[SCM] Gerris Flow Solver branch, upstream, updated. b3aa46814a06c9cb2912790b23916ffb44f1f203

[Stephane Popinet]

The following commit has been merged in the upstream branch:
commit f52164dcf3b0d215b92187b5f0505a23e1f2f3ec
Author: Stephane Popinet <popinet at users.sf.net>
Date:   Wed Apr 18 15:39:26 2007 +1000

    Solid boundaries can be defined using implicit surfaces
    
    # a cylinder of radius 0.0625
    Solid (x*x + y*y - 0.0625*0.0625)
    
    This can also be used to define volume fractions (using GfsInitFraction).
    
    darcs-hash:20070418053926-d4795-0042ceff53edb13386ec8bb93a6a06a85d78928a.gz

diff --git a/doc/examples/cylinder/cylinder.gfs b/doc/examples/cylinder/cylinder.gfs
index 3ae39c2..cc22611 100644
--- a/doc/examples/cylinder/cylinder.gfs
+++ b/doc/examples/cylinder/cylinder.gfs
@@ -33,8 +33,8 @@
 #
 # Author: St\'ephane Popinet
 # Command: gerris2D cylinder.gfs
-# Version: 0.6.4
-# Required files: cylinder.gts
+# Version: 1.1.0
+# Required files:
 # Running time: 32 minutes
 # Generated files: t.mpg vort.mpg t.eps vort.eps
 #
@@ -47,8 +47,9 @@
   # Use an initial refinement of 6 levels (i.e. 2^6=64x64 for each box)
   Refine 6
 
-  # Insert the solid boundary defined by cylinder.gts
-  Solid cylinder.gts
+  # Insert the solid boundary defined as x*x + y*y - 0.0625*0.0625 = 0
+  # (i.e. a cylinder of radius 0.0625 centered on the origin)
+  Solid (x*x + y*y - 0.0625*0.0625)
 
   # Add a passive tracer called T
   VariableTracer {} T
diff --git a/doc/examples/cylinder/cylinder.gts b/doc/examples/cylinder/cylinder.gts
deleted file mode 100644
index a804e8a..0000000
--- a/doc/examples/cylinder/cylinder.gts
+++ /dev/null
@@ -1,6591 +0,0 @@
-1100 3294 2196 GtsSurface GtsFace GtsEdge GtsVertex
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--0.02306588406 0.05808799352 -0.2
--0.01937299351 0.059421689 -0.15
-0.0481172146 0.0398871365 0.05
-0.04551773225 0.04282973325 0.05
-0.0481172146 0.0398871365 0.1
-0.003862028847 0.06238056375 0.15
--6.24999896e-05 0.06249996875 0.15
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--0.0619993045 -0.00789533034 0.1
--0.06138121115 -0.01177271925 0.1
--0.0619993045 -0.00789533034 0.15
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-3202 539 3225
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-2560 2950 3177
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-2220 129 914
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diff --git a/doc/examples/cylinder/heated/heated.gfs b/doc/examples/cylinder/heated/heated.gfs
index 8b78b31..efe6d5c 100644
--- a/doc/examples/cylinder/heated/heated.gfs
+++ b/doc/examples/cylinder/heated/heated.gfs
@@ -19,8 +19,8 @@
 #
 # Author: St\'ephane Popinet
 # Command: gerris2D heated.gfs
-# Version: 0.6.4
-# Required files: ../cylinder.gts
+# Version: 1.1.0
+# Required files:
 # Running time: 22 minutes
 # Generated files: t.mpg t.eps
 #
@@ -33,8 +33,9 @@
   # Use an initial refinement of 6 levels (i.e. 2^6=64x64 for each box)
   Refine 6
 
-  # Insert the solid boundary defined by cylinder.gts
-  Solid cylinder.gts
+  # Insert the solid boundary defined as x*x + y*y - 0.0625*0.0625 = 0
+  # (i.e. a cylinder of radius 0.0625 centered on the origin)
+  Solid (x*x + y*y - 0.0625*0.0625)
 
   # Add a passive tracer called T
   VariableTracer {} T
diff --git a/src/Makefile.am b/src/Makefile.am
index cb4e371..7b3f1da 100644
--- a/src/Makefile.am
+++ b/src/Makefile.am
@@ -59,7 +59,9 @@ GFS_HDS = \
 	$(MPI_HDS)
 
 pkginclude_HEADERS = \
-	$(GFS_HDS)
+	$(GFS_HDS) \
+	spatial.h \
+	function.h
 
 include_HEADERS = \
 	gfs.h \
diff --git a/src/event.c b/src/event.c
index bc74d38..817d288 100644
--- a/src/event.c
+++ b/src/event.c
@@ -1646,7 +1646,7 @@ static void gfs_init_fraction_read (GtsObject ** o, GtsFile * fp)
   }
   gts_file_next_token (fp);
 
-  gfs_surface_read (init->surface, fp);
+  gfs_surface_read (init->surface, gfs_object_simulation (*o), fp);
 }
 
 static void gfs_init_fraction_write (GtsObject * o, FILE * fp)
diff --git a/src/init.h b/src/function.h
similarity index 54%
copy from src/init.h
copy to src/function.h
index 425b2a2..3513155 100644
--- a/src/init.h
+++ b/src/function.h
@@ -17,21 +17,26 @@
  * 02111-1307, USA.  
  */
 
-#ifndef __INIT_H__
-#define __INIT_H__
+#ifndef __FUNCTION_H__
+#define __FUNCTION_H__
 
-#include <gts.h>
+static double Dirichlet = 1.;
+static double Neumann = 0.;
+static GfsSimulation * _sim = NULL;
+static FttCell * _cell = NULL;
 
-#ifdef __cplusplus
-extern "C" {
-#endif /* __cplusplus */
-
-GtsObjectClass ** gfs_classes             (void);
-void              gfs_init                (int * argc, 
-					   char *** argv);
-
-#ifdef __cplusplus
+static double dd (const gchar * name, FttComponent c) {
+  GfsVariable * v = gfs_variable_from_name (GFS_DOMAIN (_sim)->variables, name);
+  if (v == NULL)
+    return 0.;
+  g_return_val_if_fail (_cell != NULL, 0.);
+  return gfs_center_gradient (_cell, c, v->i)/ftt_cell_size (_cell);
 }
-#endif /* __cplusplus */
 
