B├ęziers magically work with the QuadTree (sometimes)
authorDavid Gow <david@ingeniumdigital.com>
Thu, 21 Aug 2014 10:58:24 +0000 (18:58 +0800)
committerDavid Gow <david@ingeniumdigital.com>
Thu, 21 Aug 2014 10:58:24 +0000 (18:58 +0800)
Also maybe broke qt. It fixed it for my laptop.`

src/Makefile
src/bezier.h
src/document.cpp
src/rect.h

index 26edd62..bc07e1e 100644 (file)
@@ -82,7 +82,7 @@ $(BIN) : $(LINKOBJ) ../obj/$(MAIN)
 -include $(DEPS)
 
 moc_controlpanel.cpp : controlpanel.cpp controlpanel.h
-       moc $(DEF) controlpanel.h -o moc_controlpanel.cpp
+       moc-qt4 $(DEF) controlpanel.h -o moc_controlpanel.cpp
 
 ../obj/%.o : %.cpp main.h
        @mkdir -p $(dir $@)
index 9a54d0c..9273cee 100644 (file)
@@ -151,43 +151,73 @@ namespace IPDF
                        return result;
                }
 
+               // Performs one round of De Casteljau subdivision and returns the [t,1] part.
+               Bezier DeCasteljauSubdivideRight(const Real& t)
+               {
+                       Real one_minus_t = Real(1) - t;
+
+                       // X Coordinates
+                       Real x01 = x0*t + x1*one_minus_t;
+                       Real x12 = x1*t + x2*one_minus_t;
+                       Real x23 = x2*t + x3*one_minus_t;
+
+                       Real x012 = x01*t + x12*one_minus_t;
+                       Real x123 = x12*t + x23*one_minus_t;
+
+                       Real x0123 = x012*t + x123*one_minus_t;
+
+                       // Y Coordinates
+                       Real y01 = y0*t + y1*one_minus_t;
+                       Real y12 = y1*t + y2*one_minus_t;
+                       Real y23 = y2*t + y3*one_minus_t;
+
+                       Real y012 = y01*t + y12*one_minus_t;
+                       Real y123 = y12*t + y23*one_minus_t;
+
+                       Real y0123 = y012*t + y123*one_minus_t;
+
+                       return Bezier(x0, y0, x01, y01, x012, y012, x0123, y0123);
+               }
+               // Performs one round of De Casteljau subdivision and returns the [0,t] part.
+               Bezier DeCasteljauSubdivideLeft(const Real& t)
+               {
+                       Real one_minus_t = Real(1) - t;
+
+                       // X Coordinates
+                       Real x01 = x0*t + x1*one_minus_t;
+                       Real x12 = x1*t + x2*one_minus_t;
+                       Real x23 = x2*t + x3*one_minus_t;
+
+                       Real x012 = x01*t + x12*one_minus_t;
+                       Real x123 = x12*t + x23*one_minus_t;
+
+                       Real x0123 = x012*t + x123*one_minus_t;
+
+                       // Y Coordinates
+                       Real y01 = y0*t + y1*one_minus_t;
+                       Real y12 = y1*t + y2*one_minus_t;
+                       Real y23 = y2*t + y3*one_minus_t;
+
+                       Real y012 = y01*t + y12*one_minus_t;
+                       Real y123 = y12*t + y23*one_minus_t;
+
+                       Real y0123 = y012*t + y123*one_minus_t;
+
+                       return Bezier(x0123, y0123, x123, y123, x23, y23, x3, y3);
+               }
+
                Bezier ReParametrise(const Real& t0, const Real& t1)
                {
-                       // This function is very, very ugly, but with luck my derivation is correct (even if it isn't optimal, performance wise)
-                       // (Very) rough working for the derivation is at: http://davidgow.net/stuff/cubic_bezier_reparam.pdf
                        Debug("Reparametrise: %f -> %f",t0,t1);
                        Bezier new_bezier;
-                       Real tdiff = t1 - t0;
-                       Real tdiff_squared = tdiff*tdiff;
-                       Real tdiff_cubed = tdiff*tdiff_squared;
+                       // Subdivide to get from [0,t1]
+                       new_bezier = DeCasteljauSubdivideLeft(t1);
+                       // Convert t0 from [0,1] range to [0, t1]
+                       Real new_t0 = t0 / t1;
+                       Debug("New t0 = %f", new_t0);
+                       new_bezier = new_bezier.DeCasteljauSubdivideRight(new_t0);
 
