mesh
</FONT></I><I><FONT COLOR="#B22222">// (the points, the lines and the triangles discretizing the points 1
</FONT></I><I><FONT COLOR="#B22222">// to 4, the lines 1 to 4 and the surface 6). This is achieved by the
</FONT></I><I><FONT COLOR="#B22222">// definition of Physical entities. Physical entities will group
</FONT></I><I><FONT COLOR="#B22222">// elements belonging to several elementary entities by giving them a
</FONT></I><I><FONT COLOR="#B22222">// common number (a region number), and specifying their orientation.
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// For example, the two points 1 and 2 can be grouped into the
</FONT></I><I><FONT COLOR="#B22222">// physical entity 1:
</FONT></I>
Physical Point(1) = {1,2} ;
<I><FONT COLOR="#B22222">// Consequently, two punctual elements will be saved in the output
</FONT></I><I><FONT COLOR="#B22222">// files, both with the region number 1. The mechanism is identical
</FONT></I><I><FONT COLOR="#B22222">// for line or surface elements:
</FONT></I>
Physical Line(10) = {1,2,4} ;
Physical Surface(100) = {6} ;
<I><FONT COLOR="#B22222">// All the line elements which will be created during the mesh of the
</FONT></I><I><FONT COLOR="#B22222">// lines 1, 2 and 4 will be saved in the output file with the
</FONT></I><I><FONT COLOR="#B22222">// associated region number 10; and all the triangular elements
</FONT></I><I><FONT COLOR="#B22222">// resulting from the discretization of the surface 6 will be
</FONT></I><I><FONT COLOR="#B22222">// associated the region number 100.
</FONT></I>
<I><FONT COLOR="#B22222">// It is important to notice that only those elements which belong to
</FONT></I><I><FONT COLOR="#B22222">// physical groups will be saved in the output file if the file format
</FONT></I><I><FONT COLOR="#B22222">// is the msh format (the native mesh file format for Gmsh). For a
</FONT></I><I><FONT COLOR="#B22222">// description of the mesh and post-processing formats, see the FORMATS
</FONT></I><I><FONT COLOR="#B22222">// file.
</FONT></I>
</PRE>
<HR>
<A NAME="file3">
<H1>t2.geo 3/9</H1>
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<PRE>
<I><FONT COLOR="#B22222">/*********************************************************************
*
* Gmsh tutorial 2
*
* Includes, Geometrical transformations, Elementary entities
* (Volumes), Physical entities (Volumes)
*
*********************************************************************/</FONT></I>
<I><FONT COLOR="#B22222">// The first tutorial file will serve as a basis to construct this
</FONT></I><I><FONT COLOR="#B22222">// one: it can be included like this:
</FONT></I>
Include &quot;t1.geo&quot; ;
<I><FONT COLOR="#B22222">// There are several possibilities to build a more complex geometry
</FONT></I><I><FONT COLOR="#B22222">// from the one previously defined in 't1.geo'.
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// New points, lines and surfaces can first be directly defined in the
</FONT></I><I><FONT COLOR="#B22222">// same way as in 't1.geo':
</FONT></I>
Point(5) = {0, .4, 0, lc} ;
Line(5) = {4, 5} ;
<I><FONT COLOR="#B22222">// But Gmsh also provides geometrical transformation mechanisms to
</FONT></I><I><FONT COLOR="#B22222">// move (translate, rotate, ...), add (translate, rotate, ...) or
</FONT></I><I><FONT COLOR="#B22222">// extrude (translate, rotate) elementary geometrical entities. For
</FONT></I><I><FONT COLOR="#B22222">// example, the point 3 can be moved by 0.05 units on the left with:
</FONT></I>
Translate {-0.05,0,0} { Point{3} ; }
<I><FONT COLOR="#B22222">// The resulting point can also be duplicated and translated by 0.1
</FONT></I><I><FONT COLOR="#B22222">// along the y axis:
</FONT></I>
Translate {0,0.1,0} { Duplicata{ Point{3} ; } }
<I><FONT COLOR="#B22222">// Translation, rotation and extrusion commands of course not only
</FONT></I><I><FONT COLOR="#B22222">// apply to points, but also to lines and surfaces. The following
</FONT></I><I><FONT COLOR="#B22222">// command extrudes the surface 6 defined in 't1.geo', as well as a
</FONT></I><I><FONT COLOR="#B22222">// new surface 11, along the z axis by 'h':
</FONT></I>
h = 0.12 ;
Extrude Surface { 6, {0, 0, h} } ;
Line(7) = {3, 6} ; Line(8) = {6,5} ; Line Loop(10) = {5,-8,-7,3};
Plane Surface(11) = {10};
Extrude Surface { 11, {0, 0, h} } ;
<I><FONT COLOR="#B22222">// All these geometrical transformations generate automatically new
</FONT></I><I><FONT COLOR="#B22222">// elementary entities. The following commands permit to specify
</FONT></I><I><FONT COLOR="#B22222">// manually a characteristic length for some of the automatically
</FONT></I><I><FONT COLOR="#B22222">// created points:
</FONT></I>
Characteristic Length{6,22,2,3,16,12} = lc * 3 ;
<I><FONT COLOR="#B22222">// If the transformation tools are handy to create complex geometries,
</FONT></I><I><FONT COLOR="#B22222">// it is sometimes useful to be generate the flat geometry, consisting
</FONT></I><I><FONT COLOR="#B22222">// only of the explicit list elementary entities. This can be achieved
</FONT></I><I><FONT COLOR="#B22222">// by selecting the 'File-&gt;Print-&gt;Geo' menu or by typing
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// &gt; gmsh t2.geo -0
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// on the command line.
</FONT></I>
<I><FONT COLOR="#B22222">// Volumes are the fourth type of elementary entities in Gmsh. In the
</FONT></I><I><FONT COLOR="#B22222">// same way one defines line loops to build surfaces, one has to
</FONT></I><I><FONT COLOR="#B22222">// define surface loops to build volumes. The following volumes are
</FONT></I><I><FONT COLOR="#B22222">// very simple, without holes (and thus consist of only one surface
</FONT></I><I><FONT COLOR="#B22222">// loop):
</FONT></I>
Surface Loop(145) = {121,11,131,135,139,144};
Volume(146) = {145};
Surface Loop(146) = {121,6,109,113,117,122};
Volume(147) = {146};
<I><FONT COLOR="#B22222">// To save all volumic (tetrahedral) elements of volume 146 and 147
</FONT></I><I><FONT COLOR="#B22222">// with the associate region number 1, a Physical Volume must be
</FONT></I><I><FONT COLOR="#B22222">// defined:
</FONT></I>
Physical Volume (1) = {146,147} ;
<I><FONT COLOR="#B22222">// Congratulations! You've created your first fully unstructured
</FONT></I><I><FONT COLOR="#B22222">// tetrahedral 3D mesh!
</FONT></I></PRE>
<HR>
<A NAME="file4">
<H1>t3.geo 4/9</H1>
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<PRE>
<I><FONT COLOR="#B22222">/*********************************************************************
*
* Gmsh tutorial 3
*
* Extruded meshes, Options
*
*********************************************************************/</FONT></I>
<I><FONT COLOR="#B22222">// Again, the first tutorial example is included:
</FONT></I>
Include &quot;t1.geo&quot; ;
<I><FONT COLOR="#B22222">// As in 't2.geo', an extrusion along the z axis will be performed:
</FONT></I>
h = 0.1 ;
<I><FONT COLOR="#B22222">// But contrary to 't2.geo', not only the geometry will be extruded,
</FONT></I><I><FONT COLOR="#B22222">// but we also the 2D mesh. This is done with the same Extrude
</FONT></I><I><FONT COLOR="#B22222">// command, but by specifying the number of layers (here, there will
</FONT></I><I><FONT COLOR="#B22222">// be two layers, of respectively 2 and 4 elements in depth), with
</FONT></I><I><FONT COLOR="#B22222">// volume numbers 9000 and 9001 and respective heights of 0.33*h and
</FONT></I><I><FONT COLOR="#B22222">// 0.67*h:
</FONT></I>
Extrude Surface { 6, {0,0,h} } { Layers { {2,4}, {9000,9001}, {0.33,1} } ; } ;
<I><FONT COLOR="#B22222">// The extrusion can also be combined with a rotation, and the
</FONT></I><I><FONT COLOR="#B22222">// extruded 3D mesh can be recombined into prisms (wedges). All
</FONT></I><I><FONT COLOR="#B22222">// rotations are specified by an axis direction ({0,1,0}), an axis
</FONT></I><I><FONT COLOR="#B22222">// point ({0,0,0}) and a rotation angle (Pi/2):
</FONT></I>
Extrude Surface { 122, {0,1,0} , {-0.1,0,0.1} , -Pi/2 } {
Recombine ; Layers { {7}, {9002}, {1} } ;
};
<I><FONT COLOR="#B22222">// All interactive options can also be set directly in the input file.
