Optimized view map calculation by Alexander Beels.

* View map calculation has been intensively optimized for speed by
means of:

1) new spatial grid data structures (SphericalGrid for perspective
cameras and BoxGrid for orthographic cameras; automatically switched
based on the camera type);

2) a heuristic grid density calculation algorithm; and

3) new line visibility computation algorithms: A "traditional"
algorithm for emulating old visibility algorithms, and a "cumulative"
algorithm for improved, more consistent line visibility, both exploiting
the new spatial grid data structures for fast ray casting.

A new option "Raycasting Algorithm" was added to allow users to choose
a ray casting (line visibility) algorithm.  Available choices are:

- Normal Ray Casting
- Fast Ray Casting
- Very Fast Ray Casting
- Culled Traditional Visibility Detection
- Unculled Traditional Visibility Detection
- Culled Cumulative Visibility Detection
- Unculled Cumulative Visibility Detection

The first three algorithms are those available in the original
Freestyle (the "normal" ray casting was used unconditionally, though).
The "fast" and "very fast" ray casting algorithms achieve a faster
calculation at the cost of less visibility accuracy.

The last four are newly introduced optimized options.  The culled
versions of the new algorithms will exclude from visibility
calculation those faces that lay outside the camera, which leads to a
faster view map construction.  The unculled counterparts will take all
faces into account.  The unculled visibility algorithms are useful
when culling affects stroke chaining.

The recommended options for users are the culled/unculled cumulative
visibility algorithms.  These options are meant to replace the old
algorithms in the future.

Performance improvements over the old algorithms depend on the scenes
to be rendered.

* Silhouette detection has also been considerably optimized for speed.

Performance gains by this optimization do not depend on scenes.

* Improper handling of error conditions in the view map construction
was fixed.

10 files changed, 325 insertions, 52 deletions

diff --git a/source/blender/freestyle/intern/geometry/GeomUtils.cpp b/source/blender/freestyle/intern/geometry/GeomUtils.cpp
index 2169bce0364..853f8cf82b5 100755
--- a/source/blender/freestyle/intern/geometry/GeomUtils.cpp
+++ b/source/blender/freestyle/intern/geometry/GeomUtils.cpp
@@ -370,9 +370,9 @@ namespace GeomUtils {
   // Ithaca, New York
   // wbt@graphics.cornell.edu
 
-  bool intersectRayTriangle(Vec3r& orig, Vec3r& dir,
-			    Vec3r& v0, Vec3r& v1, Vec3r& v2,
-			    real& t, real& u, real& v, real epsilon) {
+  bool intersectRayTriangle(const Vec3r& orig, const Vec3r& dir,
+			    const Vec3r& v0, const Vec3r& v1, const Vec3r& v2,
+			    real& t, real& u, real& v, const real epsilon) {
     Vec3r edge1, edge2, tvec, pvec, qvec;
     real det, inv_det;
 
@@ -424,10 +424,10 @@ namespace GeomUtils {
   }
 
   // Intersection between plane and ray, adapted from Graphics Gems, Didier Badouel
-  intersection_test intersectRayPlane(Vec3r& orig, Vec3r& dir,
-				      Vec3r& norm, real d,
+  intersection_test intersectRayPlane(const Vec3r& orig, const Vec3r& dir,
+				      const Vec3r& norm, const real d,
 				      real& t,
-				      real epsilon) { 
+				      const real epsilon) { 
     real denom = norm * dir;
 
     if(fabs(denom) <= epsilon) { // plane and ray are parallel
@@ -484,10 +484,10 @@ namespace GeomUtils {
         }
 