-#endif /* __INIT_H__ */
+static double dx (const gchar * name) { return dd (name, FTT_X); }
+static double dy (const gchar * name) { return dd (name, FTT_Y); }
+#if !FTT_2D
+static double dz (const gchar * name) { return dd (name, FTT_Z); }
+#endif /* 3D */
+
+#endif /* __FUNCTION_H__ */
diff --git a/src/refine.c b/src/refine.c
index f3f61df..8c9b799 100644
--- a/src/refine.c
+++ b/src/refine.c
@@ -175,15 +175,11 @@ static void max_kappa (GtsVertex * v, KappaData * d)
 static gdouble solid_curvature (FttCell * cell, FttCellFace * face, 
 				GfsDomain * domain, GfsSurface * s)
 {
-  if (s->s) {
-    KappaData d;
-    d.s = s->s;
-    d.kappa = gfs_solid_is_thin (cell, s) ? 1./ftt_cell_size (cell) : 0.;
-    gts_surface_foreach_vertex (d.s, (GtsFunc) max_kappa, &d);
-    return d.kappa;
-  }
-  else /* fixme: need to compute curvature for other types of surfaces */
-    return 0.;
+  KappaData d;
+  d.s = s->s;
+  d.kappa = gfs_solid_is_thin (cell, s) ? 1./ftt_cell_size (cell) : 0.;
+  gts_surface_foreach_vertex (d.s, (GtsFunc) max_kappa, &d);
+  return d.kappa;
 }
 
 static void refine_solid_read (GtsObject ** o, GtsFile * fp)
@@ -225,6 +221,7 @@ static void gfs_refine_solid_refine (GfsRefine * refine, GfsSimulation * sim)
     GSList * i = sim->solids->items;
     while (i) {
       p.surface = GFS_SOLID (i->data)->s;
+      g_assert (p.surface->s); /* fixme: this works only for GTS surfaces */
       gfs_domain_traverse_cut (GFS_DOMAIN (sim), p.surface,
 			       FTT_PRE_ORDER, FTT_TRAVERSE_LEAFS,
 			       (FttCellTraverseCutFunc) refine_cut_cell, &p);
@@ -294,7 +291,7 @@ static void refine_surface_read (GtsObject ** o, GtsFile * fp)
     return;
 
   refine = GFS_REFINE_SURFACE (*o);
-  gfs_surface_read (refine->surface, fp);
+  gfs_surface_read (refine->surface, gfs_object_simulation (*o), fp);
   if (fp->type == GTS_ERROR)
     return;
 
diff --git a/src/simulation.c b/src/simulation.c
index cecc525..dafd247 100644
--- a/src/simulation.c
+++ b/src/simulation.c
@@ -155,7 +155,7 @@ static gboolean strmatch (const gchar * s, const gchar * s1)
 static void simulation_read (GtsObject ** object, GtsFile * fp)
 {
   GfsSimulation * sim = GFS_SIMULATION (*object);
-  
+
   (* GTS_OBJECT_CLASS (gfs_simulation_class ())->parent_class->read) (object, fp);
   if (fp->type == GTS_ERROR)
     return;
diff --git a/src/solid.c b/src/solid.c
index 85e2f25..cd4ee0e 100644
--- a/src/solid.c
+++ b/src/solid.c
@@ -234,7 +234,22 @@ static void face_new (CellFace * f, FttCell * cell, GfsSurface * s, FttVector *
   f->n[0] = f->n[1] = f->n[2] = f->n[3] = 0;
   f->inside[0] = f->inside[1] = f->inside[2] = f->inside[3] = 0;
 
-  gts_surface_foreach_face (s->s, (GtsFunc) triangle_face_intersection, f);
+  if (s->s)
+    gts_surface_foreach_face (s->s, (GtsFunc) triangle_face_intersection, f);
+  else {
+    guint i;
+    
+    for (i = 0; i < 4; i++) {
+      gdouble vE = gfs_surface_implicit_value (s, f->p[i]);
+      gdouble vD = gfs_surface_implicit_value (s, f->p[(i + 1) % 4]);
+
+      if ((vE > 0. && vD <= 0.) || (vE <= 0. && vD > 0.)) {
+	f->x[i] = vE/(vE - vD);
+	f->n[i] = 1;
+	f->inside[i] = vE > 0. ? -1 : 1;
+      }
+    }
+  }
 }
 
 static gboolean solid_face_is_thin (CellFace * f)
@@ -292,10 +307,6 @@ gboolean gfs_set_2D_solid_fractions_from_surface (FttCell * cell,
   solid = GFS_STATE (cell)->solid;
   switch (n1) {
   case 0:
-    if (solid) {
-      g_free (solid);
-      GFS_STATE (cell)->solid = NULL;
-    }
     break;
   case 4:
     thin = TRUE;
@@ -304,6 +315,10 @@ gboolean gfs_set_2D_solid_fractions_from_surface (FttCell * cell,
     if (!solid)
       GFS_STATE (cell)->solid = solid = g_malloc0 (sizeof (GfsSolidVector));
     face_fractions (&f, solid, &h);
+    if (solid->a == 1.) {
+      g_free (solid);
+      GFS_STATE (cell)->solid = NULL;
+    }
     break;
   }
   default: {
@@ -497,11 +512,26 @@ static void cube_new (CellCube * cube, FttCell * cell, GfsSurface * s, FttVector
     cube->p[i].z = o->z + h->z*vertex[i].z;
   }
 