</FONT></I><I><FONT COLOR="#B22222">// For example, the following lines redefine the background color of
</FONT></I><I><FONT COLOR="#B22222">// the graphic window, the color of the points of the geometry,
</FONT></I><I><FONT COLOR="#B22222">// disable the display of the axes, and select an initial viewpoint in
</FONT></I><I><FONT COLOR="#B22222">// xyz mode (disabling the interactive trackball-like rotation mode):
</FONT></I>
General.Color.Background = Red;
Geometry.Color.Points = Orange;
General.Axes = 0;
General.Trackball = 0;
General.Rotation0 = 10;
General.Rotation1 = 70;
General.Translation0 = -0.1;
<I><FONT COLOR="#B22222">// Note: all colors can be defined literally or numerically, i.e.
</FONT></I><I><FONT COLOR="#B22222">// 'General.Color.Background = Red' is equivalent to
</FONT></I><I><FONT COLOR="#B22222">// 'General.Color.Background = {255,0,0}'. As with user-defined
</FONT></I><I><FONT COLOR="#B22222">// variables, the options can be used either as right hand or left
</FONT></I><I><FONT COLOR="#B22222">// hand sides, so that
</FONT></I>
Geometry.Color.Surfaces = Geometry.Color.Points;
<I><FONT COLOR="#B22222">// will set the color of the surfaces in the geometry to the same
</FONT></I><I><FONT COLOR="#B22222">// color as the points.
</FONT></I>
<I><FONT COLOR="#B22222">// For UNIX versions, a click on the '?' button in status bar of the
</FONT></I><I><FONT COLOR="#B22222">// graphic window will dump all current options to the terminal. To
</FONT></I><I><FONT COLOR="#B22222">// save the options to a file, use the 'File-&gt;Save_Options_as' menu.
</FONT></I>
</PRE>
<HR>
<A NAME="file5">
<H1>t4.geo 5/9</H1>
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<PRE>
<I><FONT COLOR="#B22222">/*********************************************************************
*
* Gmsh tutorial 4
*
* Built-in functions, Holes
*
*********************************************************************/</FONT></I>
cm = 1e-02 ;
e1 = 4.5*cm ; e2 = 6*cm / 2 ; e3 = 5*cm / 2 ;
h1 = 5*cm ; h2 = 10*cm ; h3 = 5*cm ; h4 = 2*cm ; h5 = 4.5*cm ;
R1 = 1*cm ; R2 = 1.5*cm ; r = 1*cm ;
ccos = ( -h5*R1 + e2 * Hypot(h5,Hypot(e2,R1)) ) / (h5^2 + e2^2) ;
ssin = Sqrt(1-ccos^2) ;
Lc1 = 0.01 ;
Lc2 = 0.003 ;
<I><FONT COLOR="#B22222">// A whole set of operators can be used, which can be combined in all
</FONT></I><I><FONT COLOR="#B22222">// the expressions. These operators are defined in a similar way to
</FONT></I><I><FONT COLOR="#B22222">// their C or C++ equivalents (with the exception of '^'):
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// '-' (in both unary and binary versions, i.e. as in '-1' and '1-2')
</FONT></I><I><FONT COLOR="#B22222">// '!' (the negation)
</FONT></I><I><FONT COLOR="#B22222">// '+'
</FONT></I><I><FONT COLOR="#B22222">// '*'
</FONT></I><I><FONT COLOR="#B22222">// '/'
</FONT></I><I><FONT COLOR="#B22222">// '%' (the rest of the integer division)
</FONT></I><I><FONT COLOR="#B22222">// '&lt;'
</FONT></I><I><FONT COLOR="#B22222">// '&gt;'
</FONT></I><I><FONT COLOR="#B22222">// '&lt;='
</FONT></I><I><FONT COLOR="#B22222">// '&gt;='
</FONT></I><I><FONT COLOR="#B22222">// '=='
</FONT></I><I><FONT COLOR="#B22222">// '!='
</FONT></I><I><FONT COLOR="#B22222">// '&amp;&amp;' (and)
</FONT></I><I><FONT COLOR="#B22222">// '||' (or)
</FONT></I><I><FONT COLOR="#B22222">// '||' (or)
</FONT></I><I><FONT COLOR="#B22222">// '^' (power)
</FONT></I><I><FONT COLOR="#B22222">// '?' ':' (the ternary operator)
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// Grouping is done, as usual, with parentheses.
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// In addition to these operators, all C mathematical functions can
</FONT></I><I><FONT COLOR="#B22222">// also be used (note the first capital letter):
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// Exp(x)
</FONT></I><I><FONT COLOR="#B22222">// Log(x)
</FONT></I><I><FONT COLOR="#B22222">// Log10(x)
</FONT></I><I><FONT COLOR="#B22222">// Sqrt(x)
</FONT></I><I><FONT COLOR="#B22222">// Sin(x)
</FONT></I><I><FONT COLOR="#B22222">// Asin(x)
</FONT></I><I><FONT COLOR="#B22222">// Cos(x)
</FONT></I><I><FONT COLOR="#B22222">// Acos(x)
</FONT></I><I><FONT COLOR="#B22222">// Tan(x)
</FONT></I><I><FONT COLOR="#B22222">// Atan(x)
</FONT></I><I><FONT COLOR="#B22222">// Atan2(x,y)
</FONT></I><I><FONT COLOR="#B22222">// Sinh(x)
</FONT></I><I><FONT COLOR="#B22222">// Cosh(x)
</FONT></I><I><FONT COLOR="#B22222">// Tanh(x)
</FONT></I><I><FONT COLOR="#B22222">// Fabs(x)
</FONT></I><I><FONT COLOR="#B22222">// Floor(x)
</FONT></I><I><FONT COLOR="#B22222">// Ceil(x)
</FONT></I><I><FONT COLOR="#B22222">// Fmod(x,y)
</FONT></I><I><FONT COLOR="#B22222">// Hypot(x,y)
</FONT></I>
<I><FONT COLOR="#B22222">// An additional function 'Rand(x)' generates an random number in
</FONT></I><I><FONT COLOR="#B22222">// [0,x]
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// Rand(x)
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// The only predefined constant in Gmsh is Pi.
</FONT></I>
Point(1) = { -e1-e2, 0.0 , 0.0 , Lc1};
Point(2) = { -e1-e2, h1 , 0.0 , Lc1};
Point(3) = { -e3-r , h1 , 0.0 , Lc2};
Point(4) = { -e3-r , h1+r , 0.0 , Lc2};
Point(5) = { -e3 , h1+r , 0.0 , Lc2};
Point(6) = { -e3 , h1+h2, 0.0 , Lc1};
Point(7) = { e3 , h1+h2, 0.0 , Lc1};
Point(8) = { e3 , h1+r , 0.0 , Lc2};
Point(9) = { e3+r , h1+r , 0.0 , Lc2};
Point(10)= { e3+r , h1 , 0.0 , Lc2};
Point(11)= { e1+e2, h1 , 0.0 , Lc1};
Point(12)= { e1+e2, 0.0 , 0.0 , Lc1};
Point(13)= { e2 , 0.0 , 0.0 , Lc1};
Point(14)= { R1 / ssin , h5+R1*ccos, 0.0 , Lc2};
Point(15)= { 0.0 , h5 , 0.0 , Lc2};
Point(16)= { -R1 / ssin , h5+R1*ccos, 0.0 , Lc2};
Point(17)= { -e2 , 0.0 , 0.0 , Lc1};
Point(18)= { -R2 , h1+h3 , 0.0 , Lc2};
Point(19)= { -R2 , h1+h3+h4, 0.0 , Lc2};
Point(20)= { 0.0 , h1+h3+h4, 0.0 , Lc2};
Point(21)= { R2 , h1+h3+h4, 0.0 , Lc2};
Point(22)= { R2 , h1+h3 , 0.0 , Lc2};
Point(23)= { 0.0 , h1+h3 , 0.0 , Lc2};
Point(24)= { 0 , h1+h3+h4+R2, 0.0 , Lc2};
Point(25)= { 0 , h1+h3-R2, 0.0 , Lc2};
Line(1) = {1 ,17};
Line(2) = {17,16};
<I><FONT COLOR="#B22222">// All curves are not straight lines... Circles are defined by a list
</FONT></I><I><FONT COLOR="#B22222">// of three point numbers, which represent the starting point, the
</FONT></I><I><FONT COLOR="#B22222">// center and the end point, respectively. All circles have to be
</FONT></I><I><FONT COLOR="#B22222">// defined in the trigonometric (counter-clockwise) sense. Note that
</FONT></I><I><FONT COLOR="#B22222">// the 3 points should not be aligned (otherwise the plane in which
</FONT></I><I><FONT COLOR="#B22222">// the circle lies has to be defined, by 'Circle(num) =
</FONT></I><I><FONT COLOR="#B22222">// {start,center,end} Plane {nx,ny,nz}').