   // Checks whether 3D points p lies inside or outside of the triangle ABC
-  bool includePointTriangle(Vec3r& P,
-			    Vec3r& A,
-			    Vec3r& B,
-			    Vec3r& C) {
+  bool includePointTriangle(const Vec3r& P,
+			    const Vec3r& A,
+			    const Vec3r& B,
+			    const Vec3r& C) {
     Vec3r AB(B - A);
     Vec3r BC(C - B);
     Vec3r CA(A - C);
diff --git a/source/blender/freestyle/intern/geometry/GeomUtils.h b/source/blender/freestyle/intern/geometry/GeomUtils.h
index 787376108e1..bbbf42b5881 100755
--- a/source/blender/freestyle/intern/geometry/GeomUtils.h
+++ b/source/blender/freestyle/intern/geometry/GeomUtils.h
@@ -121,20 +121,20 @@ namespace GeomUtils {
    * adapted from Tomas Möller and Ben Trumbore code.
    */
   LIB_GEOMETRY_EXPORT
-  bool intersectRayTriangle(Vec3r& orig, Vec3r& dir,
-			    Vec3r& v0, Vec3r& v1, Vec3r& v2,
+  bool intersectRayTriangle(const Vec3r& orig, const Vec3r& dir,
+			    const Vec3r& v0, const Vec3r& v1, const Vec3r& v2,
 			    real& t,                   // I = orig + t * dir
                 real& u, real& v,          // I = (1-u-v)*v0+u*v1+v*v2
-			    real epsilon = M_EPSILON); // the epsilon to use
+			    const real epsilon = M_EPSILON); // the epsilon to use
 
   /*! Intersection between plane and ray
    * adapted from Graphics Gems, Didier Badouel 
    */
   LIB_GEOMETRY_EXPORT
-  intersection_test intersectRayPlane(Vec3r& orig, Vec3r& dir,   // ray origin and direction
-				      Vec3r& norm, real d,       // plane's normal and offset (plane = { P / P.N + d = 0 })
+  intersection_test intersectRayPlane(const Vec3r& orig, const Vec3r& dir,   // ray origin and direction
+				      const Vec3r& norm, const real d,       // plane's normal and offset (plane = { P / P.N + d = 0 })
 				      real& t,                   // I = orig + t * dir
-				      real epsilon = M_EPSILON); // the epsilon to use
+				      const real epsilon = M_EPSILON); // the epsilon to use
 
  /*! Intersection Ray-Bounding box (axis aligned).
   *  Adapted from Williams et al, "An Efficient Robust Ray-Box Intersection Algorithm", 
@@ -151,10 +151,10 @@ namespace GeomUtils {
 
   /*! Checks whether 3D point P lies inside or outside of the triangle ABC */
   LIB_GEOMETRY_EXPORT
-  bool includePointTriangle(Vec3r& P,
-			    Vec3r& A,
-			    Vec3r& B,
-			    Vec3r& C);
+  bool includePointTriangle(const Vec3r& P,
+			    const Vec3r& A,
+			    const Vec3r& B,
+			    const Vec3r& C);
 
   LIB_GEOMETRY_EXPORT
   void transformVertex(const Vec3r& vert,
diff --git a/source/blender/freestyle/intern/geometry/Grid.cpp b/source/blender/freestyle/intern/geometry/Grid.cpp
index 2477227c410..0096297f48b 100755
--- a/source/blender/freestyle/intern/geometry/Grid.cpp
+++ b/source/blender/freestyle/intern/geometry/Grid.cpp
@@ -318,6 +318,10 @@ Polygon3r* Grid::castRayToFindFirstIntersection(const Vec3r& orig,
     }
     firstIntersectionGridVisitor visitor(orig,dir,_cell_size);
     castRayInternal(visitor);
+	// ARB: This doesn't work, because occluders are unordered within any cell
+	// visitor.occluder() will be an occluder, but we have no guarantee
+	// it will be the *first* occluder.
+	// I assume that is the reason this code is not actually used for FindOccludee.
     occluder = visitor.occluder();
     t = visitor.t_;
     u = visitor.u_;
diff --git a/source/blender/freestyle/intern/geometry/Grid.h b/source/blender/freestyle/intern/geometry/Grid.h
index e54b7b4d381..a490646ff51 100755
--- a/source/blender/freestyle/intern/geometry/Grid.h
+++ b/source/blender/freestyle/intern/geometry/Grid.h
@@ -253,6 +253,10 @@ public:
 	       const Vec3r& end,
 	       OccludersSet& occluders,
 	       unsigned timestamp);
+  // Prepares to cast ray without generating OccludersSet
+  void initAcceleratedRay(const Vec3r& orig,
+	       const Vec3r& end,
+	       unsigned timestamp);
 
