From 813591a7d8a7364003233939f52b0031f3a40d20 Mon Sep 17 00:00:00 2001 From: David Gow Date: Thu, 21 Aug 2014 18:58:24 +0800 Subject: [PATCH] =?utf8?q?B=C3=A9ziers=20magically=20work=20with=20the=20Q?= =?utf8?q?uadTree=20(sometimes)?= MIME-Version: 1.0 Content-Type: text/plain; charset=utf8 Content-Transfer-Encoding: 8bit Also maybe broke qt. It fixed it for my laptop.` --- src/Makefile | 2 +- src/bezier.h | 104 ++++++++++++++++++++++++++++++++--------------- src/document.cpp | 13 ++++-- src/rect.h | 8 ++++ 4 files changed, 90 insertions(+), 37 deletions(-) diff --git a/src/Makefile b/src/Makefile index 26edd62..bc07e1e 100644 --- a/src/Makefile +++ b/src/Makefile @@ -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 $@) diff --git a/src/bezier.h b/src/bezier.h index 9a54d0c..9273cee 100644 --- a/src/bezier.h +++ b/src/bezier.h @@ -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; diff --git a/src/document.cpp b/src/document.cpp index 0b43cfc..ead1b8e 100644 --- a/src/document.cpp +++ b/src/document.cpp @@ -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 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 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); } diff --git a/src/rect.h b/src/rect.h index a79f6ac..7b7adc1 100644 --- a/src/rect.h +++ b/src/rect.h @@ -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; + } }; } -- 2.20.1