commiting chapters 4 & 5

benchmarks/bugs/bug_elliptic.geo

+/********************************************************************* 
+ *
+ *  Gmsh tutorial 1
+ * 
+ *  Variables, Elementary entities (Points, Lines, Surfaces), Physical
+ *  entities (Points, Lines, Surfaces), Background mesh
+ *
+ *********************************************************************/
+
+// All geometry description in Gmsh is made by means of a special
+// language (looking somewhat similar to C). The simplest construction
+// of this language is the 'affectation'. 
+
+// The following command (all commands end with a semi colon) defines
+// a variable called 'lc' and affects the value 0.007 to 'lc':
+
+lc = 0.007 ;
+
+// This newly created variable can be used to define the first Gmsh
+// elementary entity, a 'Point'. A Point is defined by a list of four
+// numbers: its three coordinates (x, y and z), and a characteristic
+// length which sets the target mesh size at the point:
+
+Point(1) = {0,  0,  0, 9.e-1 * lc} ;
+
+// The mesh size is defined as the length of the segments for lines,
+// the radii of the circumscribed circles for triangles and the radii
+// of the circumscribed spheres for tetrahedra, respectively. The
+// actual distribution of the mesh sizes is obtained by interpolation
+// of the characteristic lengths prescribed at the points. There are
+// also other possibilities to specify characteristic lengths:
+// attractors (see t7.geo) and background meshes (see bgmesh.pos).
+
+// As can be seen in the previous definition, more complex expressions
+// can be 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:
+//
+//    "If a number defines a new entity, it is enclosed between
+//    parentheses. If a number refers to a previously defined entity,
+//    it is enclosed between braces."
+//
+// Three additional points are then defined:
+
+Point(2) = {.1, 0,  0, lc} ;
+Point(3) = {.1, .3, 0, lc} ;
+Point(4) = {0,  .3, 0, lc} ;
+
+// The second elementary geometrical entity in Gmsh is the
+// curve. Amongst curves, straight lines are the simplest. A straight
+// line is defined by a list of point numbers. For example, line 1
+// starts at point 1 and ends at point 2:
+
+Line(1) = {1,2} ;
+Line(2) = {3,2} ;
+Line(3) = {3,4} ;
+Line(4) = {4,1} ;
+
+// The third elementary entity is the surface. In order to define a
+// simple rectangular surface from the four lines defined above, a
+// line loop has first to be defined. A line loop is a list of
+// connected lines, a sign being associated with each line (depending
+// on the orientation of the line).
+
+Line Loop(5) = {4,1,-2,3} ;
+
+// The surface is then defined as a list of line loops (only one
+// here):
+
+Plane Surface(6) = {5} ;
+
+// At this level, Gmsh knows everything to display the rectangular
+// surface 6 and to mesh it. But a supplementary step is needed in
+// order 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:
+
+Physical Point(1) = {1,2} ;
+
+// Consequently, two punctual elements will be saved in the output
+// files, both with the region number 1. The mechanism is identical
+// for line or surface elements:
+
+Physical Line(10) = {1,2,4} ;
+MySurface = 100;
+Physical Surface(MySurface) = {6} ;
+
+// 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.
+//
+// If no physical groups are defined, all the elements in the mesh are
+// directly saved with their default orientation and with a region
+// number equal to their elementary region number. For a description
+// of the mesh and post-processing formats, see the reference manual.
+
+Transfinite Line{2,4} = 100 Using Power 2;
+Transfinite Line{1,3} = 30 ;
+
+Elliptic Surface{6} = {1,2,3,4};
+

demos/splines.geo

@@ -47,11 +47,25 @@ s = newreg;
 Line Loop(s) = {-l,-(l+1)};
 Plane Surface(s+1) = s;
 
+xx += 1;
+
+// Bezier
+p = newp;
+Point(p) = {xx,  0,  0, 0.3*lc} ;
+Point(p+1) = {xx+.5, 0,  0, lc} ;
+Point(p+2) = {xx+.5, 1, 0, 0.1*lc} ;
+Point(p+3) = {xx, 1, 0, lc} ;
+l = newreg;
+Bezier(l) = {p+3,p+2,p+1,p};
+Line(l+1) = {p,p+3};
+s = newreg;
+Line Loop(s) = {-l,-(l+1)};
+Plane Surface(s+1) = s;
 
 // Duplicate the surfaces, and use uniform mesh
 p1=newp;
 Translate {0,-1.5,0} {
-  Duplicata { Surface{6,10,14}; }
+  Duplicata { Surface{6:18:4}; }
 }
 p2=newp;
 Printf("p1 p2 = %g %g", p1, p2);

tutorial/t1.geo

@@ -101,5 +101,4 @@ Physical Surface(MySurface) = {6} ;
 //
 // If no physical groups are defined, all the elements in the mesh are
 // directly saved with their default orientation and with a region
-// number equal to their elementary region number. For a description
-// of the mesh and post-processing formats, see the reference manual.
+// number equal to their elementary region number.