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).

1 files changed, 41 insertions, 0 deletions

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;
 }