Integrate the reduced convolution method into test_minkowski_sum_with_holes

Also, put minkowski_sum_reduced_convolution_2(pwh, pwh) into the API.

Minkowski_sum_2/include/CGAL/Minkowski_sum_2/Minkowski_sum_by_reduced_convolution_2.h

@@ -2,6 +2,7 @@
 #define CGAL_MINKOWSKI_SUM_BY_REDUCED_CONVOLUTION_2_H
 
 #include <CGAL/basic.h>
+#include <CGAL/connect_holes.h>
 #include <CGAL/Arrangement_with_history_2.h>
 #include <CGAL/Arr_segment_traits_2.h>
 
@@ -28,6 +29,7 @@ private:
 
   // Basic types:
   typedef CGAL::Polygon_2<Kernel, Container> Polygon_2;
+  typedef CGAL::Polygon_with_holes_2<Kernel, Container> Polygon_with_holes_2;
   typedef typename Kernel::Point_2 Point_2;
   typedef typename Kernel::Vector_2 Vector_2;
   typedef typename Kernel::Direction_2 Direction_2;
@@ -83,6 +85,36 @@ public:
     CGAL_precondition(pgn1.orientation() == COUNTERCLOCKWISE);
     CGAL_precondition(pgn2.orientation() == COUNTERCLOCKWISE);
 
+    common_operator(pgn1, pgn2, outer_boundary, holes);
+  }
+
+  template <class OutputIterator>
+  void operator()(const Polygon_with_holes_2 &pgn1, const Polygon_with_holes_2 &pgn2,
+                  Polygon_2 &outer_boundary, OutputIterator holes) const
+  {
+    Polygon_2 p_pseudo_simple, q_pseudo_simple;
+
+    std::list<Point_2> points;
+    connect_holes(pgn1, std::back_inserter(points));
+    for (typename std::list<Point_2>::iterator it = points.begin(); it != points.end(); it++) {
+      p_pseudo_simple.push_back(*it);
+    }
+
+    points.clear();
+    connect_holes(pgn2, std::back_inserter(points));
+    for (typename std::list<Point_2>::iterator it = points.begin(); it != points.end(); it++) {
+      q_pseudo_simple.push_back(*it);
+    }
+
+    common_operator(p_pseudo_simple, q_pseudo_simple, outer_boundary, holes);
+  }
+
+private:
+
+  template <class OutputIterator>
+  void common_operator(const Polygon_2 &pgn1, const Polygon_2 &pgn2,
+                  Polygon_2 &outer_boundary, OutputIterator holes) const
+  {
     // Initialize collision detector. It operates on pgn2 and on the inversed pgn1:
     const Polygon_2 inversed_pgn1 = transform(Aff_transformation_2<Kernel>(SCALING, -1), pgn1);
     AABB_collision_detector_2<Kernel, Container> collision_detector(pgn2, inversed_pgn1);
@@ -106,8 +138,6 @@ public:
     }
   }
 
-private:
-
   // Builds the reduced convolution using a fiber grid approach. For each
   // starting vertex, try to add two outgoing next states. If a visited
   // vertex is reached, then do not explore further. This is a BFS-like

Minkowski_sum_2/include/CGAL/minkowski_sum_2.h

@@ -62,6 +62,34 @@ minkowski_sum_reduced_convolution_2(const Polygon_2<Kernel_, Container_>& pgn1,
                                                   sum_holes.end()));
 }
 
+/*!
+ * Computes the Minkowski sum \f$ P \oplus Q\f$ of the two given
+ * polygons-with-holes.
+ * The function computes the reduced convolution of the two polygons and
+ * extracts those loops of the convolution which are part of the Minkowsi
+ * sum. This method works very efficiently, regardless of whether `P` and
+ * `Q` are convex or non-convex.
+ * The result is also represented as a polygon with holes.
+*/
+template <class Kernel_, class Container_>
+Polygon_with_holes_2<Kernel_, Container_>
+minkowski_sum_reduced_convolution_2(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
+                                    const Polygon_with_holes_2<Kernel_, Container_>& pgn2)
+{
+  typedef Kernel_                                    Kernel;
+  typedef Container_                                 Container;
+
+  Minkowski_sum_by_reduced_convolution_2<Kernel, Container> mink_sum;
+  Polygon_2<Kernel,Container>                               sum_bound;
+  std::list<Polygon_2<Kernel,Container> >                   sum_holes;
+
+  mink_sum (pgn1, pgn2, sum_bound, std::back_inserter(sum_holes));
+
+  return (Polygon_with_holes_2<Kernel,Container> (sum_bound,
+                                                  sum_holes.begin(),
+                                                  sum_holes.end()));
+}
+
 /*!
  * Compute the Minkowski sum of two simple polygons using the (full)
  * convolution method.

Minkowski_sum_2/test/Minkowski_sum_2/test_minkowski_sum.cpp

@@ -40,8 +40,8 @@ static const char* strategy_names[] = {
   "small-side angle-bisector decomposition",
   "optimal convex decomposition",
   "Hertel-Mehlhorn decomposition",
-  "Greene decomosition",
-  "Vertical decomosition"
+  "Greene decomposition",
+  "vertical decomposition"
 };
 
 Polygon_with_holes_2 compute_minkowski_sum_2(Polygon_2& p, Polygon_2& q,

Minkowski_sum_2/test/Minkowski_sum_2/test_minkowski_sum_with_holes.cmd

@@ -1,4 +1,4 @@
-vt
+rvt
 data/pwh1.dat data/pwh1.dat
 data/pwh2.dat data/pwh2.dat
 data/pwh1.dat data/pwh2.dat

Minkowski_sum_2/test/Minkowski_sum_2/test_minkowski_sum_with_holes.cpp

@@ -24,13 +24,15 @@ bool are_equal(const Polygon_with_holes_2& ph1,
 }
 
 typedef enum {
+  REDUCED_CONVOLUTION,
   VERTICAL_DECOMP,
   TRIANGULATION_DECOMP
 } Strategy;
 
 static const char* strategy_names[] = {
-  "Vertical decomosition",
-  "Constrained triangulation decomosition"
+  "reduced convolution",
+  "vertical decomposition",
+  "constrained triangulation decomposition"
 };
 
 Polygon_with_holes_2 compute_minkowski_sum_2(Polygon_with_holes_2& p,
@@ -38,6 +40,10 @@ Polygon_with_holes_2 compute_minkowski_sum_2(Polygon_with_holes_2& p,
                                              Strategy strategy)
 {
   switch (strategy) {
+   case REDUCED_CONVOLUTION:
+    {
+     return minkowski_sum_reduced_convolution_2(p, q);
+    }
    case VERTICAL_DECOMP:
     {
      CGAL::Polygon_vertical_decomposition_2<Kernel> decomp;
@@ -70,6 +76,10 @@ int main(int argc, char* argv[])
   std::list<Strategy> strategies;
   for (int i = 0; i < strlen(argv[1]); ++i) {
     switch (argv[1][i]) {
+      case 'r':
+        strategies.push_back(REDUCED_CONVOLUTION);
+        break;
+
       case 'v':
         strategies.push_back(VERTICAL_DECOMP);
         break;