improve comments (thanks to Takuya OSHIMA)

tutorial/t4.geo

@@ -6,22 +6,23 @@
  *
  *********************************************************************/
 
-// As usual, we start by defining some variables, some points and some
-// lines:
+// As usual, we start by defining some variables:
 
 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;
+Lc1 = 0.01;
+Lc2 = 0.003;
 
-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;
+// We can use all the usual mathematical functions (note the
+// capitalized first letters), plus some useful functions like
+// Hypot(a, b) := Sqrt(a^2 + b^2):
 
-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);
 
-ccos = ( -h5*R1 + e2 * Hypot(h5,Hypot(e2,R1)) ) / (h5^2 + e2^2);
-ssin = Sqrt(1-ccos^2);
-
-Lc1 = 0.01;
-Lc2 = 0.003;
+// Then we define some points and some lines using these variables:
 
 Point(1) = { -e1-e2, 0.0  , 0.0 , Lc1};
 Point(2) = { -e1-e2, h1   , 0.0 , Lc1};
@@ -93,21 +94,26 @@ Plane Surface(22) = {21};
 Line Loop(23) = {11,-12,13,14,1,2,-3,4,5,6,7,-8,9,10};
 Plane Surface(24) = {23,21};
 
+// As a general rule, if a surface has N holes, it is defined by N+1
+// line loops: the first loop defines the exterior boundary; the other
+// loops define the boundaries of the holes.
+
 // Finally, we can add some comments by embedding a post-processing
 // view containing some strings, and change the color of some mesh
 // entities:
 
 View "comments" {
-  // 10 pixels from the left and 15 pixels from the top of the graphic
-  // window:
-  T2(10,15,0){StrCat("File created on ", Today)};
+  // Add a text string in window coordinates, 10 pixels from the left
+  // and 10 pixels from the bottom:
+  T2(10, -10, 0){ "Copyright (C) My Company" };
 
-  // 10 pixels from the left and 10 pixels from the bottom of the
-  // graphic window:
-  T2(10,-10,0){"Copyright (C) My Company"};
+  // Add another text string in window coordinates, 10 pixels from the
+  // left and 15 pixels from the top, using the StrCat() function to
+  // concatenate a string with the current date:
+  T2(10, 15, 0){ StrCat("File created on ", Today) };
 
-  // in the model, at (X,Y,Z) = (0.0,0.11,0.0):
-  T3(0,0.11,0,0){"Hole"};
+  // Add a text string in model coordinates at (X,Y,Z) = (0, 0.11, 0):
+  T3(0, 0.11, 0, 0){ "Hole" };
 };
 
 Color Grey50{ Surface{ 22 }; }

tutorial/t5.geo

@@ -6,27 +6,28 @@
  *
  *********************************************************************/
 
-// Again, we start be defining some characteristic lengths:
+// We start by defining some target mesh sizes:
 
 lcar1 = .1;
 lcar2 = .0005;
 lcar3 = .055;
 
-// If we wanted to change these lengths globally (without changing the
-// above definitions), we could give a global scaling factor for all
-// characteristic lengths on the command line with the `-clscale'
+// If we wanted to change these mesh sizes globally (without changing
+// the above definitions), we could give a global scaling factor for
+// all characteristic lengths on the command line with the `-clscale'
 // option (or with `Mesh.CharacteristicLengthFactor' in an option
 // file). For example, with:
 //
 // > gmsh t5.geo -clscale 1
 //
-// this input file produces a mesh of approximately 3,000 nodes and
-// 15,000 tetrahedra. With
+// this input file produces a mesh of approximately 1,300 nodes and
+// 11,000 tetrahedra. With
 //
 // > gmsh t5.geo -clscale 0.2
 //
-// the mesh counts approximately 600,000 nodes and 3.6 million
-// tetrahedra.
+// the mesh counts approximately 350,000 nodes and 2.1 million
+// tetrahedra. You can check mesh statistics in the graphical user
+// interface with the `Tools->Statistics' menu.
 
 // We proceed by defining some elementary entities describing a
 // truncated cube:
@@ -125,6 +126,8 @@ For t In {1:5}
   x += 0.166 ; 
   z += 0.166 ; 
 
+  // We call the `CheeseHole' function:
+
   Call CheeseHole ;
 
   // We define a physical volume for each hole:
@@ -134,7 +137,7 @@ For t In {1:5}
   // We also print some variables on the terminal (note that, since
   // all variables are treated internally as floating point numbers,
   // the format string should only contain valid floating point format
-  // specifiers):
+  // specifiers like `%g', `%f', '%e', etc.):
 
   Printf("Hole %g (center = {%g,%g,%g}, radius = %g) has number %g!",
 	 t, x, y, z, r, thehole) ;
@@ -149,9 +152,10 @@ theloops[0] = newreg ;
 Surface Loop(theloops[0]) = {35,31,29,37,33,23,39,25,27} ;
 
 // The volume of the cube, without the 5 holes, is now defined by 6
-// surface loops (the exterior surface and the five interior loops).
-// To reference an array of variables, its identifier is followed by
-// '[]':
+// surface loops: the first surface loop defines the exterior surface;
+// the surface loops other than the first one define holes.  (Again,
+// to reference an array of variables, its identifier is followed by
+// square brackets):
 
 Volume(186) = {theloops[]} ;