-  gts_surface_foreach_face (s->s, (GtsFunc) triangle_cube_intersection, cube);  
+  if (s->s)
+    gts_surface_foreach_face (s->s, (GtsFunc) triangle_cube_intersection, cube);  
+  else {
+    guint i;
+    
+    for (i = 0; i < 12; i++) {
+      gdouble vE = gfs_surface_implicit_value (s, cube->p[edge1[i][0]]);
+      gdouble vD = gfs_surface_implicit_value (s, cube->p[edge1[i][1]]);
+
+      if ((vE > 0. && vD <= 0.) || (vE <= 0. && vD > 0.)) {
+	cube->x[i] = vE/(vE - vD);
+	cube->n[i] = 1;
+	cube->inside[i] = vE > 0. ? -1 : 1;
+      }
+    }
+  }
 }
 
 static void set_solid_fractions_from_surface (FttCell * cell, 
-					      GfsSurface * s, 
+					      GfsSurface * surface, 
 					      InitSolidParams * p)
 {
   GfsSolidVector * solid = GFS_STATE (cell)->solid;
@@ -513,7 +543,7 @@ static void set_solid_fractions_from_surface (FttCell * cell,
 
   ftt_cell_pos (cell, &o);
   cell_size (cell, &h);
-  cube_new (&cube, cell, s, &o, &h);
+  cube_new (&cube, cell, surface, &o, &h);
 
   for (i = 0; i < 12; i++) /* for each edge of the cube */
     if (cube.n[i] % 2 != 0) { /* only for odd number of intersections */
@@ -536,13 +566,8 @@ static void set_solid_fractions_from_surface (FttCell * cell,
     else
       cube.n[i] = 0;
 
-  if (n1 == 0) { /* no intersections */
-    if (solid) {
-      g_free (solid);
-      GFS_STATE (cell)->solid = NULL;
-    }
+  if (n1 == 0) /* no intersections */
     return;
-  }
 
   if (!solid)
     GFS_STATE (cell)->solid = solid = g_malloc0 (sizeof (GfsSolidVector));
@@ -629,7 +654,13 @@ static void set_solid_fractions_from_surface (FttCell * cell,
 	sym[c] = FALSE;
       n += (&m.x)[c];
     }
-    g_assert (n > 0.);
+    if (n == 0.) { /* this is a fluid cell */
+      for (c = 0; c < FTT_NEIGHBORS; c++)
+	g_assert (solid->s[c] == 1.);
+      g_free (solid);
+      GFS_STATE (cell)->solid = NULL;
+      return;
+    }
     m.x /= n; m.y /= n; m.z /= n;
     alpha = m.x*ca.x + m.y*ca.y + m.z*ca.z;
     solid->a = gfs_plane_volume (&m, alpha);
@@ -1475,7 +1506,7 @@ static void gfs_solid_read (GtsObject ** o, GtsFile * fp)
   if (fp->type == GTS_ERROR)
     return;
 
-  gfs_surface_read (GFS_SOLID (*o)->s, fp);
+  gfs_surface_read (GFS_SOLID (*o)->s, gfs_object_simulation (*o), fp);
 }
 
 static void gfs_solid_write (GtsObject * o, FILE * fp)
diff --git a/src/init.h b/src/spatial.h
similarity index 72%
copy from src/init.h
copy to src/spatial.h
index 425b2a2..40a823f 100644
--- a/src/init.h
+++ b/src/spatial.h
@@ -17,21 +17,15 @@
  * 02111-1307, USA.  
  */
 
-#ifndef __INIT_H__
-#define __INIT_H__
+#ifndef __SPATIAL_H__
+#define __SPATIAL_H__
 
-#include <gts.h>
+static double _x = 0., _y = 0., _z = 0.;
 
-#ifdef __cplusplus
-extern "C" {
-#endif /* __cplusplus */
-
-GtsObjectClass ** gfs_classes             (void);
-void              gfs_init                (int * argc, 
-					   char *** argv);
-
-#ifdef __cplusplus
+static double ellipse (double xc, double yc, double a, double b)
+{
+  g_return_val_if_fail (a != 0. && b != 0., 0.);
+  return (_x - xc)*(_x - xc)/(a*a) + (_y - yc)*(_y - yc)/(b*b) - 1.;
 }
-#endif /* __cplusplus */
 
-#endif /* __INIT_H__ */
+#endif /* __SPATIAL_H__ */
diff --git a/src/surface.c b/src/surface.c
index 9a5605f..c3a78d7 100644
--- a/src/surface.c
+++ b/src/surface.c
@@ -17,8 +17,9 @@
  * 02111-1307, USA.  
  */
 
-#include "surface.h"
+
 #include "simulation.h"
+#include "surface.h"
 
 /* GfsSurface: Object */
 
@@ -43,10 +44,24 @@ static void surface_read (GtsObject ** o, GtsFile * fp)
 {
   GfsSurface * surface = GFS_SURFACE (*o);
 
-  if (fp->type == '{') {
+  if (fp->type == '(') { /* implicit surface */
+    gts_file_next_token (fp);
+    if (surface->f)
+      gts_object_destroy (GTS_OBJECT (surface->f));
+    surface->f = gfs_function_new (gfs_function_spatial_class (), 0.);
+    gfs_function_read (surface->f, gfs_object_simulation (*o), fp);
+    if (fp->type == GTS_ERROR)
+      return;
+    if (fp->type != ')') {
+      gts_file_error (fp, "expecting a closing bracket");
+      return;
+    }
+  }
+  else if (fp->type == '{') { /* embedded surface */
     fp->scope_max++;
     gts_file_next_token (fp);
-    g_assert (!surface->s);
+    if (surface->s)
+      gts_object_destroy (GTS_OBJECT (surface->s));
     surface->s = gts_surface_new (gts_surface_class (), 
 				  gts_face_class (), 
 				  gts_edge_class (), 
@@ -62,7 +77,7 @@ static void surface_read (GtsObject ** o, GtsFile * fp)
       return;
     fp->scope_max--;
   }
-  else {
+  else { /* surface file name */
     if (fp->type != GTS_STRING) {
       gts_file_error (fp, "expecting a string (filename)");
       return;
@@ -96,9 +111,7 @@ static void surface_read (GtsObject ** o, GtsFile * fp)
   gts_file_next_token (fp);
 
   if (fp->type == '{') {
-    GtsVector r = {0.,0.,0.}, s = {1.,1.,1.}, t = {0.,0.,0.};
-    gdouble angle = 0., scale = 1.;
-    gboolean flip = FALSE;
+    gdouble scale = 1.;
     GtsFileVariable var[] = {
       {GTS_DOUBLE, "rx", TRUE},
       {GTS_DOUBLE, "ry", TRUE},
@@ -116,74 +129,115 @@ static void surface_read (GtsObject ** o, GtsFile * fp)
     };
     GtsFileVariable * v = var;
 
