diff --git a/doc/FORMATS b/doc/FORMATS
index 369094f8fe5825223b828100e77f796d636c2b34..89ee3b762f30327c92f051725b0391529923e421 100644
--- a/doc/FORMATS
+++ b/doc/FORMATS
@@ -1,11 +1,12 @@
-$Id: FORMATS,v 1.7 2000-12-27 17:25:52 geuzaine Exp $
+$Id: FORMATS,v 1.8 2001-03-01 08:04:15 geuzaine Exp $
 
 This document describes the mesh and post-processing file formats for
 Gmsh, version >= 1.0. 
 
 (This document deals only with the import/export interfaces for
-Gmsh. The language driving Gmsh's behaviour for defining geometries,
-options, scripts, etc. is explained step by step in the tutorials.)
+Gmsh. The language driving the behaviour of Gmsh for defining
+geometries, options, scripts, etc. is explained step by step in the
+tutorials.)
 
 
 Gmsh Mesh File Format
@@ -79,9 +80,9 @@ pairs).
     $endView
 
 version-number is a floating point number giving the version of
-Gmsh to which the file is destined (e.g. 1.0).
+Gmsh for which the file is destined (e.g. 1.0).
 
-file-type is an integer equal to 0 in for the ascii file format.
+file-type is an integer equal to 0 in the ascii file format.
 
 data-size is an integer equal to the size of the floating point
 numbers used in the file (usually, data-size == sizeof(double)).
@@ -99,7 +100,7 @@ evolution was saved.
 
 scalar-point-value, vector-point-value, etc. are lists of double
 precision numbers giving the node coordinates and the values
-associated to the nodes of the nb-scalar-points, nb-vector-points,
+associated with the nodes of the nb-scalar-points, nb-vector-points,
 etc. for each time-step-value. For example, vector-triangle-value is
 defined as
 
@@ -126,11 +127,11 @@ except that:
 2) all lists of floating point numbers are written in binary format
 
 3) there is an additional integer, of value 1, written before
-   time-step-values. This integer serves to detect if the computer on
-   which the binary file was written and the computer on which the
-   file is read are of the same type (little or big endian).
+   time-step-values. This integer is used for detecting if the
+   computer on which the binary file was written and the computer on
+   which the file is read are of the same type (little or big endian).
 
-Here is an pseudo C code to write the beginning of a post-processing
+Here is a pseudo C code to write the beginning of a post-processing
 file in binary format:
 
 int one = 1;
@@ -154,7 +155,7 @@ fprintf(file, "$EndView\n");
 
 In this pseudo-code, all-scalar-point-values is the array of double
 precision numbers containing all the scalar-point-value lists, put one
-at the end of each other in order to form a long array of double. The
+after each other in order to form a long array of doubles. The
 principle is the same for all other kinds of values.
 
 
@@ -163,8 +164,8 @@ Gmsh Parsed Post-Processing Format
 
 For testing purposes (or with very small data sets, e.g. in the
 tutorials), there is an additional post-processing format which is
-parsed by the same grammar analyser as the geometry. You can thus for
-example embed small post-processing views into your geometrical
+parsed by the same grammar analyser as the geometry. You can thus, for
+example, embed small post-processing views into your geometrical
 descriptions. The format of the parsed post-processing files is the
 following:
 
diff --git a/tutorial/README b/tutorial/README
index 4547da308f23d529938451d157990e1d9b874aae..7fc9ebfde6f82ee288ba8b556ff5d141ac3072f8 100644
--- a/tutorial/README
+++ b/tutorial/README
@@ -1,4 +1,4 @@
-$Id: README,v 1.7 2001-02-19 21:55:43 geuzaine Exp $
+$Id: README,v 1.8 2001-03-01 08:04:15 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
@@ -9,58 +9,57 @@ t1.geo.
 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
+operations to run Gmsh may vary according to your operating system. In
+the folowing examples, 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 'Mesh' in the module
-menu) 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.
+first tutorial file, select the 'File->Open' menu, and choose 't1.geo'
+in the input field. To perform the mesh generation, go to the mesh
+module (by selecting 'Mesh' in the module menu) 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
 'Help->Shortcuts' 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:
+often more convenient to put the file name on the command line, 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 (you may use any
-text editor for this purpose, e.g. Wordpad on Windows, or Emacs on
-Unix), 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 'Geometry' in the module menu, 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.
+Note: Even if it is often handy to define the variables and the points
+directly in the input files (you may use any text editor for this
+purpose, e.g. Wordpad on Windows, or Emacs on Unix), it is almost
+always more simple 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 'Geometry'
+in the module menu, 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' to finish the
+selection (or 'q' to abort it). 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:
+are performed without any interaction. To mesh the first tutorial in
+non-interactive mode, just type:
 