</FONT></I>
Circle(3) = {14,15,16};
Line(4) = {14,13};
Line(5) = {13,12};
Line(6) = {12,11};
Line(7) = {11,10};
Circle(8) = { 8, 9,10};
Line(9) = { 8, 7};
Line(10) = { 7, 6};
Line(11) = { 6, 5};
Circle(12) = { 3, 4, 5};
Line(13) = { 3, 2};
Line(14) = { 2, 1};
Line(15) = {18,19};
Circle(16) = {21,20,24};
Circle(17) = {24,20,19};
Circle(18) = {18,23,25};
Circle(19) = {25,23,22};
Line(20) = {21,22};
Line Loop(21) = {17,-15,18,19,-20,16};
Plane Surface(22) = {21};
<I><FONT COLOR="#B22222">// The surface is made of two line loops, i.e. it has one hole:
</FONT></I>
Line Loop(23) = {11,-12,13,14,1,2,-3,4,5,6,7,-8,9,10};
Plane Surface(24) = {23,21};
Physical Surface(1) = {22};
Physical Surface(2) = {24};
</PRE>
<HR>
<A NAME="file6">
<H1>t5.geo 6/9</H1>
[<A HREF="#top">top</A>][<A HREF="#file5">prev</A>][<A HREF="#file7">next</A>]
<PRE>
<I><FONT COLOR="#B22222">/*********************************************************************
*
* Gmsh tutorial 5
*
* Characteristic lengths, Functions, Loops
*
*********************************************************************/</FONT></I>
<I><FONT COLOR="#B22222">// This defines some characteristic lengths:
</FONT></I>
lcar1 = .1;
lcar2 = .0005;
lcar3 = .075;
<I><FONT COLOR="#B22222">// In order to change these lengths globally (without changing the
</FONT></I><I><FONT COLOR="#B22222">// file), a global scaling factor for all characteristic lengths can
</FONT></I><I><FONT COLOR="#B22222">// be specified on the command line with the option '-clscale'. For
</FONT></I><I><FONT COLOR="#B22222">// example, with:
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// &gt; gmsh t5 -clscale 1
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// this example produces a mesh of approximately 2000 nodes and
</FONT></I><I><FONT COLOR="#B22222">// 10,000 tetrahedra (in 3 seconds on an alpha workstation running at
</FONT></I><I><FONT COLOR="#B22222">// 666MHz). With
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// &gt; gmsh t5 -clscale 0.2
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// (i.e. with all characteristic lengths divided by 5), the mesh
</FONT></I><I><FONT COLOR="#B22222">// counts approximately 170,000 nodes and one million tetrahedra
</FONT></I><I><FONT COLOR="#B22222">// (and the computation takes 16 minutes on the same machine :-( So
</FONT></I><I><FONT COLOR="#B22222">// there is still a lot of work to do to achieve decent performance
</FONT></I><I><FONT COLOR="#B22222">// with Gmsh...)
</FONT></I>
Point(1) = {0.5,0.5,0.5,lcar2}; Point(2) = {0.5,0.5,0,lcar1};
Point(3) = {0,0.5,0.5,lcar1}; Point(4) = {0,0,0.5,lcar1};
Point(5) = {0.5,0,0.5,lcar1}; Point(6) = {0.5,0,0,lcar1};
Point(7) = {0,0.5,0,lcar1}; Point(8) = {0,1,0,lcar1};
Point(9) = {1,1,0,lcar1}; Point(10) = {0,0,1,lcar1};
Point(11) = {0,1,1,lcar1}; Point(12) = {1,1,1,lcar1};
Point(13) = {1,0,1,lcar1}; Point(14) = {1,0,0,lcar1};
Line(1) = {8,9}; Line(2) = {9,12}; Line(3) = {12,11};
Line(4) = {11,8}; Line(5) = {9,14}; Line(6) = {14,13};
Line(7) = {13,12}; Line(8) = {11,10}; Line(9) = {10,13};
Line(10) = {10,4}; Line(11) = {4,5}; Line(12) = {5,6};
Line(13) = {6,2}; Line(14) = {2,1}; Line(15) = {1,3};
Line(16) = {3,7}; Line(17) = {7,2}; Line(18) = {3,4};
Line(19) = {5,1}; Line(20) = {7,8}; Line(21) = {6,14};
Line Loop(22) = {11,19,15,18}; Plane Surface(23) = {22};
Line Loop(24) = {16,17,14,15}; Plane Surface(25) = {24};
Line Loop(26) = {-17,20,1,5,-21,13}; Plane Surface(27) = {26};
Line Loop(28) = {4,1,2,3}; Plane Surface(29) = {28};
Line Loop(30) = {7,-2,5,6}; Plane Surface(31) = {30};
Line Loop(32) = {6,-9,10,11,12,21}; Plane Surface(33) = {32};
Line Loop(34) = {7,3,8,9}; Plane Surface(35) = {34};
Line Loop(36) = {10,-18,16,20,-4,8}; Plane Surface(37) = {36};
Line Loop(38) = {-14,-13,-12,19}; Plane Surface(39) = {38};
<I><FONT COLOR="#B22222">// Instead of using included files, one can also define functions. In
</FONT></I><I><FONT COLOR="#B22222">// the following function, the reserved variable 'newp' is used, which
</FONT></I><I><FONT COLOR="#B22222">// automatically selects a new point number. This number is chosen as
</FONT></I><I><FONT COLOR="#B22222">// the highest current point number, plus one. Analogously to 'newp',
</FONT></I><I><FONT COLOR="#B22222">// there exists a variable 'newreg' which selects the highest number
</FONT></I><I><FONT COLOR="#B22222">// of all entities other than points, plus one.
</FONT></I>
<I><FONT COLOR="#B22222">// Note: there are no local variables. This will be changed in a
</FONT></I><I><FONT COLOR="#B22222">// future version of Gmsh.