-    (v++)->data = &r[0];
-    (v++)->data = &r[1];
-    (v++)->data = &r[2];
+    (v++)->data = &surface->rotate[0];
+    (v++)->data = &surface->rotate[1];
+    (v++)->data = &surface->rotate[2];
 
-    (v++)->data = &s[0];
-    (v++)->data = &s[1];
-    (v++)->data = &s[2];
+    (v++)->data = &surface->scale[0];
+    (v++)->data = &surface->scale[1];
+    (v++)->data = &surface->scale[2];
 
-    (v++)->data = &t[0];
-    (v++)->data = &t[1];
-    (v++)->data = &t[2];
+    (v++)->data = &surface->translate[0];
+    (v++)->data = &surface->translate[1];
+    (v++)->data = &surface->translate[2];
 
     (v++)->data = &scale;
-    (v++)->data = &angle;
+    (v++)->data = &surface->angle;
 
-    (v++)->data = &flip;
+    (v++)->data = &surface->flip;
 
     gts_file_assign_variables (fp, var);
     if (fp->type == GTS_ERROR)
       return;
 
     if (var[9].set)
-      s[0] = s[1] = s[2] = scale;
-    if (var[10].set && gts_vector_norm (r) == 0.) {
+      surface->scale[0] = surface->scale[1] = surface->scale[2] = scale;
+    if (var[10].set && gts_vector_norm (surface->rotate) == 0.) {
       gts_file_variable_error (fp, var, "angle",
 			       "a non-zero rotation vector must be specified");
       return;
     }
     
-    GtsMatrix * m = gts_matrix_translate (NULL, t);
-    if (angle != 0.) {
-      GtsMatrix * mr = gts_matrix_rotate (NULL, r, angle*M_PI/180.);
+    GtsMatrix * m = gts_matrix_translate (NULL, surface->translate);
+    if (surface->angle != 0.) {
+      GtsMatrix * mr = gts_matrix_rotate (NULL, surface->rotate, surface->angle*M_PI/180.);
       GtsMatrix * m1 = gts_matrix_product (m, mr);
       gts_matrix_destroy (m);
       gts_matrix_destroy (mr);
       m = m1;
     }
-    GtsMatrix * ms = gts_matrix_scale (NULL, s);
-    GtsMatrix * M = gts_matrix_product (m, ms);
+    GtsMatrix * ms = gts_matrix_scale (NULL, surface->scale);
+    if (surface->m)
+      gts_matrix_destroy (surface->m);
+    surface->m = gts_matrix_product (m, ms);
     gts_matrix_destroy (m);
     gts_matrix_destroy (ms);
-    gts_surface_foreach_vertex (surface->s, (GtsFunc) gts_point_transform, M);
-    gts_matrix_destroy (M);
 
-    if (flip)
-      gts_surface_foreach_face (surface->s, (GtsFunc) gts_triangle_revert, NULL);
+    if (surface->s) {
+      gts_surface_foreach_vertex (surface->s, (GtsFunc) gts_point_transform, surface->m);
+      gts_matrix_destroy (surface->m);
+      surface->m = NULL;
+      if (surface->flip)
+	gts_surface_foreach_face (surface->s, (GtsFunc) gts_triangle_revert, NULL);
+    }
+    else {
+      GtsMatrix * i = gts_matrix_inverse (surface->m);
+      gts_matrix_destroy (surface->m);
+      surface->m = i;
+    }
   }
 }
 
 static void surface_write (GtsObject * o, FILE * fp)
 {
-  fputs (" { ", fp);
-  GtsSurface * s = GFS_SURFACE (o)->s;
-  if (GFS_DOMAIN (gfs_object_simulation (o))->binary) {
-    gboolean binary = GTS_POINT_CLASS (s->vertex_class)->binary;
-    GTS_POINT_CLASS (s->vertex_class)->binary = TRUE;
-    gts_surface_write (s, fp);
-    GTS_POINT_CLASS (s->vertex_class)->binary = binary;
+  GfsSurface * surface = GFS_SURFACE (o);
+  if (surface->s) {
+    fputs (" { ", fp);
+    GtsSurface * s = surface->s;
+    if (GFS_DOMAIN (gfs_object_simulation (o))->binary) {
+      gboolean binary = GTS_POINT_CLASS (s->vertex_class)->binary;
+      GTS_POINT_CLASS (s->vertex_class)->binary = TRUE;
+      gts_surface_write (s, fp);
+      GTS_POINT_CLASS (s->vertex_class)->binary = binary;
+    }
+    else
+      gts_surface_write (s, fp);
+    fputc ('}', fp);
+  }
+  else if (surface->f) {
+    fputs (" (", fp);
+    gfs_function_write (surface->f, fp);
+    fputs (" )", fp);
+  }
+  if (surface->m) {
+    fputs (" {\n", fp);
+    if (gts_vector_norm (surface->translate) > 0.)
+      fprintf (fp, "  tx = %g ty = %g tz = %g\n",
+	       surface->translate[0], surface->translate[1], surface->translate[2]);
+    if (surface->scale[0] != 1. || surface->scale[1] != 1. || surface->scale[2] != 1.)
+      fprintf (fp, "  sx = %g sy = %g sz = %g\n",
+	       surface->scale[0], surface->scale[1], surface->scale[2]);
+    if (surface->angle != 0.)
+      fprintf (fp,
+	       "  rx = %g ry = %g rz = %g\n"
+	       "  angle = %g\n",
+	       surface->rotate[0], surface->rotate[1], surface->rotate[2],
+	       surface->angle);
+    if (surface->flip)
+      fputs ("  flip = 1\n", fp);
+    fputc ('}', fp);
   }
-  else
-    gts_surface_write (s, fp);
-  fputc ('}', fp);
 }
 
 static void surface_destroy (GtsObject * object)
 {
-  if (GFS_SURFACE (object)->s)
-    gts_object_destroy (GTS_OBJECT (GFS_SURFACE (object)->s));
+  GfsSurface * s = GFS_SURFACE (object);
+  if (s->s)
+    gts_object_destroy (GTS_OBJECT (s->s));
+  if (s->f)
+    gts_object_destroy (GTS_OBJECT (s->f));
+  if (s->m)
+    gts_matrix_destroy (s->m);
 