 > gmsh t1.geo -2
 
@@ -77,10 +76,10 @@ the following line on the command line:
 
 In the Post-Processing module (select 'Post_Processing' in the module
 menu), 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. If you want the modifications made to one view to
-affect also all other views, select the 'Link all views' option in the
+map" and "a vector map". A left mouse click toggles the visibility of
+the selected view. A right mouse click provides access to the view's
+options. If you want the modifications made to one view to affect also
+all the other views, select the 'Link all views' option in the
 'Options->Post-Processing' menu.
 
 Note: all the options specified interactively can also be directly
diff --git a/tutorial/t1.geo b/tutorial/t1.geo
index 5435ed72634f4077da131c7546219f4b963ea64f..238f9943125a049c3b81849ed9d5b80c8ab9f59e 100644
--- a/tutorial/t1.geo
+++ b/tutorial/t1.geo
@@ -19,14 +19,14 @@ 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:
+// 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.
+// constructed from variables. 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:
@@ -43,7 +43,7 @@ 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
+// line is defined by a list of point numbers. For example, line 1
 // starts at point 1 and ends at point 2:
 
 Line(1) = {1,2} ;
@@ -54,8 +54,8 @@ 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.
+// connected lines, a sign being associated with each line (depending
+// on the orientation of the line).
 
 Line Loop(5) = {4,1,-2,3} ;
 
@@ -66,12 +66,12 @@ 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.
+// order to assign region numbers to the various elements in the mesh
+// (the points, the lines and the triangles discretizing points 1 to
+// 4, lines 1 to 4 and 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:
@@ -85,14 +85,13 @@ Physical Point(1) = {1,2} ;
 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. 
+// All the line elements which will be created during the mesh of
+// lines 1, 2 and 4 will be saved in the output file with the region
+// number 10; and all the triangular elements resulting from the
+// discretization of surface 6 will be given 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.
+// description of the mesh and post-processing formats, see the
+// FORMATS file.
diff --git a/tutorial/t2.geo b/tutorial/t2.geo
index eee5024edfbf34c03c89e9366cfd3a9b5c69d71d..1cfc91ac22a1a2a4e4d9813812aeaf4a85a07a2c 100644
--- a/tutorial/t2.geo
+++ b/tutorial/t2.geo
@@ -33,10 +33,10 @@ Translate {-0.05,0,0} { Point{3} ; }
 
 Translate {0,0.1,0} { Duplicata{ Point{3} ; } }
 
-// Translation, rotation and extrusion commands of course not only
+// Of course, translation, rotation and extrusion commands 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':
+// command extrudes 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} } ;
@@ -47,7 +47,7 @@ Plane Surface(11) = {10};
 
 Extrude Surface { 11, {0, 0, h} } ;
 
-// All these geometrical transformations generate automatically new
+// All these geometrical transformations automatically generate new
 // elementary entities. The following commands permit to specify
 // manually a characteristic length for some of the automatically
 // created points:
@@ -55,7 +55,7 @@ Extrude Surface { 11, {0, 0, h} } ;
 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
+// it is sometimes useful to 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
 //
diff --git a/tutorial/t3.geo b/tutorial/t3.geo
index ee091c84b382d79e178ded42bdd6e30de2a070ec..820fbbf3bc32e5cf2da384ae0be409b312c05b5d 100644
--- a/tutorial/t3.geo
+++ b/tutorial/t3.geo
@@ -15,11 +15,10 @@ Include "t1.geo" ;
 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:
+// but 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} } ; } ;
 