</FONT></I>
Function CheeseHole
p1 = newp; Point(p1) = {x, y, z, lcar3} ;
p2 = newp; Point(p2) = {x+r,y, z, lcar3} ;
p3 = newp; Point(p3) = {x, y+r,z, lcar3} ;
p4 = newp; Point(p4) = {x, y, z+r,lcar3} ;
p5 = newp; Point(p5) = {x-r,y, z, lcar3} ;
p6 = newp; Point(p6) = {x, y-r,z, lcar3} ;
p7 = newp; Point(p7) = {x, y, z-r,lcar3} ;
c1 = newreg; Circle(c1) = {p2,p1,p7};
c2 = newreg; Circle(c2) = {p7,p1,p5};
c3 = newreg; Circle(c3) = {p5,p1,p4};
c4 = newreg; Circle(c4) = {p4,p1,p2};
c5 = newreg; Circle(c5) = {p2,p1,p3};
c6 = newreg; Circle(c6) = {p3,p1,p5};
c7 = newreg; Circle(c7) = {p5,p1,p6};
c8 = newreg; Circle(c8) = {p6,p1,p2};
c9 = newreg; Circle(c9) = {p7,p1,p3};
c10 = newreg; Circle(c10) = {p3,p1,p4};
c11 = newreg; Circle(c11) = {p4,p1,p6};
c12 = newreg; Circle(c12) = {p6,p1,p7};
<I><FONT COLOR="#B22222">// All surfaces are not plane... Here is the way to define ruled
</FONT></I><I><FONT COLOR="#B22222">// surfaces (which have 3 or 4 borders):
</FONT></I>
l1 = newreg; Line Loop(l1) = {c5,c10,c4}; Ruled Surface(newreg) = {l1};
l2 = newreg; Line Loop(l2) = {c9,-c5,c1}; Ruled Surface(newreg) = {l2};
l3 = newreg; Line Loop(l3) = {-c12,c8,c1}; Ruled Surface(newreg) = {l3};
l4 = newreg; Line Loop(l4) = {c8,-c4,c11}; Ruled Surface(newreg) = {l4};
l5 = newreg; Line Loop(l5) = {-c10,c6,c3}; Ruled Surface(newreg) = {l5};
l6 = newreg; Line Loop(l6) = {-c11,-c3,c7}; Ruled Surface(newreg) = {l6};
l7 = newreg; Line Loop(l7) = {c2,c7,c12}; Ruled Surface(newreg) = {l7};
l8 = newreg; Line Loop(l8) = {-c6,-c9,c2}; Ruled Surface(newreg) = {l8};
l9 = newreg; Surface Loop(l9) = {l8+1, l5+1, l1+1, l2+1, -(l3+1), -(l7+1), l6+1, l4+1};
thehole = newreg; Volume(thehole) = {l9};
Return
x = 0; y = 0.75; z = 0; r = 0.09;
<I><FONT COLOR="#B22222">// A For loop is used to generate five holes in the cube:
</FONT></I>
For t In {1:5}
x += 0.166 ;
z += 0.166 ;
<I><FONT COLOR="#B22222">// This command calls the function CheeseHole. Note that, instead of
</FONT></I><I><FONT COLOR="#B22222">// defining a function, we could have define a file containing the
</FONT></I><I><FONT COLOR="#B22222">// same code, and used the Include command to include this file.
</FONT></I>
Call CheeseHole;
<I><FONT COLOR="#B22222">// A physical volume is defined for each cheese hole
</FONT></I>
Physical Volume (t) = thehole ;
<I><FONT COLOR="#B22222">// The Printf function permits to print the value of variables on the
</FONT></I><I><FONT COLOR="#B22222">// terminal:
</FONT></I>
Printf(&quot;The cheese hole has number %g!&quot;, thehole);
EndFor
<I><FONT COLOR="#B22222">// This is the surface loop for the exterior surface of the cube:
</FONT></I>
Surface Loop(185) = {35,31,29,37,33,23,39,25,27};
<I><FONT COLOR="#B22222">// The volume of the cube, without the 5 cheese holes, is defined by 6
</FONT></I><I><FONT COLOR="#B22222">// surface loops (the exterior surface and the five interior loops):
</FONT></I>
Volume(186) = {185,184,155,126,97,68};
<I><FONT COLOR="#B22222">// This physical volume assigns the region number 10 to the tetrahedra
</FONT></I><I><FONT COLOR="#B22222">// paving the cube (but not the holes, whose elements were tagged from
</FONT></I><I><FONT COLOR="#B22222">// 1 to 5 in the 'For' loop)
</FONT></I>
Physical Volume (10) = 186 ;
</PRE>
<HR>
<A NAME="file7">
<H1>t6.geo 7/9</H1>
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<PRE>
<I><FONT COLOR="#B22222">/*********************************************************************
*
* Gmsh tutorial 6
*
* Transfinite meshes
*
*********************************************************************/</FONT></I>
r_int = 0.05 ;
r_ext = 0.051 ;
r_far = 0.125 ;
r_inf = 0.4 ;
phi1 = 30. * (Pi/180.) ;
angl = 45. * (Pi/180.) ;
nbpt_phi = 5 ; nbpt_int = 20 ;
nbpt_arc1 = 10 ; nbpt_arc2 = 10 ;
nbpt_shell = 10 ; nbpt_far = 25 ; nbpt_inf = 15 ;
lc0 = 0.1 ; lc1 = 0.1 ; lc2 = 0.3 ;
Point(1) = {0, 0, 0, lc0} ;
Point(2) = {r_int, 0, 0, lc0} ;
Point(3) = {r_ext, 0, 0, lc1} ;
Point(4) = {r_far, 0, 0, lc2} ;
Point(5) = {r_inf, 0, 0, lc2} ;
Point(6) = {0, 0, r_int, lc0} ;
Point(7) = {0, 0, r_ext, lc1} ;
Point(8) = {0, 0, r_far, lc2} ;
Point(9) = {0, 0, r_inf, lc2} ;
Point(10) = {r_int*Cos(phi1), r_int*Sin(phi1), 0, lc0} ;
Point(11) = {r_ext*Cos(phi1), r_ext*Sin(phi1), 0, lc1} ;
Point(12) = {r_far*Cos(phi1), r_far*Sin(phi1), 0, lc2} ;
Point(13) = {r_inf*Cos(phi1), r_inf*Sin(phi1), 0, lc2} ;
Point(14) = {r_int/2, 0, 0, lc2} ;
Point(15) = {r_int/2*Cos(phi1), r_int/2*Sin(phi1), 0, lc2} ;
Point(16) = {r_int/2, 0, r_int/2, lc2} ;
Point(17) = {r_int/2*Cos(phi1), r_int/2*Sin(phi1), r_int/2, lc2} ;
Point(18) = {0, 0, r_int/2, lc2} ;
Point(19) = {r_int*Cos(angl), 0, r_int*Sin(angl), lc2} ;
Point(20) = {r_int*Cos(angl)*Cos(phi1), r_int*Cos(angl)*Sin(phi1), r_int*Sin(angl), lc2} ;
Point(21) = {r_ext*Cos(angl), 0, r_ext*Sin(angl), lc2} ;
Point(22) = {r_ext*Cos(angl)*Cos(phi1), r_ext*Cos(angl)*Sin(phi1), r_ext*Sin(angl), lc2} ;
Point(23) = {r_far*Cos(angl), 0, r_far*Sin(angl), lc2} ;
Point(24) = {r_far*Cos(angl)*Cos(phi1), r_far*Cos(angl)*Sin(phi1), r_far*Sin(angl), lc2} ;
Point(25) = {r_inf, 0, r_inf, lc2} ;
Point(26) = {r_inf*Cos(phi1), r_inf*Sin(phi1), r_inf, lc2} ;
Circle(1) = {2,1,19}; Circle(2) = {19,1,6}; Circle(3) = {3,1,21};
Circle(4) = {21,1,7}; Circle(5) = {4,1,23}; Circle(6) = {23,1,8};
Line(7) = {5,25}; Line(8) = {25,9};
Circle(9) = {10,1,20}; Circle(10) = {20,1,6}; Circle(11) = {11,1,22};
Circle(12) = {22,1,7}; Circle(13) = {12,1,24}; Circle(14) = {24,1,8};
Line(15) = {13,26}; Line(16) = {26,9};
Circle(17) = {19,1,20}; Circle(18) = {21,1,22}; Circle(19) = {23,1,24};
Circle(20) = {25,1,26}; Circle(21) = {2,1,10}; Circle(22) = {3,1,11};
Circle(23) = {4,1,12}; Circle(24) = {5,1,13};
Line(25) = {1,14}; Line(26) = {14,2}; Line(27) = {2,3}; Line(28) = {3,4};
Line(29) = {4,5}; Line(30) = {1,15}; Line(31) = {15,10}; Line(32) = {10,11};
Line(33) = {11,12}; Line(34) = {12,13}; Line(35) = {14,15}; Line(36) = {14,16};
Line(37) = {15,17}; Line(38) = {16,17}; Line(39) = {18,16}; Line(40) = {18,17};
Line(41) = {1,18}; Line(42) = {18,6}; Line(43) = {6,7}; Line(44) = {16,19};
Line(45) = {19,21}; Line(46) = {21,23}; Line(47) = {23,25}; Line(48) = {17,20};
Line(49) = {20,22}; Line(50) = {22,24}; Line(51) = {24,26}; Line(52) = {7,8};
Line(53) = {8,9};
Line Loop(54) = {39,-36,-25,41}; Ruled Surface(55) = {54};