-                       Real t0_squared = t0*t0;
-                       Real t0_cubed = t0*t0_squared;
-                       
-                       // X coordinates
-                       Real Dx0 = x0 / tdiff_cubed;
-                       Real Dx1 = x1 / (tdiff_squared - tdiff_cubed);
-                       Real Dx2 = x2 / (tdiff - Real(2)*tdiff_squared + tdiff_cubed);
-                       Real Dx3 = x3 / (Real(1) - Real(3)*tdiff + Real(3)*tdiff_squared - tdiff_cubed);
-
-                       new_bezier.x3 = Dx3*t0_cubed + Real(3)*Dx3*t0_squared + Real(3)*Dx3*t0 + Dx3 - Dx2*t0_cubed - Real(2)*Dx2*t0_squared - Dx2*t0 + Dx1*t0_cubed + Dx1*t0_squared - Dx0*t0_cubed;
-                       new_bezier.x2 = Real(3)*Dx0*t0_squared - Real(2)*Dx1*t0 - Real(3)*Dx1*t0_squared + Dx2 + Real(4)*Dx2*t0 + Real(3)*Dx2*t0_squared - Real(3)*Dx3 - Real(6)*Dx3*t0 - Real(3)*Dx3*t0_squared + Real(3)*new_bezier.x3;
-                       new_bezier.x1 = Real(-3)*Dx0*t0 + Real(3)*Dx1*t0 + Dx1 - Real(2)*Dx2 - Real(3)*Dx2*t0 + Real(3)*Dx3 + Real(3)*Dx3*t0 + Real(2)*new_bezier.x2 - Real(3)*new_bezier.x3;
-                       new_bezier.x0 = Dx0 - Dx1 + Dx2 - Dx3 + new_bezier.x1 - new_bezier.x2 + new_bezier.x3;
-
-                       // Y coordinates
-                       Real Dy0 = y0 / tdiff_cubed;
-                       Real Dy1 = y1 / (tdiff_squared - tdiff_cubed);
-                       Real Dy2 = y2 / (tdiff - Real(2)*tdiff_squared + tdiff_cubed);
-                       Real Dy3 = y3 / (Real(1) - Real(3)*tdiff + Real(3)*tdiff_squared - tdiff_cubed);
-
-                       new_bezier.y3 = Dy3*t0_cubed + Real(3)*Dy3*t0_squared + Real(3)*Dy3*t0 + Dy3 - Dy2*t0_cubed - Real(2)*Dy2*t0_squared - Dy2*t0 + Dy1*t0_cubed + Dy1*t0_squared - Dy0*t0_cubed;
-                       new_bezier.y2 = Real(3)*Dy0*t0_squared - Real(2)*Dy1*t0 - Real(3)*Dy1*t0_squared + Dy2 + Real(4)*Dy2*t0 + Real(3)*Dy2*t0_squared - Real(3)*Dy3 - Real(6)*Dy3*t0 - Real(3)*Dy3*t0_squared + Real(3)*new_bezier.y3;
-                       new_bezier.y1 = Real(-3)*Dy0*t0 + Real(3)*Dy1*t0 + Dy1 - Real(2)*Dy2 - Real(3)*Dy2*t0 + Real(3)*Dy3 + Real(3)*Dy3*t0 + Real(2)*new_bezier.y2 - Real(3)*new_bezier.y3;
-                       new_bezier.y0 = Dy0 - Dy1 + Dy2 - Dy3 + new_bezier.y1 - new_bezier.y2 + new_bezier.y3;
-
-
-                       Debug("(%f,%f),(%f,%f),(%f,%f),(%f,%f) -> (%f,%f),(%f,%f),(%f,%f),(%f,%f)", x0, y0, x1, y1, x2, y2, x3, y3, new_bezier.x0, new_bezier.y0, new_bezier.x1, new_bezier.y1, new_bezier.x2, new_bezier.y2, new_bezier.x3, new_bezier.y3);
+                       Debug("%s becomes %s", this->Str().c_str(), new_bezier.Str().c_str());
                        return new_bezier;
                }
                