@@ -34,9 +33,10 @@ Extrude Surface { 122, {0,1,0} , {-0.1,0,0.1} , -Pi/2 } {
 
 // 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):
+// the graphic window, redefine 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;
@@ -55,11 +55,11 @@ General.TranslationX = -0.1;
 
 Geometry.Color.Surfaces = Geometry.Color.Points;
 
-// will set the color of the surfaces in the geometry to the same
+// will assign the color of the surfaces in the geometry to the same
 // color as the points.
 
-// A click on the '?'  button in status bar of the graphic window will
-// dump all current options to the terminal. To save all available
-// options to a file, use the 'File->Save_as->GEO complete options'
-// menu. To save the current options as the default options for all
-// future Gmsh sessions, use the 'File->Save_Options' menu.
+// A click on the '?'  button in the status bar of the graphic window
+// will dump all current options to the terminal. To save all
+// available options to a file, use the 'File->Save_as->GEO complete
+// options' menu. To save the current options as the default options
+// for all future Gmsh sessions, use the 'File->Save_Options' menu.
diff --git a/tutorial/t4.geo b/tutorial/t4.geo
index 1b7332b4ce4fbd1b98b577686f4179ac140d200e..c03610acc556d1a640cc36954c4f479f317e8f3c 100644
--- a/tutorial/t4.geo
+++ b/tutorial/t4.geo
@@ -67,8 +67,7 @@ Lc2 = 0.003 ;
 //   Fmod(x,y)
 //   Hypot(x,y)
 
-// An additional function 'Rand(x)' generates an random number in
-// [0,x]
+// An additional function 'Rand(x)' generates a random number in [0,x]
 //
 //   Rand(x)
 //
diff --git a/tutorial/t5.geo b/tutorial/t5.geo
index 112a0d4285e1d47035359795dc099520e73059ef..d29929551b92d2528a86caa6b2c0ac53d736d108 100644
--- a/tutorial/t5.geo
+++ b/tutorial/t5.geo
@@ -105,7 +105,7 @@ Function CheeseHole
 // Arrays of variables can be manipulated in the same way as classical
 // variables. Warning: accessing an uninitialized element in an array
 // will produce an unpredictable result. Note that whole arrays can
-// also be initialized on the fly (e.g. l[]={1,2,7} is valid).
+// also be instantly initialized (e.g. l[]={1,2,7} is valid).
 
   theloops[t] = newreg ; 
 
diff --git a/tutorial/tutorial.html b/tutorial/tutorial.html
index 44f7611e02a3e21f781af19c242140fede0cf524..5e50d0a8b1316f045347ce3097dbc8fca25a788a 100644
--- a/tutorial/tutorial.html
+++ b/tutorial/tutorial.html
@@ -22,7 +22,7 @@
 <H1>README 1/9</H1>
 [<A HREF="#top">top</A>][prev][<A HREF="#file2">next</A>]
 <PRE>
-$Id: tutorial.html,v 1.6 2001-02-18 18:41:05 geuzaine Exp $
+$Id: tutorial.html,v 1.7 2001-03-01 08:04:15 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
@@ -33,56 +33,57 @@ t1.geo.
 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
+operations to run Gmsh may vary according to your operating system. In
+the folowing examples, 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 'Mesh' in the module
-menu) 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.
+first tutorial file, select the 'File-&gt;Open' menu, and choose 't1.geo'
+in the input field. To perform the mesh generation, go to the mesh
+module (by selecting 'Mesh' in the module menu) 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
-'Help-&gt;Short_Help' in the menu bar to learn about these shortcuts.
+'Help-&gt;Shortcuts' 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:
+often more convenient to put the file name on the command line, 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
+Note: Even if it is often handy to define the variables and the points
+directly in the input files (you may use any text editor for this
+purpose, e.g. Wordpad on Windows, or Emacs on Unix), it is almost
+always more simple 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 'Geometry'
 in the module menu, 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.
+window) to select a list of points, and to click 'e' to finish the
+selection (or 'q' to abort it). 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:
+are performed without any interaction. To mesh the first tutorial in
+non-interactive mode, just type:
 