Line Loop(56) = {44,-1,-26,36}; Ruled Surface(57) = {56};
Line Loop(58) = {3,-45,-1,27}; Ruled Surface(59) = {58};
Line Loop(60) = {5,-46,-3,28}; Ruled Surface(61) = {60};
Line Loop(62) = {7,-47,-5,29}; Ruled Surface(63) = {62};
Line Loop(64) = {-2,-44,-39,42}; Ruled Surface(65) = {64};
Line Loop(66) = {-4,-45,2,43}; Ruled Surface(67) = {66};
Line Loop(68) = {-6,-46,4,52}; Ruled Surface(69) = {68};
Line Loop(70) = {-8,-47,6,53}; Ruled Surface(71) = {70};
Line Loop(72) = {-40,-41,30,37}; Ruled Surface(73) = {72};
Line Loop(74) = {48,-9,-31,37}; Ruled Surface(75) = {74};
Line Loop(76) = {49,-11,-32,9}; Ruled Surface(77) = {76};
Line Loop(78) = {-50,-11,33,13}; Ruled Surface(79) = {78};
Line Loop(80) = {-51,-13,34,15}; Ruled Surface(81) = {80};
Line Loop(82) = {10,-42,40,48}; Ruled Surface(83) = {82};
Line Loop(84) = {12,-43,-10,49}; Ruled Surface(85) = {84};
Line Loop(86) = {14,-52,-12,50}; Ruled Surface(87) = {86};
Line Loop(88) = {16,-53,-14,51}; Ruled Surface(89) = {88};
Line Loop(90) = {-30,25,35}; Ruled Surface(91) = {90};
Line Loop(92) = {-40,39,38}; Ruled Surface(93) = {92};
Line Loop(94) = {37,-38,-36,35}; Ruled Surface(95) = {94};
Line Loop(96) = {-48,-38,44,17}; Ruled Surface(97) = {96};
Line Loop(98) = {18,-49,-17,45}; Ruled Surface(99) = {98};
Line Loop(100) = {19,-50,-18,46}; Ruled Surface(101) = {100};
Line Loop(102) = {20,-51,-19,47}; Ruled Surface(103) = {102};
Line Loop(104) = {-2,17,10}; Ruled Surface(105) = {104};
Line Loop(106) = {-9,-21,1,17}; Ruled Surface(107) = {106};
Line Loop(108) = {-4,18,12}; Ruled Surface(109) = {108};
Line Loop(110) = {-11,-22,3,18}; Ruled Surface(111) = {110};
Line Loop(112) = {-13,-23,5,19}; Ruled Surface(113) = {112};
Line Loop(114) = {-6,19,14}; Ruled Surface(115) = {114};
Line Loop(116) = {-15,-24,7,20}; Ruled Surface(117) = {116};
Line Loop(118) = {-8,20,16}; Ruled Surface(119) = {118};
Line Loop(120) = {-31,-35,26,21}; Ruled Surface(121) = {120};
Line Loop(122) = {32,-22,-27,21}; Ruled Surface(123) = {122};
Line Loop(124) = {33,-23,-28,22}; Ruled Surface(125) = {124};
Line Loop(126) = {34,-24,-29,23}; Ruled Surface(127) = {126};
Surface Loop(128) = {93,-73,-55,95,-91}; Volume(129) = {128}; <I><FONT COLOR="#B22222">// int
</FONT></I>Surface Loop(130) = {107,-75,-97,95,57,121}; Volume(131) = {130}; <I><FONT COLOR="#B22222">// int b
</FONT></I>Surface Loop(132) = {105,-65,-97,-83,-93}; Volume(133) = {132}; <I><FONT COLOR="#B22222">// int h
</FONT></I>Surface Loop(134) = {99,-111,77,123,59,107}; Volume(135) = {134}; <I><FONT COLOR="#B22222">// shell b
</FONT></I>Surface Loop(136) = {99,-109,67,105,85}; Volume(137) = {136}; <I><FONT COLOR="#B22222">// shell h
</FONT></I>Surface Loop(138) = {113,79,-101,-111,-125,-61}; Volume(139) = {138}; <I><FONT COLOR="#B22222">// ext b
</FONT></I>Surface Loop(140) = {115,-69,-101,-87,-109}; Volume(141) = {140}; <I><FONT COLOR="#B22222">// ext h
</FONT></I>Surface Loop(142) = {103,-117,-81,113,127,63}; Volume(143) = {142}; <I><FONT COLOR="#B22222">// inf b
</FONT></I>Surface Loop(144) = {89,-119,71,103,115}; Volume(145) = {144}; <I><FONT COLOR="#B22222">// inf h
</FONT></I>
<I><FONT COLOR="#B22222">// Transfinite line commands explicitly specify the number of points
</FONT></I><I><FONT COLOR="#B22222">// and their distribution. A minus sign in the argument list of the
</FONT></I><I><FONT COLOR="#B22222">// transfinite command will produce the reversed mesh.
</FONT></I>
Transfinite Line{35,21,22,23,24,38,17,18,19,20} = nbpt_phi ;
Transfinite Line{31,26,48,44,42} = nbpt_int Using Progression 0.95;
Transfinite Line{41,37,36,9,11,1,3,13,5,15,7} = nbpt_arc1 ;
Transfinite Line{30,25,40,39,10,2,12,4,14,6,16,8} = nbpt_arc2 ;
Transfinite Line{32,27,49,45,43} = nbpt_shell ;
Transfinite Line{33,28,46,50,52} = nbpt_far Using Progression 1.05 ;
Transfinite Line{34,29,51,47,53} = nbpt_inf Using Progression 0.01;
<I><FONT COLOR="#B22222">// *All* 2D and 3D transfinite entities are defined in respect to
</FONT></I><I><FONT COLOR="#B22222">// points. The ordering of the points defines the ordering of the mesh
</FONT></I><I><FONT COLOR="#B22222">// elements.
</FONT></I>
Transfinite Surface{55} = {1,14,16,18};
Transfinite Surface{57} = {14,2,19,16};
Transfinite Surface{59} = {2,3,21,19};
Transfinite Surface{61} = {3,4,23,21};
Transfinite Surface{63} = {4,5,25,23};
Transfinite Surface{73} = {1,15,17,18};
Transfinite Surface{75} = {15,10,20,17};
Transfinite Surface{77} = {10,11,22,20};
Transfinite Surface{79} = {11,12,24,22};
Transfinite Surface{81} = {12,13,26,24};
Transfinite Surface{65} = {18,16,19,6};
Transfinite Surface{67} = {6,19,21,7};
Transfinite Surface{69} = {7,21,23,8};
Transfinite Surface{71} = {8,23,25,9};
Transfinite Surface{83} = {17,18,6,20};
Transfinite Surface{85} = {20,6,7,22};
Transfinite Surface{87} = {22,7,8,24};
Transfinite Surface{89} = {24,8,9,26};
Transfinite Surface{91} = {1,14,15};
Transfinite Surface{95} = {15,14,16,17};
Transfinite Surface{93} = {18,16,17};
Transfinite Surface{121} = {15,14,2,10};
Transfinite Surface{97} = {17,16,19,20};
Transfinite Surface{123} = {10,2,3,11};
Transfinite Surface{99} = {20,19,21,22};
Transfinite Surface{107} = {10,2,19,20};
Transfinite Surface{105} = {6,20,19};
Transfinite Surface{109} = {7,22,21};
Transfinite Surface{111} = {11,3,21,22};
Transfinite Surface{101} = {22,21,23,24};
Transfinite Surface{125} = {11,3,4,12};
Transfinite Surface{115} = {8,24,23};
Transfinite Surface{113} = {24,12,4,23};
Transfinite Surface{127} = {12,13,5,4};
Transfinite Surface{103} = {24,23,25,26};
Transfinite Surface{119} = {9,26,25};
Transfinite Surface{117} = {13,5,25,26};
<I><FONT COLOR="#B22222">// As with Extruded meshes, the Recombine command tells Gmsh to
</FONT></I><I><FONT COLOR="#B22222">// recombine the simplices into quadrangles, prisms or hexahedra when
</FONT></I><I><FONT COLOR="#B22222">// possible. A colon in a list acts as in the 'For' loop: all surfaces
</FONT></I><I><FONT COLOR="#B22222">// having numbers between 55 and 127 are considered.
</FONT></I>
Recombine Surface {55:127};
<I><FONT COLOR="#B22222">// *All* 2D and 3D transfinite entities are defined in respect to
</FONT></I><I><FONT COLOR="#B22222">// points. The ordering of the points defines the ordering of the mesh
</FONT></I><I><FONT COLOR="#B22222">// elements.