   (* GTS_OBJECT_CLASS (gfs_surface_class ())->parent_class->destroy) (object);
 }
@@ -195,6 +249,12 @@ static void gfs_surface_class_init (GtsObjectClass * klass)
   klass->destroy = surface_destroy;
 }
 
+static void gfs_surface_init (GfsSurface * s)
+{
+  s->scale[0] = 1.; s->scale[1] = 1.; s->scale[2] = 1.;
+  s->flip = FALSE;
+}
+
 GtsObjectClass * gfs_surface_class (void)
 {
   static GtsObjectClass * klass = NULL;
@@ -205,7 +265,7 @@ GtsObjectClass * gfs_surface_class (void)
       sizeof (GfsSurface),
       sizeof (GtsObjectClass),
       (GtsObjectClassInitFunc) gfs_surface_class_init,
-      (GtsObjectInitFunc) NULL,
+      (GtsObjectInitFunc) gfs_surface_init,
       (GtsArgSetFunc) NULL,
       (GtsArgGetFunc) NULL
     };
@@ -218,17 +278,19 @@ GtsObjectClass * gfs_surface_class (void)
 /**
  * gfs_surface_read:
  * @s: a #GfsSurface.
+ * @sim: a #GfsSimulation.
  * @fp: a #GtsFile.
  * 
  * Calls the read() method of @s.
  */
-void gfs_surface_read (GfsSurface * s, GtsFile * fp)
+void gfs_surface_read (GfsSurface * s, gpointer sim, GtsFile * fp)
 {
   GtsObject * o = (GtsObject *) s;
 
   g_return_if_fail (s != NULL);
   g_return_if_fail (fp != NULL);
 
+  o->reserved = sim;
   (* GTS_OBJECT (s)->klass->read) (&o, fp);
 }
 
@@ -249,6 +311,23 @@ void gfs_surface_write (GfsSurface * s, gpointer sim, FILE * fp)
   (* GTS_OBJECT (s)->klass->write) (GTS_OBJECT (s), fp);
 }
 
+/**
+ * gfs_surface_implicit_value:
+ * @s: an (implicit) #GfsSurface.
+ * @p: a #GtsPoint.
+ *
+ * Returns: the value of the implicit surface a location @p.
+ */
+gdouble gfs_surface_implicit_value (GfsSurface * s, GtsPoint p)
+{
+  g_return_val_if_fail (s != NULL, 0.);
+  g_return_val_if_fail (s->f != NULL, 0.);
+
+  if (s->m)
+    gts_point_transform (&p, s->m);
+  return (s->flip ? -1. : 1.)*gfs_function_spatial_value (s->f, (FttVector *)&p.x);
+}
+
 static void face_overlaps_box (GtsTriangle * t, gpointer * data)
 {
   GtsBBox * bb = data[0];
@@ -270,7 +349,7 @@ static void face_overlaps_box (GtsTriangle * t, gpointer * data)
  * @s: a #GfsSurface.
  * @flatten: if set to %TRUE, @cell is flattened in the z direction.
  *
- * Returns: a new #GfsSurface containing a subset of @s which may
+ * Returns: a (possibly new) #GfsSurface containing a subset of @s which may
  * intersect @cell or %NULL if @s does not intersect @cell.
  */
 GfsSurface * gfs_cell_is_cut (FttCell * cell, GfsSurface * s, gboolean flatten)
@@ -282,7 +361,6 @@ GfsSurface * gfs_cell_is_cut (FttCell * cell, GfsSurface * s, gboolean flatten)
     GtsSurface * s1 = NULL;
     gpointer data[2];
     GtsBBox bb;
-    
     ftt_cell_bbox (cell, &bb);
     if (flatten)
       bb.z1 = bb.z2 = 0.;
@@ -295,8 +373,10 @@ GfsSurface * gfs_cell_is_cut (FttCell * cell, GfsSurface * s, gboolean flatten)
     s2->s = s1;
     return s2;
   }
-
-  g_assert_not_implemented ();
+  else if (s->f)
+    return s;
+  g_assert_not_reached ();
+  return NULL;
 }
 
 static void cell_traverse_cut (FttCell * cell,
@@ -332,7 +412,8 @@ static void cell_traverse_cut (FttCell * cell,
        ((flags & FTT_TRAVERSE_LEAFS) != 0 && FTT_CELL_IS_LEAF (cell)) ||
        ((flags & FTT_TRAVERSE_NON_LEAFS) != 0 && !FTT_CELL_IS_LEAF (cell))))
     (* func) (cell, s1, data);
-  gts_object_destroy (GTS_OBJECT (s1));
+  if (s1 != s)
+    gts_object_destroy (GTS_OBJECT (s1));
 }
 
 /**
diff --git a/src/surface.h b/src/surface.h
index 13ab673..ee2e5ef 100644
--- a/src/surface.h
+++ b/src/surface.h
@@ -30,9 +30,14 @@ typedef struct _GfsSurface         GfsSurface;
 struct _GfsSurface {
   /*< private >*/
   GtsObject parent;
+  GtsVector rotate, scale, translate;
+  gdouble angle;
+  gboolean flip;
 
   /*< public >*/
   GtsSurface * s;
+  GfsFunction * f;
+  GtsMatrix * m;
 };
 
 #define GFS_SURFACE(obj)            GTS_OBJECT_CAST (obj,\
@@ -43,10 +48,13 @@ struct _GfsSurface {
 
