Fixed a bug in SilhouetteGeomEngine::ImageToWorldParameter() that caused

instability issues regarding the view map creation.  A new iterative
solver of the 2D-to-3D inverse projection transformation problem was
implemented.  Instead of directly solving the problem in the direction
from the 2D to 3D space, the new solver starts with an initial guess of
an approximated solution and asymptotically approaches to the true
solution by iteratively performing the forward 3D-to-2D projection
transformation and improving the approximation.  Preliminary tests with
one simple and another complex scenes showed that the solver converges
quickly (more and less 20 iterations in many cases, with a stopping
criterion of a residual distance between the true and approximated
solutions less than 1e-6 Blender Unit).

5 files changed, 77 insertions, 9 deletions

diff --git a/source/blender/freestyle/intern/blender_interface/BlenderFileLoader.cpp b/source/blender/freestyle/intern/blender_interface/BlenderFileLoader.cpp
index 114dd1bc7e2..6efa80431fc 100644
--- a/source/blender/freestyle/intern/blender_interface/BlenderFileLoader.cpp
+++ b/source/blender/freestyle/intern/blender_interface/BlenderFileLoader.cpp
@@ -21,8 +21,20 @@ NodeGroup* BlenderFileLoader::Load()
 
 	cout << "\n===  Importing triangular meshes into Blender  ===" << endl;
 
-  // creation of the scene root node
-  _Scene = new NodeGroup;
+	// creation of the scene root node
+	_Scene = new NodeGroup;
+
+	_viewplane_left=   _re->viewplane.xmin;
+	_viewplane_right=  _re->viewplane.xmax;
+	_viewplane_bottom= _re->viewplane.ymin;
+	_viewplane_top=    _re->viewplane.ymax;
+	_z_near= _re->clipsta;
+	_z_far=  _re->clipend;
+#if 0
+	cout << "frustrum: l " << _viewplane_left << " r " << _viewplane_right
+		<< " b " << _viewplane_bottom << " t " << _viewplane_top
+		<< " n " << _z_near << " f " << _z_far << endl;
+#endif
 
 	int id = 0;
 	for(obi= (ObjectInstanceRen *) _re->instancetable.first; obi; obi=obi->next) {
@@ -37,8 +49,8 @@ NodeGroup* BlenderFileLoader::Load()
 			cout << "  Sorry, only vlak-based shapes are supported." << endl;
 	}
 
-  //Returns the built scene.
-  return _Scene;
+	//Returns the built scene.
+	return _Scene;
 }
 
 void BlenderFileLoader::insertShapeNode(ObjectRen *obr, int id)
diff --git a/source/blender/freestyle/intern/blender_interface/BlenderFileLoader.h b/source/blender/freestyle/intern/blender_interface/BlenderFileLoader.h
index 8068eaf1bcf..29acbfc203f 100644
--- a/source/blender/freestyle/intern/blender_interface/BlenderFileLoader.h
+++ b/source/blender/freestyle/intern/blender_interface/BlenderFileLoader.h
@@ -55,9 +55,14 @@ protected:
 protected:
 	Render* _re;
 	SceneRenderLayer* _srl;
-  NodeGroup* _Scene;
-  unsigned _numFacesRead;
-  real _minEdgeSize;
+	NodeGroup* _Scene;
+	unsigned _numFacesRead;
+	real _minEdgeSize;
+	float _viewplane_left;
+	float _viewplane_right;
+	float _viewplane_bottom;
+	float _viewplane_top;
+	float _z_near, _z_far;
 };
 
 #endif // BLENDER_FILE_LOADER_H
diff --git a/source/blender/freestyle/intern/blender_interface/FRS_freestyle.cpp b/source/blender/freestyle/intern/blender_interface/FRS_freestyle.cpp
index 393cd1b2dd9..4ef3abe54d8 100644
--- a/source/blender/freestyle/intern/blender_interface/FRS_freestyle.cpp
+++ b/source/blender/freestyle/intern/blender_interface/FRS_freestyle.cpp
@@ -19,6 +19,7 @@ extern "C" {
 
 #include "BKE_main.h"
 #include "BLI_blenlib.h"
+#include "BLI_math.h"
 #include "BPY_extern.h"
 
 #include "renderpipeline.h"
@@ -106,6 +107,9 @@ extern "C" {
 		for( int i = 0; i < 4; i++ )
 		   for( int j = 0; j < 4; j++ )
 			freestyle_proj[i][j] = re->winmat[i][j];
+
+		//print_m4("mv", freestyle_mv);
+		//print_m4("proj", freestyle_proj);
 	}
 
 	
diff --git a/source/blender/freestyle/intern/view_map/SilhouetteGeomEngine.cpp b/source/blender/freestyle/intern/view_map/SilhouetteGeomEngine.cpp
index ecb0a4979f0..bb9ef5d574b 100755
--- a/source/blender/freestyle/intern/view_map/SilhouetteGeomEngine.cpp
+++ b/source/blender/freestyle/intern/view_map/SilhouetteGeomEngine.cpp
@@ -155,6 +155,7 @@ real SilhouetteGeomEngine::ImageToWorldParameter(FEdge *fe, real t)
 	