</FONT></I>
Transfinite Volume{129} = {1,14,15,18,16,17};
Transfinite Volume{131} = {17,16,14,15,20,19,2,10};
Transfinite Volume{133} = {18,17,16,6,20,19};
Transfinite Volume{135} = {10,2,19,20,11,3,21,22};
Transfinite Volume{137} = {6,20,19,7,22,21};
Transfinite Volume{139} = {11,3,4,12,22,21,23,24};
Transfinite Volume{141} = {7,22,21,8,24,23};
Transfinite Volume{143} = {12,4,5,13,24,23,25,26};
Transfinite Volume{145} = {8,24,23,9,26,25};
VolInt = 1000 ;
SurfIntPhi0 = 1001 ;
SurfIntPhi1 = 1002 ;
SurfIntZ0 = 1003 ;
VolShell = 2000 ;
SurfShellInt = 2001 ;
SurfShellExt = 2002 ;
SurfShellPhi0 = 2003 ;
SurfShellPhi1 = 2004 ;
SurfShellZ0 = 2005 ;
LineShellIntPhi0 = 2006 ;
LineShellIntPhi1 = 2007 ;
LineShellIntZ0 = 2008 ;
PointShellInt = 2009 ;
VolExt = 3000 ;
VolInf = 3001 ;
SurfInf = 3002 ;
SurfExtInfPhi0 = 3003 ;
SurfExtInfPhi1 = 3004 ;
SurfExtInfZ0 = 3005 ;
SurfInfRight = 3006 ;
SurfInfTop = 3007 ;
Physical Volume (VolInt) = {129,131,133} ;
Physical Surface (SurfIntPhi0) = {55,57,65} ;
Physical Surface (SurfIntPhi1) = {73,75,83} ;
Physical Surface (SurfIntZ0) = {91,121} ;
Physical Volume (VolShell) = {135,137} ;
Physical Surface (SurfShellInt) = {105,107} ;
Physical Surface (SurfShellExt) = {109,111} ;
Physical Surface (SurfShellPhi0) = {59,67} ;
Physical Surface (SurfShellPhi1) = {77,85} ;
Physical Surface (SurfShellZ0) = {123} ;
Physical Line (LineShellIntPhi0) = {1,2} ;
Physical Line (LineShellIntPhi1) = {9,10} ;
Physical Line (LineShellIntZ0) = 21 ;
Physical Point (PointShellInt) = 6 ;
Physical Volume (VolExt) = {139,141} ;
Physical Volume (VolInf) = {143,145} ;
Physical Surface (SurfExtInfPhi0) = {61,63,69,71} ;
Physical Surface (SurfExtInfPhi1) = {79,87,81,89} ;
Physical Surface (SurfExtInfZ0) = {125,127} ;
Physical Surface (SurfInfRight) = {117} ;
Physical Surface (SurfInfTop) = {119} ;
</PRE>
<HR>
<A NAME="file8">
<H1>t7.geo 8/9</H1>
[<A HREF="#top">top</A>][<A HREF="#file7">prev</A>][<A HREF="#file9">next</A>]
<PRE>
<I><FONT COLOR="#B22222">/*********************************************************************
*
* Gmsh tutorial 7
*
* Anisotropic meshes, Attractors
*
*********************************************************************/</FONT></I>
<I><FONT COLOR="#B22222">// The new anisotropic 2D mesh generator can be selected with:
</FONT></I>
Mesh.Algorithm = 2 ;
<I><FONT COLOR="#B22222">// One can force a 4 step Laplacian smoothing of the mesh with:
</FONT></I>
Mesh.Smoothing = 4 ;
lc = .1;
Point(1) = {0.0,0.0,0,lc};
Point(2) = {1,0.0,0,lc};
Point(3) = {1,1,0,lc};
Point(4) = {0,1,0,lc};
Line(1) = {3,2};
Line(2) = {2,1};
Line(3) = {1,4};
Line(4) = {4,3};
Line Loop(5) = {1,2,3,4};
Plane Surface(6) = {5};
Point(5) = {0.1,0.2,0,lc};
Point(11) = {0.5,0.5,-1,lc};
Point(22) = {0.6,0.6,1,lc};
Line(5) = {11,22};
<I><FONT COLOR="#B22222">// Anisotropic attractors can be defined on points and lines:
</FONT></I>
Attractor Line{5} = {1, 0.1, 7};
Attractor Point{5} = {0.1, 0.5, 3};
</PRE>
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<H1>t8.geo 9/9</H1>
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<PRE>
<I><FONT COLOR="#B22222">/*********************************************************************
*
* Gmsh tutorial 8
*
* Post-Processing, Scripting, Animations, Options
*
*********************************************************************/</FONT></I>
<I><FONT COLOR="#B22222">// The first example is included, as well as two post-processing maps
</FONT></I><I><FONT COLOR="#B22222">// (for the format of the post-processing maps, see the FORMATS file):
</FONT></I>
Include &quot;t1.geo&quot; ;
Include &quot;view1.pos&quot; ;
Include &quot;view1.pos&quot; ;
<I><FONT COLOR="#B22222">// Some general options are set (all the options specified
</FONT></I><I><FONT COLOR="#B22222">// interactively can be directly specified in the ascii input
</FONT></I><I><FONT COLOR="#B22222">// files. The current options can be saved into a file by selecting
</FONT></I><I><FONT COLOR="#B22222">// 'File-&gt;Save_Options_as')...
</FONT></I>
General.Trackball = 0 ;
General.Rotation0 = 0 ;
General.Rotation1 = 0 ;
General.Rotation2 = 0 ;
General.Color.Background = White ;
General.Color.Text = Black ;
General.Orthographic = 0 ;
General.Axes = 0 ;
<I><FONT COLOR="#B22222">// ...as well as some options for each post-processing view...