@@ -229,6 +259,8 @@ namespace IPDF
 
                        // Merge and sort.
                        x_intersection.insert(x_intersection.end(), y_intersection.begin(), y_intersection.end());
+                       x_intersection.push_back(Real(0));
+                       x_intersection.push_back(Real(1));
                        std::sort(x_intersection.begin(), x_intersection.end());
 
                        Debug("Found %d intersections.\n", x_intersection.size());
@@ -243,8 +275,14 @@ namespace IPDF
                        for (auto it = x_intersection.begin()+1; it != x_intersection.end(); ++it)
                        {
                                Real t1 = *it;
+                               if (t1 == t0) continue;
                                Debug(" -- t0: %f to t1: %f", t0, t1);
-                               all_beziers.push_back(this->ReParametrise(t0, t1));
+                               Real ptx, pty;
+                               Evaluate(ptx, pty, ((t1 + t0) / Real(2)));
+                               if (r.PointIn(ptx, pty))
+                               {
+                                       all_beziers.push_back(this->ReParametrise(t0, t1));
+                               }
                                t0 = t1;
                        }
                        return all_beziers;
index 0b43cfc..ead1b8e 100644 (file)
@@ -133,12 +133,19 @@ int Document::ClipObjectToQuadChild(int object_id, QuadTreeNodeChildren type)
        case BEZIER:
                {
                Rect child_node_bounds = TransformFromQuadChild({0,0,1,1}, type);
-               std::vector<Bezier> new_curves = m_objects.beziers[m_objects.data_indices[object_id]].ClipToRectangle(child_node_bounds);
-               Rect obj_bounds = TransformToQuadChild(m_objects.bounds[object_id], type);
+               Rect clip_bezier_bounds;
+               clip_bezier_bounds.x = (child_node_bounds.x - m_objects.bounds[object_id].x) / m_objects.bounds[object_id].w;
+               clip_bezier_bounds.y = (child_node_bounds.y - m_objects.bounds[object_id].y) / m_objects.bounds[object_id].h;
+               clip_bezier_bounds.w = child_node_bounds.w / m_objects.bounds[object_id].w;
+               clip_bezier_bounds.h = child_node_bounds.h / m_objects.bounds[object_id].h;
+               std::vector<Bezier> new_curves = m_objects.beziers[m_objects.data_indices[object_id]].ClipToRectangle(clip_bezier_bounds);
                for (size_t i = 0; i < new_curves.size(); ++i)
                {
+                       Rect new_bounds = TransformToQuadChild(m_objects.bounds[object_id], type);
+                       //new_bounds = TransformToQuadChild(new_bounds, type);
+                       //Bezier new_curve_data = new_curves[i].ToRelative(new_bounds);
                        unsigned index = AddBezierData(new_curves[i]);
-                       m_objects.bounds.push_back(obj_bounds);
+                       m_objects.bounds.push_back(new_bounds);
                        m_objects.types.push_back(BEZIER);
                        m_objects.data_indices.push_back(index);
                }
index a79f6ac..7b7adc1 100644 (file)
@@ -18,6 +18,14 @@ namespace IPDF
                        s << "{" << Float(x) << ", " << Float(y) << ", " << Float(w) << ", " << Float(h) << "}";
                        return s.str();
                }
+               inline bool PointIn(Real pt_x, Real pt_y) const
+               {
+                       if (pt_x < x) return false;
+                       if (pt_y < y) return false;
+                       if (pt_x > x + w) return false;
+                       if (pt_y > y + h) return false;
+                       return true;
+               }
        };
 }
 

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