 GtsObjectClass *   gfs_surface_class          (void);
 void               gfs_surface_read           (GfsSurface * s, 
+					       gpointer sim,
 					       GtsFile * fp);
 void               gfs_surface_write          (GfsSurface * s,
 					       gpointer sim,
 					       FILE * fp);
+gdouble            gfs_surface_implicit_value (GfsSurface * s, 
+					       GtsPoint p);
 GfsSurface *       gfs_cell_is_cut            (FttCell * cell,
 					       GfsSurface * s,
 					       gboolean flatten);
diff --git a/src/utils.c b/src/utils.c
index c7b7af9..b887f99 100644
--- a/src/utils.c
+++ b/src/utils.c
@@ -195,6 +195,7 @@ struct _GfsFunction {
   GfsVariable * v;
   GfsDerivedVariable * dv;
   gdouble val;
+  gboolean spatial;
 };
 
 static GtsSurface * read_surface (gchar * name, GtsFile * fp)
@@ -406,6 +407,10 @@ GString * gfs_function_expression (GtsFile * fp, gboolean * is_expression)
       else {
 	if (c == '(') scope++;
 	else if (c == ')') scope--;
+	if (scope < 0) {
+	  fp->next_token = c;
+	  break;
+	}
 	g_string_append_c (expr, c);
 	c = gts_file_getc (fp);
       }
@@ -540,7 +545,7 @@ static void function_read (GtsObject ** o, GtsFile * fp)
 	return;
       }
     }
-    else if (fp->type == GTS_STRING) {
+    else if (fp->type == GTS_STRING && !f->spatial) {
       if (strlen (f->expr->str) > 3 &&
 	  !strcmp (&(f->expr->str[strlen (f->expr->str) - 4]), ".gts")) {
 	if ((f->s = read_surface (f->expr->str, fp)) == NULL)
@@ -592,6 +597,10 @@ static void function_read (GtsObject ** o, GtsFile * fp)
 	   "#include <math.h>\n"
 	   "#include <gfs.h>\n",
 	   fin);
+    if (f->spatial)
+      fputs ("#include <gerris/spatial.h>\n", fin);
+    else
+      fputs ("#include <gerris/function.h>\n", fin);
     i = sim->globals;
     while (i) {
       fprintf (fin, "#line %d \"GfsGlobal\"\n", GFS_GLOBAL (i->data)->line);
@@ -599,84 +608,74 @@ static void function_read (GtsObject ** o, GtsFile * fp)
       fputc ('\n', fin);
       i = i->next;
     }
-    fputs ("typedef double (* Func) (const FttCell * cell,\n"
-	   "                         const FttCellFace * face,\n"
-	   "                         GfsSimulation * sim,\n"
-	   "                         gpointer data);\n"
-	   "static double Dirichlet = 1.;\n"
-	   "static double Neumann = 0.;\n"
-	   "static GfsSimulation * gsim = NULL;\n"
-	   "static FttCell * gcell = NULL;\n"
-	   "static double dd (const gchar * name, FttComponent c) {\n"
-	   "  GfsVariable * v = gfs_variable_from_name (GFS_DOMAIN (gsim)->variables, name);\n"
-	   "  if (v == NULL)\n"
-	   "    return 0.;\n"
-	   "  g_return_val_if_fail (gcell != NULL, 0.);\n"
- 	   "  return gfs_center_gradient (gcell, c, v->i)/ftt_cell_size (gcell);\n"
-	   "}\n"
-	   "static double dx (const gchar * name) { return dd (name, FTT_X); }\n"
-	   "static double dy (const gchar * name) { return dd (name, FTT_Y); }\n"
-  #if !FTT_2D
-	   "static double dz (const gchar * name) { return dd (name, FTT_Z); }\n"
-  #endif /* 3D */
-	   "double f (FttCell * cell, FttCellFace * face, GfsSimulation * sim) {\n"
-	   "  gsim = sim; gcell = cell;\n"
-	   , fin);
-    i = domain->variables;
-    while (i) {
-      if (GFS_VARIABLE1 (i->data)->name && 
-	  find_identifier (f->expr->str, GFS_VARIABLE1 (i->data)->name))
-	lv = g_slist_prepend (lv, i->data);
-      i = i->next;
-    }
-    i = domain->derived_variables;
-    while (i) {
-      GfsDerivedVariable * v = i->data;
-      if (find_identifier (f->expr->str, v->name))
-	ldv = g_slist_prepend (ldv, v);
-      i = i->next;
-    }
-    if (lv || ldv) {
-      GSList * i = lv;
-
+    if (f->spatial)
+      fputs ("double f (double x, double y, double z) {\n"
+	     "  _x = x; _y = y;\n", 
+	     fin);
+    else {
+      fputs ("typedef double (* Func) (const FttCell * cell,\n"
+	     "                         const FttCellFace * face,\n"
+	     "                         GfsSimulation * sim,\n"
+	     "                         gpointer data);\n"
+	     "double f (FttCell * cell, FttCellFace * face, GfsSimulation * sim) {\n"
+	     "  _sim = sim; _cell = cell;\n",
+	     fin);
+      i = domain->variables;
       while (i) {
-	GfsVariable * v = i->data;
-	fprintf (fin, "  double %s;\n", v->name);
+	if (GFS_VARIABLE1 (i->data)->name && 
+	    find_identifier (f->expr->str, GFS_VARIABLE1 (i->data)->name))
+	  lv = g_slist_prepend (lv, i->data);
 	i = i->next;
       }
-      i = ldv;
+      i = domain->derived_variables;
       while (i) {
 	GfsDerivedVariable * v = i->data;
-	fprintf (fin, "  double %s;\n", v->name);
+	if (find_identifier (f->expr->str, v->name))
+	  ldv = g_slist_prepend (ldv, v);
 	i = i->next;
       }
-      if (lv) {
-	fputs ("  if (cell) {\n", fin);
-	i = lv;
-	while (i) {
-	  GfsVariable * v = i->data;
-	  fprintf (fin, "    %s = GFS_VARIABLE (cell, %d);\n", v->name, v->i);
-	  i = i->next;
-	}
-	fputs ("  } else {\n", fin);
-	i = lv;
+      if (lv || ldv) {
+	GSList * i = lv;
+
 	while (i) {
 	  GfsVariable * v = i->data;
-	  fprintf (fin, "    %s = gfs_face_interpolated_value (face, %d);\n", v->name, v->i);
+	  fprintf (fin, "  double %s;\n", v->name);
 	  i = i->next;
 	}
-	fputs ("  }\n", fin);
-	g_slist_free (lv);
-      }
-      if (ldv) {
 	i = ldv;
 	while (i) {
 	  GfsDerivedVariable * v = i->data;
-	  fprintf (fin, "  %s = (* (Func) %p) (cell, face, sim, ((GfsDerivedVariable *) %p)->data);\n", 
-		   v->name, v->func, v);
+	  fprintf (fin, "  double %s;\n", v->name);
 	  i = i->next;
 	}
-	g_slist_free (ldv);
+	if (lv) {
+	  fputs ("  if (cell) {\n", fin);
+	  i = lv;
+	  while (i) {
+	    GfsVariable * v = i->data;
+	    fprintf (fin, "    %s = GFS_VARIABLE (cell, %d);\n", v->name, v->i);
+	    i = i->next;
+	  }
+	  fputs ("  } else {\n", fin);
+	  i = lv;
+	  while (i) {
+	    GfsVariable * v = i->data;
+	    fprintf (fin, "    %s = gfs_face_interpolated_value (face, %d);\n", v->name, v->i);
+	    i = i->next;
+	  }
+	  fputs ("  }\n", fin);
+	  g_slist_free (lv);
+	}
+	if (ldv) {
+	  i = ldv;
+	  while (i) {
+	    GfsDerivedVariable * v = i->data;
+	    fprintf (fin, "  %s = (* (Func) %p) (cell, face, sim, ((GfsDerivedVariable *) %p)->data);\n", 
+		     v->name, v->func, v);
+	    i = i->next;
+	  }
+	  g_slist_free (ldv);
+	}
       }
     }
     fprintf (fin, "#line %d \"GfsFunction\"\n", fp->line);
@@ -770,6 +769,13 @@ GfsFunctionClass * gfs_function_class (void)
   return klass;
 }
 