</FONT></I>
PostProcessing.View[0].Name = &quot;This is a very stupid demonstration...&quot; ;
PostProcessing.View[0].IntervalsType = 2 ;
PostProcessing.View[0].Offset = {0,0,0.05} ;
PostProcessing.View[0].Raise = {0,0,0} ;
PostProcessing.View[0].Light = 1 ;
PostProcessing.View[1].Name = &quot;...of Gmsh's scripting capabilities&quot; ;
PostProcessing.View[1].IntervalsType = 1 ;
PostProcessing.View[1].Color = { Green, Blue } ;
PostProcessing.View[1].NbIso = 10 ;
<I><FONT COLOR="#B22222">// ...and loop from 1 to 255 with a step of 1 is performed (to use a
</FONT></I><I><FONT COLOR="#B22222">// step different from 1, just add a third argument in the list,
</FONT></I><I><FONT COLOR="#B22222">// e.g. 'For num In {0.5:1.5:0.1}' increments num from 0.5 to 1.5 with
</FONT></I><I><FONT COLOR="#B22222">// a step of 0.1):
</FONT></I>
t = 0 ;
For num In {1:255}
PostProcessing.View[0].TimeStep = t ;
PostProcessing.View[1].TimeStep = t ;
t = (PostProcessing.View[0].TimeStep &lt; PostProcessing.View[0].NbTimeStep-1) ? t+1 : 0 ;
PostProcessing.View[0].Raise += {0,0,0.001*t} ;
<I><FONT COLOR="#B22222">// It is possible to nest loops:
</FONT></I>
For num2 In {1:10}
General.Rotation0 += 10 ;
General.Rotation1 = General.Rotation0 / 3 ;
General.Rotation2 += 0.1 ;
Sleep 0.01; <I><FONT COLOR="#B22222">// sleep for 0.01 second
</FONT></I> Draw; <I><FONT COLOR="#B22222">// draw the scene
</FONT></I>
EndFor
<I><FONT COLOR="#B22222">// It is also possible make tests
</FONT></I>
If (!(num % 20))
Print Sprintf(&quot;t8-%g.gif&quot;, num); <I><FONT COLOR="#B22222">// print the scene in a gif file
</FONT></I>
EndIf
EndFor
<I><FONT COLOR="#B22222">// Here is the list of available scripting commands:
</FONT></I><I><FONT COLOR="#B22222">//
</FONT></I><I><FONT COLOR="#B22222">// Merge string; (to merge a file)
</FONT></I><I><FONT COLOR="#B22222">// Draw; (to draw the scene)
</FONT></I><I><FONT COLOR="#B22222">// Mesh int; (to perform the mesh generation; 'int' = 0, 1, 2 or 3)
</FONT></I><I><FONT COLOR="#B22222">// Save string; (to save the mesh)
</FONT></I><I><FONT COLOR="#B22222">// Print string; (to print the graphic window)
</FONT></I><I><FONT COLOR="#B22222">// Sleep expr; (to sleep during expr seconds)
</FONT></I>
</PRE>
<HR>
<ADDRESS>Generated by <A HREF="http://www.iki.fi/~mtr/genscript/">GNU enscript 1.6.1</A>.</ADDRESS>
</BODY>
</HTML>
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/*
Gmsh demo file (C) 2000 C. Geuzaine, J.-F. Remacle
Vector map on points
All important comments are marked with "README"
*/
View "a vector map" {
VP(1e-06,1e-06,0){0,0,122.26654,0,0,122.45426,0,0,122.82769,0,0,123.38417,0,0,124.20759};
VP(1e-06,0.010000933,0){0,0,121.95116,0,0,120.60823,0,0,117.93735,0,0,113.96957,0,0,108.76298};
VP(1e-06,0.020000867,0){0,0,121.76276,0,0,116.4134,0,0,105.95451,0,0,90.855892,0,0,71.867727};
VP(1e-06,0.0300008,0){0,0,120.79673,0,0,108.95219,0,0,86.42978,0,0,55.448276,0,0,19.067191};
VP(1e-06,0.040000733,0){0,0,119.6291,0,0,98.888056,0,0,61.048627,0,0,12.75009,0,0,-37.476665};
VP(1e-06,0.050000667,0){0,0,118.01437,0,0,86.430423,0,0,31.638139,0,0,-31.806471,0,0,-86.912688};
VP(1e-06,0.0600006,0){0,0,116.49231,0,0,71.947632,0,0,0.0082419918,0,0,-71.673337,0,0,-115.66034};
VP(1e-06,0.070000533,0){0,0,114.18838,0,0,55.530819,0,0,-31.604761,0,0,-102.40655,0,0,-120.49233};
VP(1e-06,0.080000467,0){0,0,111.73884,0,0,37.77248,0,0,-61.122995,0,0,-119.44024,0,0,-98.690267};
VP(1e-06,0.0900004,0){0,0,109.02764,0,0,19.140014,0,0,-86.347807,0,0,-120.39736,0,0,-55.210037};
VP(1e-06,0.10000033,0){0,0,105.89652,0,0,-0.0065380069,0,0,-106.09757,0,0,-106.26766,0,0,0.10907541};
VP(1e-06,0.11000027,0){0,0,102.73901,0,0,-19.150688,0,0,-118.07603,0,0,-76.769682,0,0,55.222067};
VP(1e-06,0.1200002,0){0,0,98.952931,0,0,-37.767065,0,0,-122.22482,0,0,-37.780096,0,0,98.736188};
VP(1e-06,0.13000013,0){0,0,95.122755,0,0,-55.584271,0,0,-118.15756,0,0,6.4473841,0,0,120.69955};
VP(1e-06,0.14000007,0){0,0,90.852382,0,0,-71.806307,0,0,-105.6782,0,0,49.526055,0,0,115.53689};
VP(1e-06,0.15,0){0,0,86.563988,0,0,-86.610866,0,0,-86.776431,0,0,86.913071,0,0,87.233235};
VP(1e-06,0.15999993,0){0,0,81.861739,0,0,-98.925044,0,0,-61.054707,0,0,111.37293,0,0,37.582303};
VP(1e-06,0.16999987,0){0,0,76.880554,0,0,-108.83108,0,0,-31.635178,0,0,121.95453,0,0,-19.051124};
VP(1e-06,0.1799998,0){0,0,71.93248,0,0,-116.3445,0,0,0.0051803424,0,0,116.09977,0,0,-71.614187};
VP(1e-06,0.18999973,0){0,0,66.655881,0,0,-120.84615,0,0,31.684673,0,0,94.843218,0,0,-108.67685};
VP(1e-06,0.19999967,0){0,0,61.126812,0,0,-122.30122,0,0,61.195533,0,0,61.281721,0,0,-122.75882};
VP(1e-06,0.2099996,0){0,0,55.454746,0,0,-120.62189,0,0,86.3266,0,0,19.057229,0,0,-108.50779};
VP(1e-06,0.21999953,0){0,0,49.765538,0,0,-116.57634,0,0,106.4713,0,0,-25.419128,0,0,-73.667176};
VP(1e-06,0.22999947,0){0,0,43.853336,0,0,-109.05425,0,0,118.28173,0,0,-66.779805,0,0,-19.027558};
VP(1e-06,0.2399994,0){0,0,37.808977,0,0,-98.930918,0,0,122.15279,0,0,-98.667764,0,0,37.647079};
VP(1e-06,0.24999933,0){0,0,31.614973,0,0,-86.420956,0,0,118.17907,0,0,-118.35504,0,0,86.812866};
VP(1e-06,0.25999927,0){0,0,25.446319,0,0,-71.890336,0,0,105.77788,0,0,-121.22558,0,0,115.63648};
VP(1e-06,0.2699992,0){0,0,19.147235,0,0,-55.558139,0,0,86.505401,0,0,-108.94986,0,0,120.6783};
VP(1e-06,0.27999913,0){0,0,12.792336,0,0,-37.809277,0,0,61.14898,0,0,-81.777482,0,0,98.845675};
VP(1e-06,0.28999907,0){0,0,6.3850865,0,0,-19.083517,0,0,31.567694,0,0,-43.697424,0,0,55.414892};
VP(1e-06,0.299999,0){0,0,0.0095385519,0,0,-0.03787688,0,0,0.093923584,0,0,-0.19582795,0,0,0.49155762};
VP(0.0100008,1e-06,0){0,0,1199420,0,0,1199413.7,0,0,1199397.9,0,0,1199378.4,0,0,1199403.4};
VP(0.0100008,0.010000933,0){0,0,1197824.3,0,0,1184734.2,0,0,1158699.2,0,0,1120019.6,0,0,1069149};
VP(0.0100008,0.020000867,0){0,0,1192912,0,0,1140722,0,0,1038620.8,0,0,891080.74,0,0,704676.89};
VP(0.0100008,0.0300008,0){0,0,1184493.3,0,0,1068498.7,0,0,847865.42,0,0,544204.94,0,0,187350.11};
VP(0.0100008,0.040000733,0){0,0,1173023.5,0,0,970311.11,0,0,599870.71,0,0,125642.73,0,0,-370468.19};
