ie > i.e.

Arrangement_on_surface_2/demo/Arrangement_on_surface_2/ArrangementPainterOstream.h

@@ -232,7 +232,7 @@ protected: // methods
   // Assumes that clippingRect is valid.
   std::vector< X_monotone_curve_2 > visibleParts( X_monotone_curve_2 curve );
 
-  // keep only the intersection points ie. throw out overlapping curve segments
+  // keep only the intersection points i.e. throw out overlapping curve segments
   void filterIntersectionPoints( std::vector< CGAL::Object >& res );
 
 protected: // members

Combinatorial_map/include/CGAL/Combinatorial_map.h

@@ -969,7 +969,7 @@ namespace CGAL {
     { return mnb_used_marks; }
 
     /** Test if a given mark is reserved.
-     *  @return true iff the mark is reserved (ie in used).
+     *  @return true iff the mark is reserved (i.e. in used).
      */
     bool is_reserved(size_type amark) const
     {

Combinatorial_map/include/CGAL/Combinatorial_map/internal/Combinatorial_map_internal_functors.h

@@ -64,7 +64,7 @@
  *   darts have the same info.
  *
  * internal::Test_is_same_attribute_functor<Map1, Map2> to test if two
- *   i-attributes of two darts are isomorphic (ie they have the same info).
+ *   i-attributes of two darts are isomorphic (i.e. they have the same info).
  *
  * internal::Test_is_same_attribute_point_functor<Map1, Map2, i> to test if
  *   the point of two i-attributes are equal.
@@ -208,7 +208,7 @@ template<typename CMap>
 struct Test_is_valid_attribute_functor
 {
   /** Test the validity of a i-cell-attribute.
-   * ie all the darts belonging to a i-cell are linked to the same attribute.
+   * In other words, all the darts belonging to a i-cell are linked to the same attribute.
    * @param adart a dart.
    * @param amark a mark used to mark darts of the i-cell.
    * @return true iff all the darts of the i-cell link to the same attribute.

Generalized_map/include/CGAL/GMap_dart_iterators.h

@@ -134,7 +134,7 @@ namespace CGAL {
   //****************************************************************************
   /* Class CMap_dart_iterator_basic_of_two_alpha<Ai,delta>: to iterate
    * on the darts of the orbit <Ai,Ai+delta>: Ai<Ai+delta<=dimension.
-   * This general case if for delta>1 (ie at most 4 darts).
+   * This general case if for delta>1 (i.e. at most 4 darts).
    * Basic classes do not guaranty correct marks (i.e. do not unmark darts in
    * the destructor, possible problem with the rewind). If you are not sure,
    * use CMap_dart_iterator_basic_of_two_alpha.
@@ -445,7 +445,7 @@ namespace CGAL {
   /* Class CMap_dart_iterator_basic_of_three_alpha<Ai,delta1,delta2>: to iterate
    * on the darts of the orbit <Ai,Ai+delta1,Ai+delta2>:
    * Ai<Ai+delta1<Ai+delta2<=dimension.
-   * This general case if for delta1>1 and delta2>1 (ie at most 8 darts).
+   * This general case if for delta1>1 and delta2>1 (i.e. at most 8 darts).
    * Basic classes do not guaranty correct marks (i.e. do not unmark darts in
    * the destructor, possible problem with the rewind). If you are not sure,
    * use CMap_dart_iterator_basic_of_two_alpha.

Generalized_map/include/CGAL/Generalized_map.h

@@ -876,7 +876,7 @@ namespace CGAL {
     { return mnb_used_marks; }
 
     /** Test if a given mark is reserved.
-     *  @return true iff the mark is reserved (ie in used).
+     *  @return true iff the mark is reserved (i.e. in used).
      */
     bool is_reserved(size_type amark) const
     {

Optimal_transportation_reconstruction_2/include/CGAL/Optimal_transportation_reconstruction_2.h

@@ -234,7 +234,7 @@ public:
   /*!
           If `sample_size == 0`, the simplification is performed using an exhaustive priority queue.
           If `sample_size` is strictly positive the simplification is performed using a
-          multiple choice approach, ie, a best-choice selection in a random sample of
+          multiple choice approach, i.e., a best-choice selection in a random sample of
           edge collapse operators, of size `sample_size`. A typical value for the sample
           size is 15, but this value must be enlarged when targeting a very coarse simplification.
           \param sample_size If `sample_size != 0`, the size of the random sample replaces the priority queue.