+/**
+ * gfs_function_new:
+ * @klass: a #GfsFunctionClass.
+ * @val: a value.
+ *
+ * Returns: a new #GfsFunction with constant value @val.
+ */
 GfsFunction * gfs_function_new (GfsFunctionClass * klass, 
 				gdouble val)
 {
@@ -989,6 +995,55 @@ void gfs_function_write (GfsFunction * f, FILE * fp)
   (* GTS_OBJECT (f)->klass->write) (GTS_OBJECT (f), fp);
 }
 
+/* GfsFunctionSpatial: object */
+
+static void gfs_function_spatial_init (GfsFunction * f)
+{
+  f->spatial = TRUE;
+}
+
+GfsFunctionClass * gfs_function_spatial_class (void)
+{
+  static GfsFunctionClass * klass = NULL;
+
+  if (klass == NULL) {
+    GtsObjectClassInfo gfs_function_info = {
+      "GfsFunctionSpatial",
+      sizeof (GfsFunction),
+      sizeof (GfsFunctionClass),
+      (GtsObjectClassInitFunc) NULL,
+      (GtsObjectInitFunc) gfs_function_spatial_init,
+      (GtsArgSetFunc) NULL,
+      (GtsArgGetFunc) NULL
+    };
+    klass = gts_object_class_new (GTS_OBJECT_CLASS (gfs_function_class ()),
+				  &gfs_function_info);
+  }
+
+  return klass;
+}
+
+typedef gdouble (* GfsFunctionSpatialFunc) (double x, double y, double z);
+
+/**
+ * gfs_function_spatial_value:
+ * @f: a #GfsFunction.
+ * @p: a #FttVector.
+ *
+ * Returns: the value of function @f at location @p.
+ */
+gdouble gfs_function_spatial_value (GfsFunction * f, FttVector * p)
+{
+  g_return_val_if_fail (f != NULL, 0.);
+  g_return_val_if_fail (GFS_IS_FUNCTION_SPATIAL (f), 0.);
+  g_return_val_if_fail (p != NULL, 0.);
+
+  if (f->f)
+    return (* (GfsFunctionSpatialFunc) f->f) (p->x, p->y, p->z);
+  else
+    return f->val;
+}
+
 /**
  * gfs_object_class_from_name:
  * @name: the name of the class.
diff --git a/src/utils.h b/src/utils.h
index 80d3c34..a19c5f7 100644
--- a/src/utils.h
+++ b/src/utils.h
@@ -85,6 +85,15 @@ void               gfs_function_write       (GfsFunction * f,
 					     FILE * fp);
 GString *          gfs_function_expression  (GtsFile * fp, 
 					     gboolean * is_expression);
+
+/* GfsFunctionSpatial: Header */
+
+#define GFS_IS_FUNCTION_SPATIAL(obj)         (gts_object_is_from_class (obj,\
+					      gfs_function_spatial_class ()))
+
+GfsFunctionClass * gfs_function_spatial_class (void);
+gdouble            gfs_function_spatial_value (GfsFunction * f, FttVector * p);
+
 GtsObjectClass *   gfs_object_class_from_name (const gchar * name);
 