 &gt; gmsh t1.geo -2
 
@@ -99,16 +100,19 @@ the following line on the command line:
 
 In the Post-Processing module (select 'Post_Processing' in the module
 menu), 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. If you want the modifications made to one view to
-affect also all other views, select the 'Link all views' option in the
+map&quot; and &quot;a vector map&quot;. A left mouse click toggles the visibility of
+the selected view. A right mouse click provides access to the view's
+options. If you want the modifications made to one view to affect also
+all the 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_as', or simply viewed by pressing
-the '?' button in the status bar.
+specified in the ascii input files. All available options, with their
+current values, can be saved into a file by selecting
+'File-&gt;Save_as-&gt;GEO complete options', or simply viewed by pressing
+the '?' button in the status bar. To save the current options as the
+default options for all future Gmsh sessions, use the
+'File-&gt;Save_Options' menu.
 
 
 OK, that's all, folks. Enjoy the tutorial.
@@ -140,14 +144,14 @@ 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><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">// constructed from variables. Here, the product of the variable 'lc'
+</FONT></I><I><FONT COLOR="#B22222">// by the constant 9.e-1 is given as the fourth argument of the list
+</FONT></I><I><FONT COLOR="#B22222">// 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:
@@ -164,7 +168,7 @@ 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">// line is defined by a list of point numbers. For example, line 1
 </FONT></I><I><FONT COLOR="#B22222">// starts at point 1 and ends at point 2:
 </FONT></I>
 Line(1) = {1,2} ;
@@ -175,8 +179,8 @@ 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><I><FONT COLOR="#B22222">// connected lines, a sign being associated with each line (depending
+</FONT></I><I><FONT COLOR="#B22222">// on the orientation of the line).
 </FONT></I>
 Line Loop(5) = {4,1,-2,3} ;
 
@@ -187,12 +191,12 @@ 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">// order to assign region numbers to the various elements in the mesh
+</FONT></I><I><FONT COLOR="#B22222">// (the points, the lines and the triangles discretizing points 1 to
+</FONT></I><I><FONT COLOR="#B22222">// 4, lines 1 to 4 and surface 6). This is achieved by the definition
+</FONT></I><I><FONT COLOR="#B22222">// of Physical entities. Physical entities will group elements
+</FONT></I><I><FONT COLOR="#B22222">// belonging to several elementary entities by giving them a common
+</FONT></I><I><FONT COLOR="#B22222">// 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:
@@ -206,17 +210,16 @@ Physical Point(1) = {1,2} ;
 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. 
+<I><FONT COLOR="#B22222">// All the line elements which will be created during the mesh of
+</FONT></I><I><FONT COLOR="#B22222">// lines 1, 2 and 4 will be saved in the output file with the region
+</FONT></I><I><FONT COLOR="#B22222">// number 10; and all the triangular elements resulting from the
+</FONT></I><I><FONT COLOR="#B22222">// discretization of surface 6 will be given 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><I><FONT COLOR="#B22222">// description of the mesh and post-processing formats, see the
+</FONT></I><I><FONT COLOR="#B22222">// FORMATS file.
 </FONT></I></PRE>
 <HR>
 <A NAME="file3">
@@ -233,7 +236,7 @@ Physical Surface(100) = {6} ;
  *********************************************************************/</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><I><FONT COLOR="#B22222">// one. It can be included with:
 </FONT></I>
 Include &quot;t1.geo&quot; ;
 
@@ -258,10 +261,10 @@ Translate {-0.05,0,0} { Point{3} ; }
 </FONT></I>
 Translate {0,0.1,0} { Duplicata{ Point{3} ; } }
 