   /*! Casts an infinite ray (still finishing at the end of the grid) from a starting point and in a given direction.
    *  Returns the list of occluders contained
@@ -263,6 +267,10 @@ public:
 		       const Vec3r& dir,
 		       OccludersSet& occluders,
 		       unsigned timestamp);
+  // Prepares to cast ray without generating OccludersSet.
+  bool initAcceleratedInfiniteRay(const Vec3r& orig,
+		       const Vec3r& dir,
+		       unsigned timestamp);
 
   /*! Casts an infinite ray (still finishing at the end of the grid) from a starting point and in a given direction.
   *  Returns the first intersection (occluder,t,u,v) or null.
@@ -303,6 +311,10 @@ public:
   inline Vec3r getCellSize() const {
     return _cell_size;
   }
+//ARB profiling only:
+  inline OccludersSet* getOccluders() {
+    return &_occluders;
+  }
 
   void displayDebug() {
     cerr << "Cells nb     : " << _cells_nb << endl;
@@ -360,4 +372,21 @@ public:
   OccludersSet _occluders;     // List of all occluders inserted in the grid
 };
 
+//
+// Class to walk through occluders in grid without building intermediate data structures
+//
+///////////////////////////////////////////////////////////////////////////////
+
+class VirtualOccludersSet {
+	public:
+		VirtualOccludersSet(Grid& _grid) : grid (_grid) {};
+		Polygon3r* begin();
+		Polygon3r* next();
+		Polygon3r* next(bool stopOnNewCell);
+	private:
+		Polygon3r* firstOccluderFromNextCell();
+		Grid& grid;
+		OccludersSet::iterator it, end;
+};
+
 #endif // GRID_H
diff --git a/source/blender/freestyle/intern/geometry/GridHelpers.cpp b/source/blender/freestyle/intern/geometry/GridHelpers.cpp
new file mode 100644
index 00000000000..dcf24a72efb
--- /dev/null
+++ b/source/blender/freestyle/intern/geometry/GridHelpers.cpp
@@ -0,0 +1,56 @@
+//
+//  Filename         : GridHelpers.cpp
+//  Author(s)        : Alexander Beels
+//  Purpose          : Class to define a cell grid surrounding
+//                     the projected image of a scene
+//  Date of creation : 2010-12-21
+//
+///////////////////////////////////////////////////////////////////////////////
+
+//
+//  Copyright (C) : Please refer to the COPYRIGHT file distributed 
+//   with this source distribution. 
+//
+//  This program is free software; you can redistribute it and/or
+//  modify it under the terms of the GNU General Public License
+//  as published by the Free Software Foundation; either version 2
+//  of the License, or (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+//  You should have received a copy of the GNU General Public License
+//  along with this program; if not, write to the Free Software
+//  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
+//
+///////////////////////////////////////////////////////////////////////////////
+
+#include <math.h>
+#include "GridHelpers.h"
+
+void GridHelpers::getDefaultViewProscenium(real viewProscenium[4]) {
+	// Get proscenium boundary for culling
+	// bufferZone determines the amount by which the area processed
+	// should exceed the actual image area.  This is intended to
+	// avoid visible artifacts generated along the proscenium edge.
+	// Perhaps this is no longer needed now that entire view edges
+	// are culled at once, since that theoretically should eliminate
+	// visible artifacts.
+	// To the extent it is still useful, bufferZone should be put into 
+	// the UI as configurable percentage value
+	const real bufferZone = 0.05;
+	// borderZone describes a blank border outside the proscenium, but
+	// still inside the image area.  Only intended for exposing possible