VP(0.0100008,0.050000667,0){0,0,1158406,0,0,848028.9,0,0,310455.27,0,0,-310247.58,0,0,-847690.45};
VP(0.0100008,0.0600006,0){0,0,1141160.6,0,0,705256.28,0,0,-99.915745,0,0,-705541.47,0,0,-1141600.4};
VP(0.0100008,0.070000533,0){0,0,1119507.8,0,0,544453.75,0,0,-310310.46,0,0,-1005770.5,0,0,-1184662.4};
VP(0.0100008,0.080000467,0){0,0,1095510.9,0,0,370556.44,0,0,-599794.43,0,0,-1173524.1,0,0,-970723.46};
VP(0.0100008,0.0900004,0){0,0,1068561,0,0,187606.05,0,0,-848133.51,0,0,-1184824.1,0,0,-544820.04};
VP(0.0100008,0.10000033,0){0,0,1038622.4,0,0,59.994402,0,0,-1038526.3,0,0,-1038609.6,0,0,-114.10057};
VP(0.0100008,0.11000027,0){0,0,1006283.9,0,0,-187756.34,0,0,-1159127,0,0,-755186.39,0,0,544970.98};
VP(0.0100008,0.1200002,0){0,0,970146.83,0,0,-370533.83,0,0,-1199206,0,0,-370700.66,0,0,970167.63};
VP(0.0100008,0.13000013,0){0,0,932049.4,0,0,-544524.54,0,0,-1158572.3,0,0,62773.626,0,0,1184972.7};
VP(0.0100008,0.14000007,0){0,0,891093.35,0,0,-704750.35,0,0,-1038220.5,0,0,487590.9,0,0,1139583.1};
VP(0.0100008,0.15,0){0,0,848043.94,0,0,-848162.19,0,0,-847974.76,0,0,848328.9,0,0,847991.67};
VP(0.0100008,0.15999993,0){0,0,802591.51,0,0,-970520.77,0,0,-600078.94,0,0,1096713.1,0,0,371678.95};
VP(0.0100008,0.16999987,0){0,0,754801.61,0,0,-1068627.9,0,0,-310284.17,0,0,1197257.1,0,0,-187594.97};
VP(0.0100008,0.1799998,0){0,0,704861.79,0,0,-1140475,0,0,-9.7592105,0,0,1140481.7,0,0,-704943.27};
VP(0.0100008,0.18999973,0){0,0,653101.17,0,0,-1184459.4,0,0,310527.61,0,0,931931.51,0,0,-1068734.2};
VP(0.0100008,0.19999967,0){0,0,599592.55,0,0,-1199104.4,0,0,599503.9,0,0,599267.34,0,0,-1198494.7};
VP(0.0100008,0.2099996,0){0,0,544384.89,0,0,-1184212.9,0,0,847613.27,0,0,187425.67,0,0,-1067044.3};
VP(0.0100008,0.21999953,0){0,0,487650.97,0,0,-1140248.2,0,0,1038317,0,0,-249363.16,0,0,-704669.35};
VP(0.0100008,0.22999947,0){0,0,429775.49,0,0,-1068467.4,0,0,1158136.7,0,0,-652849.84,0,0,-187529.03};
VP(0.0100008,0.2399994,0){0,0,370742.76,0,0,-970651.21,0,0,1199863,0,0,-970733.39,0,0,370606.77};
VP(0.0100008,0.24999933,0){0,0,310389.76,0,0,-847996.97,0,0,1158383,0,0,-1158385.8,0,0,848238.2};
VP(0.0100008,0.25999927,0){0,0,249381.35,0,0,-705070.58,0,0,1038980.9,0,0,-1193427.1,0,0,1141624.8};
VP(0.0100008,0.2699992,0){0,0,187667.19,0,0,-544609.42,0,0,848186.21,0,0,-1068663.7,0,0,1184526.1};
VP(0.0100008,0.27999913,0){0,0,125343.27,0,0,-370542.57,0,0,599521.08,0,0,-802247.4,0,0,969885.37};
VP(0.0100008,0.28999907,0){0,0,62767.644,0,0,-187609.66,0,0,310381.87,0,0,-429732.38,0,0,544296.89};
VP(0.0100008,0.299999,0){0,0,6.2613191,0,0,-18.79568,0,0,31.365281,0,0,-43.993284,0,0,56.787457};
VP(0.0200006,1e-06,0){0,0,2280709.8,0,0,2280750.8,0,0,2280828.8,0,0,2280959.2,0,0,2281129.6};
VP(0.0200006,0.010000933,0){0,0,2278084.8,0,0,2253198.7,0,0,2203663.2,0,0,2129974,0,0,2032919.9};
VP(0.0200006,0.020000867,0){0,0,2268407.5,0,0,2169311.8,0,0,1975439,0,0,1695261.3,0,0,1341077.3};
VP(0.0200006,0.0300008,0){0,0,2252723.5,0,0,2032071.2,0,0,1612411.9,0,0,1034928.7,0,0,356247.55};
VP(0.0200006,0.040000733,0){0,0,2231113.2,0,0,1845403.9,0,0,1140636.4,0,0,238607.96,0,0,-704725};
VP(0.0200006,0.050000667,0){0,0,2203326.5,0,0,1612958.8,0,0,590304.13,0,0,-590735.99,0,0,-1613764.5};
VP(0.0200006,0.0600006,0){0,0,2169459.4,0,0,1340689.5,0,0,-253.26048,0,0,-1341167.5,0,0,-2169964.1};
VP(0.0200006,0.070000533,0){0,0,2129890.6,0,0,1035882.8,0,0,-590292.11,0,0,-1913508.9,0,0,-2254296.8};
VP(0.0200006,0.080000467,0){0,0,2083910,0,0,704847.45,0,0,-1140765.6,0,0,-2231594.2,0,0,-1845800.6};
VP(0.0200006,0.0900004,0){0,0,2032367.2,0,0,356748.59,0,0,-1612959.6,0,0,-2252643.6,0,0,-1034806.6};
VP(0.0200006,0.10000033,0){0,0,1975611.2,0,0,57.943352,0,0,-1975420.4,0,0,-1975504.9,0,0,-426.45724};
VP(0.0200006,0.11000027,0){0,0,1913315.4,0,0,-356703.47,0,0,-2203743.9,0,0,-1436328.1,0,0,1035508.3};
VP(0.0200006,0.1200002,0){0,0,1845574.3,0,0,-704966.07,0,0,-2281489.6,0,0,-705279.75,0,0,1845900.6};
VP(0.0200006,0.13000013,0){0,0,1772685.9,0,0,-1035509.4,0,0,-2203500.9,0,0,119407.19,0,0,2253641.5};
VP(0.0200006,0.14000007,0){0,0,1695112.7,0,0,-1340923.1,0,0,-1975160.6,0,0,928234.38,0,0,2168753.8};
VP(0.0200006,0.15,0){0,0,1612735.8,0,0,-1612718.7,0,0,-1612310.8,0,0,1612112.4,0,0,1611635.4};
VP(0.0200006,0.15999993,0){0,0,1526063.3,0,0,-1845120.2,0,0,-1140155.4,0,0,2083304.9,0,0,704343.18};
VP(0.0200006,0.16999987,0){0,0,1435361,0,0,-2032273.5,0,0,-590286.74,0,0,2277973.9,0,0,-357113.77};
VP(0.0200006,0.1799998,0){0,0,1340603.7,0,0,-2169104.8,0,0,-187.59264,0,0,2169344.4,0,0,-1340174.3};
VP(0.0200006,0.18999973,0){0,0,1242326.7,0,0,-2253004.8,0,0,590488.21,0,0,1772854.2,0,0,-2032869.4};
VP(0.0200006,0.19999967,0){0,0,1140484.2,0,0,-2281080.6,0,0,1140863.6,0,0,1140070,0,0,-2281239};
VP(0.0200006,0.2099996,0){0,0,1035459.2,0,0,-2252611.6,0,0,1612490.4,0,0,356944.25,0,0,-2031783};
VP(0.0200006,0.21999953,0){0,0,927776.85,0,0,-2169354.9,0,0,1975370.5,0,0,-474298.34,0,0,-1340371.5};
VP(0.0200006,0.22999947,0){0,0,817407.12,0,0,-2032357.3,0,0,2203356.6,0,0,-1242461.5,0,0,-356900.43};
VP(0.0200006,0.2399994,0){0,0,704976.55,0,0,-1845571.3,0,0,2281095,0,0,-1845366.1,0,0,705164.78};
VP(0.0200006,0.24999933,0){0,0,590364.42,0,0,-1612953.4,0,0,2203467,0,0,-2203634.2,0,0,1613249.1};
VP(0.0200006,0.25999927,0){0,0,474194.23,0,0,-1340559.8,0,0,1975062.6,0,0,-2267979.5,0,0,2168670.2};
VP(0.0200006,0.2699992,0){0,0,356872.34,0,0,-1035606,0,0,1612764.1,0,0,-2031781.9,0,0,2251747.9};
VP(0.0200006,0.27999913,0){0,0,238392.68,0,0,-704748.96,0,0,1140275,0,0,-1525901.8,0,0,1844805.9};
VP(0.0200006,0.28999907,0){0,0,119394.11,0,0,-356902.82,0,0,590587.11,0,0,-817934.15,0,0,1036489.1};
VP(0.0200006,0.299999,0){0,0,11.932618,0,0,-35.829397,0,0,59.820438,0,0,-83.966334,0,0,108.36963};
VP(0.0300004,1e-06,0){0,0,3139675.3,0,0,3139674.2,0,0,3139668.3,0,0,3139681.7,0,0,3139723.8};
VP(0.0300004,0.010000933,0){0,0,3135081.7,0,0,3100734,0,0,3032371.9,0,0,2930692.9,0,0,2796805.3};
VP(0.0300004,0.020000867,0){0,0,3122126.6,0,0,2985595.8,0,0,2718520.5,0,0,2332639.4,0,0,1845013.2};
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