diff --git a/tutorial/t12.geo b/tutorial/t12.geo
index 88b8c747692499b36bde4a0a2e2aa44724982232..9cd5194a88aa6d0fee685b7fd1a40b3caa572054 100644
--- a/tutorial/t12.geo
+++ b/tutorial/t12.geo
@@ -2,56 +2,65 @@
*
* Gmsh tutorial 12
*
- * Remeshing STL with compounds
+ * Cross-patch meshing with compounds
*
*********************************************************************/
// Compound geometrical entities can be defined to compute a new
// parametrization of groups of elementary geometrical entities. This
// parametrization can then be used for remeshing the compound as if
-// it were a CAD entity.
+// it were a single CAD entity.
-// Merge the original mesh, that we would like to remesh. This mesh
-// was reclassified ("colored") from an initial STL triangulation
-// using the "Reclassify 2D" tool in Gmsh, so that we can preserve
-// sharp geometrical features.
-Merge "t12_data.msh";
+lc = 0.2;
+Point(1) = {0, 0, 0, lc};
+Point(2) = {1, 0, 0, lc};
+Point(3) = {1, 1, 0.5, lc};
+Point(4) = {0, 1, 0.4, lc};
+Point(5) = {0.3, 0.2, 0, lc};
+Point(6) = {0, 0.01, 0.01, lc};
+Point(7) = {0, 0.02, 0.02, lc};
+Point(8) = {1, 0.05, 0.02, lc};
+Point(9) = {1, 0.32, 0.02, lc};
+Line(1) = {1, 2};
+Line(2) = {2, 8};
+Line(3) = {8, 9};
+Line(4) = {9, 3};
+Line(5) = {3, 4};
+Line(6) = {4, 7};
+Line(7) = {7, 6};
+Line(8) = {6, 1};
+Spline(9) = {7, 5, 9};
+Line(10) = {6, 8};
+Line Loop(11) = {5, 6, 9, 4};
+Ruled Surface(12) = {11};
+Line Loop(13) = {9, -3, -10, -7};
+Ruled Surface(14) = {13};
+Line Loop(15) = {10, -2, -1, -8};
+Ruled Surface(16) = {15};
-// Since the original mesh is a bit coarse, we refine it once
-RefineMesh;
+// Treat lines 2, 3 and 4 as a single line
+Compound Line(100) = {2, 3, 4};
+// Idem with lines 6, 7 and 8
+Compound Line(101) = {6, 7, 8};
-// Create the topology of the discrete model
-CreateTopology;
-
-// We can now define a compound line (resp. surface) for each discrete
-// line (resp. surface) in the model
-ll[] = Line "*";
-For j In {0 : #ll[]-1}
- Compound Line(newl) = ll[j];
-EndFor
-
-ss[] = Surface "*";
-s = news;
-For i In {0 : #ss[]-1}
- Compound Surface(s+i) = ss[i];
-EndFor
-
-Surface Loop(1) = {s : s + #ss[]-1};
-Volume(1) = {1};
-
-Physical Surface(1) = {s : s + #ss[]-1};
-Physical Volume(1) = 1;
-
-// Apply a funny mesh size field, just because we can :-)
-Field[1] = MathEval;
-Field[1].F = "2*Sin((x+y)/5) + 3.3";
-Background Field = 1;
-
-Mesh.RemeshAlgorithm = 1; // (0) no split (1) automatic (2) automatic only with metis
-Mesh.RemeshParametrization = 1; // (0) harmonic (1) conformal
+// Treat surfaces 12, 14 and 16 as a single surface
+Compound Surface(200) = {12, 14, 16};
// More details about the reparametrization technique can be found in
// the following papers:
//
+// * J.-F. Remacle, C. Geuzaine, G. Compère and E. Marchandise,
+// "High-Quality Surface Remeshing Using Harmonic Maps",
+// International Journal for Numerical Methods in Engineering,
+// 83 (4), pp. 403-425, 2010.
//
-//
+// * E. Marchandise, G. Compère, M. Willemet, G. Bricteux, C. Geuzaine
+// and J-F Remacle, "Quality meshing based on STL triangulations for
+// biomedical simulations", International Journal for Numerical
+// Methods in Biomedical Engineering", 26 (7), pp. 876-889, 2010.
+//
+// * E. Marchandise, C. Carton de Wiart, W. G. Vos, C. Geuzaine and
+// J.-F. Remacle, "High Quality Surface Remeshing Using Harmonic
+// Maps. Part II: Surfaces with High Genus and of Large Aspect
+// Ratio", International Journal for Numerical Methods in
+// Engineering, 86 (11), pp. 1303-1321, 2011.
diff --git a/tutorial/t13.geo b/tutorial/t13.geo
index 62a15a318d7b35c8bbd695a0d053f99a618436f6..be64a48eb0fedec0b7fbbc4228d555f26a94d734 100644
--- a/tutorial/t13.geo
+++ b/tutorial/t13.geo
@@ -2,12 +2,50 @@
*
* Gmsh tutorial 13
*
- * Cross-patch meshing with compounds
+ * Remeshing STL with compounds
*
*********************************************************************/
-// Compound geometrical entities can be defined to compute a new
-// parametrization of groups of elementary geometrical entities. This
-// parametrization can then be used for remeshing the compound as if
-// it were a CAD entity.
+// Since compound geometrical compute a new parametrization, one can
+// also use them to remesh STL files, even if there's only a single
+// elementary per compound.
+
+// Let's merge the mesh that we would like to remesh. This mesh was
+// reclassified ("colored") from an initial STL triangulation using
+// the "Reclassify 2D" tool in Gmsh, so that we could split it along
+// sharp geometrical features.
+Merge "t13_data.msh";
+
+// Since the original mesh is a bit coarse, we refine it once
+RefineMesh;
+
+// Create the topology of the discrete model
+CreateTopology;
+
+// We can now define a compound line (resp. surface) for each discrete
+// line (resp. surface) in the model
+ll[] = Line "*";
+For j In {0 : #ll[]-1}
+ Compound Line(newl) = ll[j];
+EndFor
+ss[] = Surface "*";
+s = news;
+For i In {0 : #ss[]-1}
+ Compound Surface(s+i) = ss[i];
+EndFor
+
+// And we can create the volume based on the new compound entities
+Surface Loop(1) = {s : s + #ss[]-1};
+Volume(1) = {1};
+
+Physical Surface(1) = {s : s + #ss[]-1};
+Physical Volume(1) = 1;
+
+// Apply a funny mesh size field, just because we can :-)
+Field[1] = MathEval;
+Field[1].F = "2*Sin((x+y)/5) + 3.3";
+Background Field = 1;
+
+Mesh.RemeshAlgorithm = 1; // (0) no split (1) automatic (2) automatic only with metis
+Mesh.RemeshParametrization = 1; // (0) harmonic (1) conformal
diff --git a/tutorial/t12_data.msh b/tutorial/t13_data.msh
similarity index 100%
rename from tutorial/t12_data.msh
rename to tutorial/t13_data.msh