+	// artifacts along or outside the proscenium edge during debugging.
+	const real borderZone = 0.0;
+	viewProscenium[0] = freestyle_viewport[2] * (borderZone - bufferZone);
+	viewProscenium[1] = freestyle_viewport[2] * (1.0f - borderZone + bufferZone);
+	viewProscenium[2] = freestyle_viewport[3] * (borderZone - bufferZone);
+	viewProscenium[3] = freestyle_viewport[3] * (1.0f - borderZone + bufferZone);
+}
+
+GridHelpers::Transform::~Transform () {}
+
+
diff --git a/source/blender/freestyle/intern/geometry/GridHelpers.h b/source/blender/freestyle/intern/geometry/GridHelpers.h
new file mode 100644
index 00000000000..b079005c1b5
--- /dev/null
+++ b/source/blender/freestyle/intern/geometry/GridHelpers.h
@@ -0,0 +1,199 @@
+//
+//  Filename         : GridHelpers.h
+//  Author(s)        : Alexander Beels
+//  Purpose          : Class to define a cell grid surrounding
+//                     the projected image of a scene
+//  Date of creation : 2010-12-13
+//
+///////////////////////////////////////////////////////////////////////////////
+
+
+//
+//  Copyright (C) : Please refer to the COPYRIGHT file distributed 
+//   with this source distribution. 
+//
+//  This program is free software; you can redistribute it and/or
+//  modify it under the terms of the GNU General Public License
+//  as published by the Free Software Foundation; either version 2
+//  of the License, or (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+//  You should have received a copy of the GNU General Public License
+//  along with this program; if not, write to the Free Software
+//  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
+//
+///////////////////////////////////////////////////////////////////////////////
+
+#ifndef  GRIDHELPERS_H
+#define GRIDHELPERS_H
+
+#include <vector>
+#include "Polygon.h"
+#include "../winged_edge/WEdge.h"
+#include "FRS_freestyle.h"
+#include "GeomUtils.h"
+
+namespace GridHelpers {
+
+/*! Computes the distance from a point P to a segment AB */
+template<class T>
+T closestPointToSegment(const T& P, const T& A , const T& B, real& distance) { 
+	T AB, AP, BP;
+	AB = B - A;
+	AP = P - A;
+	BP = P - B;
+
+	real c1(AB * AP);
+	if (c1 <= 0) {
+		distance = AP.norm();
+		return A; // A is closest point
+	}
+
+	real c2(AB * AB);
+	if (c2 <= c1) {
+		distance = BP.norm();
+		return B; // B is closest point
+	}
+
+    real b = c1 / c2;
+    T Pb, PPb;
+    Pb = A + b * AB;
+    PPb = P - Pb;
+
+    distance = PPb.norm();
+	return Pb; // closest point lies on AB
+} 
+
+inline Vec3r closestPointOnPolygon(const Vec3r& point, const Polygon3r& poly) {
+	// First cast a ray from the point onto the polygon plane
+	// If the ray intersects the polygon, then the intersection point
+	// is the closest point on the polygon
+	real t, u, v;
+	if ( poly.rayIntersect(point, poly.getNormal(), t, u, v) ) {
+		return point + poly.getNormal() * t;
+	}
+
+	// Otherwise, get the nearest point on each edge, and take the closest
+	real distance;
+	Vec3r closest = closestPointToSegment(point, poly.getVertices()[2], poly.getVertices()[0], distance);
+	for ( unsigned i = 0; i < 2; ++i ) {
+		real t;
+		Vec3r p = closestPointToSegment(point, poly.getVertices()[i], poly.getVertices()[i + 1], t);
+		if ( t < distance ) {
+			distance = t;
+			closest = p;
+		}
+	}
+	return closest;
+}
+
+inline real distancePointToPolygon(const Vec3r& point, const Polygon3r& poly) {
+	// First cast a ray from the point onto the polygon plane
+	// If the ray intersects the polygon, then the intersection point
+	// is the closest point on the polygon
