From 6a9a12dc73040942810536d7992edef5063193e8 Mon Sep 17 00:00:00 2001
From: Christophe Geuzaine <cgeuzaine@ulg.ac.be>
Date: Wed, 13 Dec 2000 10:12:43 +0000
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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 1.4 2000-12-12 16:37:18 geuzaine Exp $
-
-Here are the examples in the Gmsh tutorial. These examples are
-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.
-
-</PRE>
-<HR>
-<A NAME="file2">
-<H1>t1.geo 2/9</H1>
-[<A HREF="#top">top</A>][<A HREF="#file1">prev</A>][<A HREF="#file3">next</A>]
-<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">// "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."
-</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>
-[<A HREF="#top">top</A>][<A HREF="#file2">prev</A>][<A HREF="#file4">next</A>]
-<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 "t1.geo" ;
-
-<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->Print->Geo' menu or by typing
-</FONT></I><I><FONT COLOR="#B22222">//
-</FONT></I><I><FONT COLOR="#B22222">// > 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>
-[<A HREF="#top">top</A>][<A HREF="#file3">prev</A>][<A HREF="#file5">next</A>]
-<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 "t1.geo" ;
-
-<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->Save_Options_as' menu.
-</FONT></I>
-</PRE>
-<HR>
-<A NAME="file5">
-<H1>t4.geo 5/9</H1>
-[<A HREF="#top">top</A>][<A HREF="#file4">prev</A>][<A HREF="#file6">next</A>]
-<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">// '<'
-</FONT></I><I><FONT COLOR="#B22222">// '>'
-</FONT></I><I><FONT COLOR="#B22222">// '<='
-</FONT></I><I><FONT COLOR="#B22222">// '>='
-</FONT></I><I><FONT COLOR="#B22222">// '=='
-</FONT></I><I><FONT COLOR="#B22222">// '!='
-</FONT></I><I><FONT COLOR="#B22222">// '&&' (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, Arrays of variables, 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">// > 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">// > 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};
-
-<I><FONT COLOR="#B22222">// Arrays of variables can be manipulated in the same way as classical
-</FONT></I><I><FONT COLOR="#B22222">// variables. Warning: accessing an uninitialized element in an array
-</FONT></I><I><FONT COLOR="#B22222">// will produce an unpredictable result.
-</FONT></I>
- theloops[t] = newreg ;
-
- Surface Loop(theloops[t]) = {l8+1, l5+1, l1+1, l2+1, -(l3+1), -(l7+1), l6+1, l4+1};
-
- thehole = newreg ;
- Volume(thehole) = theloops[t] ;
-
-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, in a way similar to the 'printf' C function:
-</FONT></I>
- Printf("The cheese hole %g (center = {%g,%g,%g}, radius = %g) has number %g!",
- t, x, y, z, r, thehole) ;
-
-<I><FONT COLOR="#B22222">// Note: All Gmsh variables are treated internally as double precision
-</FONT></I><I><FONT COLOR="#B22222">// numbers. The format string should thus only contain valid double
-</FONT></I><I><FONT COLOR="#B22222">// precision number format specifiers (see the C or C++ language
-</FONT></I><I><FONT COLOR="#B22222">// reference for more details).
-</FONT></I>
-EndFor
-
-<I><FONT COLOR="#B22222">// This is the surface loop for the exterior surface of the cube:
-</FONT></I>
-theloops[0] = newreg ;
-
-Surface Loop(theloops[0]) = {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><I><FONT COLOR="#B22222">// To reference an array of variables, its identifier is followed by
-</FONT></I><I><FONT COLOR="#B22222">// '[]':
-</FONT></I>
-Volume(186) = {theloops[]} ;
-
-<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>
-[<A HREF="#top">top</A>][<A HREF="#file6">prev</A>][<A HREF="#file8">next</A>]
-<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>
-<HR>
-<A NAME="file9">
-<H1>t8.geo 9/9</H1>
-[<A HREF="#top">top</A>][<A HREF="#file8">prev</A>][next]
-<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 "t1.geo" ;
-Include "view1.pos" ;
-Include "view1.pos" ;
-
-<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->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 = "This is a very stupid demonstration..." ;
-PostProcessing.View[0].IntervalsType = 2 ;
-PostProcessing.View[0].Offset2 = 0.05 ;
-PostProcessing.View[0].Raise2 = 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 ;
-
-<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 < PostProcessing.View[0].NbTimeStep-1) ? t+1 : 0 ;
-
- PostProcessing.View[0].Raise2 += 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))
-
-<I><FONT COLOR="#B22222">// The Sprintf function permits to create complex strings using
-</FONT></I><I><FONT COLOR="#B22222">// variables (since all Gmsh variables are treated internally as
-</FONT></I><I><FONT COLOR="#B22222">// double precision numbers, the format should only contain valid
-</FONT></I><I><FONT COLOR="#B22222">// double precision number format specifiers):
-</FONT></I>
- Print Sprintf("t8-%g.gif", 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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