TDS_3/include/CGAL/Triangulation_data_structure_3.h

@@ -1736,7 +1736,7 @@ create_star_3(Vertex_handle v, Cell_handle c, int li, int prev_ind2)
       Cell_handle nnn = n->neighbor(next_around_edge(jj2, jj1));
       int zzz = nnn->index(vvv);
       if (nnn == cur) {
-        // Neighbor relation is reciprocal, ie
+        // Neighbor relation is reciprocal, i.e.
         // the cell we are looking for is not yet created.
         nnn = create_star_3(v, nnn, zz, zzz);
       }
@@ -1794,7 +1794,7 @@ recursive_create_star_3(Vertex_handle v, Cell_handle c, int li,
       Cell_handle nnn = n->neighbor(next_around_edge(jj2, jj1));
       int zzz = nnn->index(vvv);
       if (nnn == cur) {
-        // Neighbor relation is reciprocal, ie
+        // Neighbor relation is reciprocal, i.e.
         // the cell we are looking for is not yet created.
         nnn = recursive_create_star_3(v, nnn, zz, zzz,depth+1);
       }
@@ -1855,7 +1855,7 @@ non_recursive_create_star_3(Vertex_handle v, Cell_handle c, int li, int prev_ind
         Cell_handle nnn = n->neighbor(next_around_edge(jj2, jj1));
         int zzz = nnn->index(vvv);
         if (nnn == cur) {
-          // Neighbor relation is reciprocal, ie
+          // Neighbor relation is reciprocal, i.e.
           // the cell we are looking for is not yet created.
           //re-run the loop
           adjacency_info_stack.push( iAdjacency_info(zzz,cnew,ii,c,li,prev_ind2) );
@@ -2344,7 +2344,7 @@ flip( Cell_handle c, int i )
   int in = n->index(c);
 
   // checks that the facet is flippable,
-  // ie the future edge does not already exist
+  // i.e. the future edge does not already exist
   if (is_edge(c->vertex(i), n->vertex(in)))
       return false;
 
@@ -2367,7 +2367,7 @@ flip_flippable(Cell_handle c, int i )
   int in = n->index(c);
 
   // checks that the facet is flippable,
-  // ie the future edge does not already exist
+  // i.e. the future edge does not already exist
   CGAL_expensive_precondition( !is_edge(c->vertex(i),
                                                       n->vertex(in)));
   flip_really(c,i,n,in);
@@ -2429,7 +2429,7 @@ flip( Cell_handle c, int i, int j )
                                    && (number_of_vertices() >= 6) );
   CGAL_expensive_precondition( is_cell(c) );
 
-  // checks that the edge is flippable ie degree 3
+  // checks that the edge is flippable, i.e. degree 3
   int degree = 0;
   Cell_circulator ccir = incident_cells(c,i,j);
   Cell_circulator cdone = ccir;
@@ -2479,7 +2479,7 @@ flip_flippable( Cell_handle c, int i, int j )
                                    && (number_of_vertices() >= 6) );
   CGAL_expensive_precondition( is_cell(c) );
 
-  // checks that the edge is flippable ie degree 3
+  // checks that the edge is flippable, i.e. degree 3
   CGAL_precondition_code( int degree = 0; );
   CGAL_precondition_code
     ( Cell_circulator ccir = incident_cells(c,i,j); );

Triangulation_3/demo/Triangulation_3/Viewer.cpp

@@ -2040,7 +2040,7 @@ void Viewer::mouseReleaseEvent(QMouseEvent *event)
             } else {
                 displayMessage( tr("No point is selected.") );
             }
-        } else {  /* select multiple points, ie. selection window > 1 */
+        } else {  /* select multiple points, i.e. selection window > 1 */
             // define selection window
             if( m_rectSel.width() < 10 )
                 setSelectRegionWidth( 10 );

Triangulation_3/include/CGAL/Delaunay_triangulation_3.h

@@ -1542,7 +1542,7 @@ side_of_circle(Cell_handle c, int i, const Point& p, bool perturb) const
   if(dimension() == 2)
   {
     CGAL_precondition(i == 3);
-    // the triangulation is supposed to be valid, ie the facet
+    // the triangulation is supposed to be valid, i.e. the facet
     // with vertices 0 1 2 in this order is positively oriented
     if(! c->has_vertex(infinite_vertex(), i3))
       return coplanar_side_of_bounded_circle(c->vertex(0)->point(),

Triangulation_3/include/CGAL/Regular_triangulation_3.h

@@ -2148,7 +2148,7 @@ side_of_power_circle(Cell_handle c, int i, const Weighted_point& p,
   if(dimension() == 2)
   {
     CGAL_precondition(i == 3);
-    // the triangulation is supposed to be valid, ie the facet
+    // the triangulation is supposed to be valid, i.e. the facet
     // with vertices 0 1 2 in this order is positively oriented
     if(! c->has_vertex(infinite_vertex(), i3))
       return Bounded_side(side_of_oriented_power_circle(c->vertex(0)->point(),

Weights/include/CGAL/Weights/tangent_weights.h

@@ -401,7 +401,7 @@ public:
       return FT(0);
 
     FT weight = FT(0);
-    if (is_border_edge(he, m_pmesh)) // ie, opp(he, pmesh) is a border halfedge
+    if (is_border_edge(he, m_pmesh)) // i.e., opp(he, pmesh) is a border halfedge
     {
       const halfedge_descriptor h1 = next(he, m_pmesh);