+	real t, u, v;
+	if ( poly.rayIntersect(point, poly.getNormal(), t, u, v) ) {
+		return t > 0.0 ? t : -t;
+	}
+
+	// Otherwise, get the nearest point on each edge, and take the closest
+	real distance = GeomUtils::distPointSegment(point, poly.getVertices()[2], poly.getVertices()[0]);
+	for ( unsigned i = 0; i < 2; ++i ) {
+		real t = GeomUtils::distPointSegment(point, poly.getVertices()[i], poly.getVertices()[i + 1]);
+		if ( t < distance ) {
+			distance = t;
+		}
+	}
+	return distance;
+}
+
+class Transform {
+public:
+	virtual ~Transform () =0;
+	virtual Vec3r operator()(const Vec3r& point) const =0;
+};
+
+inline bool insideProscenium (const real proscenium[4], const Polygon3r& polygon) {
+	// N.B. The bounding box check is redundant for inserting occluders into
+	// cells, because the cell selection code in insertOccluders has already
+	// guaranteed that the bounding boxes will overlap.
+	// First check the viewport edges, since they are the easiest case
+	// Check if the bounding box is entirely outside the proscenium
+	Vec3r bbMin, bbMax;
+	polygon.getBBox(bbMin, bbMax);
+	if ( bbMax[0] < proscenium[0] 
+			|| bbMin[0] > proscenium[1] 
+			|| bbMax[1] < proscenium[2] 
+			|| bbMin[1] > proscenium[3] ) {
+		return false;
+	}
+
+	Vec3r boxCenter(proscenium[0] + (proscenium[1] - proscenium[0]) / 2.0, proscenium[2] + (proscenium[3] - proscenium[2]) / 2.0, 0.0);
+	Vec3r boxHalfSize((proscenium[1] - proscenium[0]) / 2.0, (proscenium[3] - proscenium[2]) / 2.0, 1.0);
+	Vec3r triverts[3] = { Vec3r(polygon.getVertices()[0][0], polygon.getVertices()[0][1], 0.0), Vec3r(polygon.getVertices()[1][0], polygon.getVertices()[1][1], 0.0), Vec3r(polygon.getVertices()[2][0], polygon.getVertices()[2][1], 0.0) };
+	return GeomUtils::overlapTriangleBox(boxCenter, boxHalfSize, triverts);
+}
+
+inline vector<Vec3r> enumerateVertices(const vector<WOEdge*>& fedges) {
+	vector<Vec3r> points;
+	// Iterate over vertices, storing projections in points
+	for(vector<WOEdge*>::const_iterator woe=fedges.begin(), woend=fedges.end(); woe!=woend; woe++) {
+		points.push_back((*woe)->GetaVertex()->GetVertex());
+	}
+
+	return points;
+}
+
+void getDefaultViewProscenium(real viewProscenium[4]);
+
+inline void expandProscenium (real proscenium[4], const Polygon3r& polygon) {
+	Vec3r bbMin, bbMax;
+	polygon.getBBox(bbMin, bbMax);
+
+	const real epsilon = 1.0e-6;
+
+	if ( bbMin[0] <= proscenium[0] ) {
+		proscenium[0] = bbMin[0] - epsilon;
+	}
+
+	if ( bbMin[1] <= proscenium[2] ) {
+		proscenium[2] = bbMin[1] - epsilon;
+	}
+
+	if ( bbMax[0] >= proscenium[1] ) {
+		proscenium[1] = bbMax[0] + epsilon;
+	}
+
+	if ( bbMax[1] >= proscenium[3] ) {
+		proscenium[3] = bbMax[1] + epsilon;
+	}
+}
+
+inline void expandProscenium (real proscenium[4], const Vec3r& point) {
+	const real epsilon = 1.0e-6;
+
+	if ( point[0] <= proscenium[0] ) {
+		proscenium[0] = point[0] - epsilon;
+	}
+
+	if ( point[1] <= proscenium[2] ) {
+		proscenium[2] = point[1] - epsilon;
+	}
+
+	if ( point[0] >= proscenium[1] ) {
+		proscenium[1] = point[0] + epsilon;
+	}
+
+	if ( point[1] >= proscenium[3] ) {
+		proscenium[3] = point[1] + epsilon;
+	}
+}
+
+};
+
+#endif // GRIDHELPERS_H
+
diff --git a/source/blender/freestyle/intern/geometry/Polygon.h b/source/blender/freestyle/intern/geometry/Polygon.h
index f9c4c78d424..911804d80f7 100755
--- a/source/blender/freestyle/intern/geometry/Polygon.h
+++ b/source/blender/freestyle/intern/geometry/Polygon.h
@@ -175,7 +175,6 @@ class Polygon
 class Polygon3r : public Polygon<Vec3r>
 {
  public:
-
   inline Polygon3r() : Polygon<Vec3r>() {}
 