 void               gfs_eigenvalues          (gdouble a[FTT_DIMENSION][FTT_DIMENSION],
diff --git a/test/boundaries/boundaries.gfs b/test/boundaries/boundaries.gfs
index cc3be9d..d5a1bd0 100644
--- a/test/boundaries/boundaries.gfs
+++ b/test/boundaries/boundaries.gfs
@@ -30,17 +30,19 @@
 # Generated files: convergence.tex
 #
 1 0 GfsSimulation GfsBox GfsGEdge {} {
-  Time { iend = 0 end = 1 }
-  AdvectionParams { scheme = none }
-  ApproxProjectionParams { tolerance = 1e-6 }
-  Refine LEVEL
-  Solid boundaries.gts
-  Init {} { U = 1 }
-  OutputSimulation { start = end } sim-LEVEL {
-    variables = U,V,P
-  }
+    Time { iend = 0 end = 1 }
+    AdvectionParams { scheme = none }
+    ApproxProjectionParams { tolerance = 1e-6 }
+    Refine LEVEL
+    Solid (ellipse(0.25, 0.25, 0.1, 0.1))
+    Solid (ellipse(-0.25, 0.125, 0.15, 0.1))
+    Solid (ellipse(0., -0.25, 0.2, 0.1))
+    Init {} { U = 1 }
+    OutputSimulation { start = end } sim-LEVEL {
+	variables = U,V,P
+    }
 }
 GfsBox {
-  left = Boundary { BcDirichlet U 1 }
-  right = Boundary { BcDirichlet U 1 }
+    left = Boundary { BcDirichlet U 1 }
+    right = Boundary { BcDirichlet U 1 }
 }
diff --git a/test/boundaries/boundaries.sh b/test/boundaries/boundaries.sh
index 8dafe10..e87c5f2 100644
--- a/test/boundaries/boundaries.sh
+++ b/test/boundaries/boundaries.sh
@@ -1,5 +1,4 @@
 if ! $donotrun; then
-    shapes almgren > boundaries.gts
     for level in 7 8 9; do
 	if sed "s/LEVEL/$level/g" < $1 | \
            gerris2D -; then :
diff --git a/test/boundaries/orderU.ref b/test/boundaries/orderU.ref
index d1da241..34320a7 100644
--- a/test/boundaries/orderU.ref
+++ b/test/boundaries/orderU.ref
@@ -1,2 +1,2 @@
-7 3.765e-04 2.149e-03 6.698e-02
-8 1.181e-04 9.742e-04 4.444e-02
+7 5.168e-04 2.198e-03 6.725e-02
+8 1.412e-04 9.084e-04 4.422e-02
diff --git a/test/boundaries/orderV.ref b/test/boundaries/orderV.ref
index b9efc5d..3f06870 100644
--- a/test/boundaries/orderV.ref
+++ b/test/boundaries/orderV.ref
@@ -1,2 +1,2 @@
-7 4.151e-04 1.750e-03 4.910e-02
-8 1.269e-04 7.389e-04 5.034e-02
+7 4.849e-04 1.947e-03 5.346e-02
+8 1.277e-04 7.183e-04 3.567e-02
diff --git a/test/boundaries/orderfU.ref b/test/boundaries/orderfU.ref
index d5ea7ff..909adb3 100644
--- a/test/boundaries/orderfU.ref
+++ b/test/boundaries/orderfU.ref
@@ -1,2 +1,2 @@
-7 2.247e-04 4.772e-04 6.828e-03
-8 6.153e-05 1.533e-04 5.224e-03
+7 3.623e-04 6.652e-04 8.708e-03
+8 9.237e-05 1.765e-04 3.870e-03
diff --git a/test/boundaries/orderfV.ref b/test/boundaries/orderfV.ref
index cd7860b..150019d 100644
--- a/test/boundaries/orderfV.ref
+++ b/test/boundaries/orderfV.ref
@@ -1,2 +1,2 @@
-7 2.961e-04 7.718e-04 8.718e-03
-8 8.136e-05 2.569e-04 3.745e-03
+7 3.487e-04 8.671e-04 9.910e-03
+8 8.572e-05 2.579e-04 4.012e-03
diff --git a/test/channel/channel.gfs b/test/channel/channel.gfs
index c60e8c7..8c37288 100644
--- a/test/channel/channel.gfs
+++ b/test/channel/channel.gfs
@@ -23,22 +23,33 @@
 #
 # Author: St\'ephane Popinet
 # Command: sh channel.sh channel.gfs
-# Version: 0.6.4
+# Version: 1.1.0
 # Required files: channel.sh orderU.ref orderfU.ref orderV.ref orderfV.ref
 # Running time: 3 minutes
 # Generated files: convergence.tex
 #
 4 3 GfsSimulation GfsBox GfsGEdge {} {
-  Time { end = 1 }
-  AdvectionParams { cfl = 0.9 }
-  ProjectionParams { tolerance = 1e-6 }
-  ApproxProjectionParams { tolerance = 1e-6 }
-  Refine LEVEL
-  Solid channel.gts
-  Init {} { U = 1 }
-  OutputSimulation { start = end } sim-LEVEL {
-    variables = U,V,P
-  }
+    Time { end = 1 }
+    AdvectionParams { cfl = 0.9 }
+    ProjectionParams { tolerance = 1e-6 }
+    ApproxProjectionParams { tolerance = 1e-6 }
+    Refine LEVEL
+    Global {
+	double channel (double x) {
+	    double y1 = 0.2/4.;
+	    double y2 = 1e-6/4.;
+	    
+	    return x <= -0.25 ? y1 : 
+	           x < 0.25 ? y2 + 0.5*(y1 - y2)*(1. + cos (2.*M_PI*(x + 0.25))) : 
+		   y2;
+	}
+    }
+    Solid (0.125 - channel(x) - y) { scale = 4 tx = 1.5 }
+    Solid (y + 0.125 - channel(x)) { scale = 4 tx = 1.5 }
+    Init {} { U = 1 }
+    OutputSimulation { start = end } sim-LEVEL {
+	variables = U,V,P
+    }
 }
 GfsBox { left = Boundary { BcDirichlet U 1 } }
 GfsBox {}
diff --git a/test/circle/circle.gfs b/test/circle/circle.gfs
index cbcf268..c90ba0f 100644
--- a/test/circle/circle.gfs
+++ b/test/circle/circle.gfs
@@ -46,15 +46,15 @@
 # \end{figure}
 #
 # Author: St\'ephane Popinet
-# Command: shapes -n 500 ellipse > shape.gts && sh circle.sh circle.gfs
-# Version: 0.8.0
+# Command: sh circle.sh circle.gfs
+# Version: 1.1.0
 # Required files: circle.sh res-7.ref error.ref order.ref solution.gfv
 # Generated files: residual.eps rate.eps error.eps order.eps solution.eps
 #
 1 0 GfsPoisson GfsBox GfsGEdge {} {
   Time { iend = 10 }
   Refine LEVEL
-  Solid shape.gts
+  Solid (ellipse(0,0,0.25,0.25))
   ApproxProjectionParams { nrelax = 4 tolerance = 1e-30 erelax = 2 }
   Init {} {
     Div = {

-- 
Gerris Flow Solver