   // we need to compute for each parameter t the corresponding 
   // parameter T which gives the intersection in 3D.
+#if 0
   //currentEdge = (*fe);
   Vec3r A = (fe)->vertexA()->point3D();
   Vec3r B = (fe)->vertexB()->point3D();
@@ -175,6 +176,46 @@ real SilhouetteGeomEngine::ImageToWorldParameter(FEdge *fe, real t)
   
   real T;
   T = (Ic[2]*Ac[1] - Ic[1]*Ac[2])/(Ic[1]*(Bc[2]-Ac[2])-Ic[2]*(Bc[1]-Ac[1]));
+#else
+	// suffix w for world, i for image
+	Vec3r Aw = (fe)->vertexA()->point3D();
+	Vec3r Bw = (fe)->vertexB()->point3D();
+	Vec3r Ai = (fe)->vertexA()->point2D();
+	Vec3r Bi = (fe)->vertexB()->point2D();
+	Vec3r Ii = Ai + t * (Bi - Ai); // the intersection point in 2D
+	Vec3r Pw, Pi;
+	real T_sta = 0.0;
+	real T_end = 1.0;
+	real T;
+	real delta_x, delta_y, dist, dist_threshold = 1e-6;
+	int i, max_iters = 100;
+	for (i = 0; i < max_iters; i++) {
+        T = T_sta + 0.5 * (T_end - T_sta);
+        Pw = Aw + T * (Bw - Aw);
+		GeomUtils::fromWorldToImage(Pw, Pi, _transform, _viewport);
+		delta_x = Ii[0] - Pi[0];
+		delta_y = Ii[1] - Pi[1];
+        dist = sqrt(delta_x * delta_x + delta_y * delta_y);
+        if (dist < dist_threshold)
+            break;
+		if (Ai[0] < Bi[0]) {
+            if (Pi[0] < Ii[0])
+                T_sta = T;
+            else
+                T_end = T;
+		} else {
+            if (Pi[0] > Ii[0])
+                T_sta = T;
+            else
+                T_end = T;
+		}
+	}
+#if 0
+	printf("SilhouetteGeomEngine::ImageToWorldParameter(): #iters = %d, dist = %e\n", i, dist);
+#endif
+	if (i == max_iters)
+		printf("SilhouetteGeomEngine::ImageToWorldParameter(): reached to max_iters (dist = %e)\n", dist);
+#endif
   
   return T;
 }
diff --git a/source/blender/freestyle/intern/view_map/ViewMapBuilder.cpp b/source/blender/freestyle/intern/view_map/ViewMapBuilder.cpp
index 3a4d86ea16f..9c7a084c204 100755
--- a/source/blender/freestyle/intern/view_map/ViewMapBuilder.cpp
+++ b/source/blender/freestyle/intern/view_map/ViewMapBuilder.cpp
@@ -946,14 +946,20 @@ void ViewMapBuilder::ComputeSweepLineIntersections(ViewMap *ioViewMap, real epsi
     real tb = (*i)->tB;
 
     if((ta < -epsilon) || (ta > 1+epsilon))
-        cerr << "Warning: intersection out of range for edge " << fA->vertexA()->getId() << " - " << fA->vertexB()->getId() << endl;
+        cerr << "Warning: 2D intersection out of range for edge " << fA->vertexA()->getId() << " - " << fA->vertexB()->getId() << endl;
     
     if((tb < -epsilon) || (tb > 1+epsilon))
-        cerr << "Warning: intersection out of range for edge " << fB->vertexA()->getId() << " - " << fB->vertexB()->getId() << endl;
+        cerr << "Warning: 2D intersection out of range for edge " << fB->vertexA()->getId() << " - " << fB->vertexB()->getId() << endl;
     
     real Ta = SilhouetteGeomEngine::ImageToWorldParameter(fA, ta);
     real Tb = SilhouetteGeomEngine::ImageToWorldParameter(fB, tb);
 
+    if((Ta < -epsilon) || (Ta > 1+epsilon))
+        cerr << "Warning: 3D intersection out of range for edge " << fA->vertexA()->getId() << " - " << fA->vertexB()->getId() << endl;
+    
+    if((Tb < -epsilon) || (Tb > 1+epsilon))
+        cerr << "Warning: 3D intersection out of range for edge " << fB->vertexA()->getId() << " - " << fB->vertexB()->getId() << endl;
+
     TVertex * tvertex = ioViewMap->CreateTVertex(Vec3r(A1 + Ta*(A2-A1)), Vec3r(a1 + ta*(a2-a1)), fA, 
                                                  Vec3r(B1 + Tb*(B2-B1)), Vec3r(b1 + tb*(b2-b1)), fB, id);