   inline Polygon3r(const vector<Vec3r>& vertices,
@@ -183,7 +182,7 @@ class Polygon3r : public Polygon<Vec3r>
     setNormal(normal);
   }
 
-  inline Polygon3r(const Polygon3r& poly) : Polygon<Vec3r>(poly) {}
+  inline Polygon3r(const Polygon3r& poly) : Polygon<Vec3r>(poly), _normal(poly._normal) {}
   
   virtual ~Polygon3r() {}
 
@@ -191,13 +190,13 @@ class Polygon3r : public Polygon<Vec3r>
     _normal = normal;
   }
 
-  Vec3r getNormal() const {
+  inline Vec3r getNormal() const {
     return _normal;
   }
 
   /*! Check whether the Polygon intersects with the ray or not */
-  inline bool rayIntersect(Vec3r& orig, Vec3r& dir,
-			   real& t, real& u, real& v, real epsilon = M_EPSILON) {
+  inline bool rayIntersect(const Vec3r& orig, const Vec3r& dir,
+			   real& t, real& u, real& v, real epsilon = M_EPSILON) const {
     //    if (_vertices.size() < 3)
     //      return false;
     return GeomUtils::intersectRayTriangle(orig, dir,
diff --git a/source/blender/freestyle/intern/geometry/SweepLine.h b/source/blender/freestyle/intern/geometry/SweepLine.h
index cf4c86d006d..deecf3c5485 100755
--- a/source/blender/freestyle/intern/geometry/SweepLine.h
+++ b/source/blender/freestyle/intern/geometry/SweepLine.h
@@ -210,17 +210,6 @@ public:
     {
       delete (*i);
     }
-    _Intersections.clear();
-
-    for(typename vector<Segment<T,Point>* >::iterator ie=_IntersectedEdges.begin(),ieend=_IntersectedEdges.end();
-    ie!=ieend;
-    ie++)
-    {
-      delete (*ie);
-    }
-    _IntersectedEdges.clear();
-
-    _set.clear();
   }
 
   
diff --git a/source/blender/freestyle/intern/geometry/normal_cycle.cpp b/source/blender/freestyle/intern/geometry/normal_cycle.cpp
index b456ced8331..3a697d54731 100755
--- a/source/blender/freestyle/intern/geometry/normal_cycle.cpp
+++ b/source/blender/freestyle/intern/geometry/normal_cycle.cpp
@@ -82,22 +82,6 @@ namespace OGF {
 
     }
 
-    void NormalCycle::accumulate_dihedral_angle(
-        const Vec3r& edge, double beta, double neigh_area
-    ) {
-        Vec3r e = edge ;
-        e.normalize() ;
-
-        double s = edge.norm() * beta * neigh_area ;
-
-        M_[0] += s * e.x() * e.x() ;
-        M_[1] += s * e.x() * e.y() ;
-        M_[2] += s * e.y() * e.y() ;
-        M_[3] += s * e.x() * e.z() ;
-        M_[4] += s * e.y() * e.z() ;
-        M_[5] += s * e.z() * e.z() ;        
-    }
-    
 //_________________________________________________________
 
 }
diff --git a/source/blender/freestyle/intern/geometry/normal_cycle.h b/source/blender/freestyle/intern/geometry/normal_cycle.h
index 41fbf7b3fab..cdf00a0b4c5 100755
--- a/source/blender/freestyle/intern/geometry/normal_cycle.h
+++ b/source/blender/freestyle/intern/geometry/normal_cycle.h
@@ -90,6 +90,19 @@ template <class T> inline void ogf_swap(T& x, T& y) {
         int i_[3] ;
     } ;
     
+    inline void NormalCycle::accumulate_dihedral_angle(
+        const Vec3r& edge, const double beta, double neigh_area
+    ) {
+        double s = beta * neigh_area / edge.norm();
+
+        M_[0] += s * edge.x() * edge.x() ;
+        M_[1] += s * edge.x() * edge.y() ;
+        M_[2] += s * edge.y() * edge.y() ;
+        M_[3] += s * edge.x() * edge.z() ;
+        M_[4] += s * edge.y() * edge.z() ;
+        M_[5] += s * edge.z() * edge.z() ;        
+    }
+    
 //_________________________________________________________
 
 }