-<I><FONT COLOR="#B22222">// Translation, rotation and extrusion commands of course not only
+<I><FONT COLOR="#B22222">// Of course, translation, rotation and extrusion commands 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><I><FONT COLOR="#B22222">// command extrudes surface 6 defined in 't1.geo', as well as a new
+</FONT></I><I><FONT COLOR="#B22222">// surface 11, along the z axis by 'h':
 </FONT></I>
 h = 0.12 ;
 Extrude Surface { 6, {0, 0, h} } ;
@@ -272,7 +275,7 @@ Plane Surface(11) = {10};
 
 Extrude Surface { 11, {0, 0, h} } ;
 
-<I><FONT COLOR="#B22222">// All these geometrical transformations generate automatically new
+<I><FONT COLOR="#B22222">// All these geometrical transformations automatically generate 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:
@@ -280,7 +283,7 @@ Extrude Surface { 11, {0, 0, h} } ;
 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">// it is sometimes useful to 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">//
@@ -331,11 +334,10 @@ Include &quot;t1.geo&quot; ;
 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><I><FONT COLOR="#B22222">// but also the 2D mesh. This is done with the same Extrude command,
+</FONT></I><I><FONT COLOR="#B22222">// but by specifying the number of layers (here, there will be two
+</FONT></I><I><FONT COLOR="#B22222">// layers, of respectively 2 and 4 elements in depth), with volume
+</FONT></I><I><FONT COLOR="#B22222">// numbers 9000 and 9001 and respective heights of 0.33*h and 0.67*h:
 </FONT></I>
 Extrude Surface { 6, {0,0,h} } { Layers { {2,4}, {9000,9001}, {0.33,1} } ; } ;
 
@@ -350,9 +352,10 @@ Extrude Surface { 122, {0,1,0} , {-0.1,0,0.1} , -Pi/2 } {
 
 <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><I><FONT COLOR="#B22222">// the graphic window, redefine the color of the points of the
+</FONT></I><I><FONT COLOR="#B22222">// geometry, disable the display of the axes, and select an initial
+</FONT></I><I><FONT COLOR="#B22222">// viewpoint in XYZ mode (disabling the interactive trackball-like
+</FONT></I><I><FONT COLOR="#B22222">// rotation mode):
 </FONT></I>
 General.Color.Background = Red;
 Geometry.Color.Points = Orange;
@@ -371,14 +374,15 @@ General.TranslationX = -0.1;
 </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
+<I><FONT COLOR="#B22222">// will assign 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>
+<I><FONT COLOR="#B22222">// A click on the '?'  button in the status bar of the graphic window
+</FONT></I><I><FONT COLOR="#B22222">// will dump all current options to the terminal. To save all
+</FONT></I><I><FONT COLOR="#B22222">// available options to a file, use the 'File-&gt;Save_as-&gt;GEO complete
+</FONT></I><I><FONT COLOR="#B22222">// options' menu. To save the current options as the default options
+</FONT></I><I><FONT COLOR="#B22222">// for all future Gmsh sessions, use the 'File-&gt;Save_Options' menu.
+</FONT></I></PRE>
 <HR>
 <A NAME="file5">
 <H1>t4.geo 5/9</H1>
@@ -453,8 +457,7 @@ Lc2 = 0.003 ;
 </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]
+<I><FONT COLOR="#B22222">// An additional function 'Rand(x)' generates a random number in [0,x]
 </FONT></I><I><FONT COLOR="#B22222">//
 </FONT></I><I><FONT COLOR="#B22222">//   Rand(x)
 </FONT></I><I><FONT COLOR="#B22222">//
@@ -642,7 +645,7 @@ Function CheeseHole
 <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. Note that whole arrays can
-</FONT></I><I><FONT COLOR="#B22222">// also be initialized on the fly (e.g. l[]={1,2,7} is valid).
+</FONT></I><I><FONT COLOR="#B22222">// also be instantly initialized (e.g. l[]={1,2,7} is valid).
 </FONT></I>
   theloops[t] = newreg ; 
 
@@ -664,7 +667,7 @@ For t In {1:5}
   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">// defining a function, we could have defined 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 ;