From 441976b6cd6631af1d77fc60efc56948c562be1a Mon Sep 17 00:00:00 2001 From: David Gow Date: Mon, 25 Aug 2014 16:30:00 +0800 Subject: [PATCH] Some half-done quadtree experiments. --- src/bezier.h | 48 ++++++++++++++++++++++++++++++++++-------------- src/document.cpp | 29 ++++++++++++++++++++++++----- 2 files changed, 58 insertions(+), 19 deletions(-) diff --git a/src/bezier.h b/src/bezier.h index 9273cee..07f2178 100644 --- a/src/bezier.h +++ b/src/bezier.h @@ -25,20 +25,36 @@ namespace IPDF // See http://en.wikipedia.org/wiki/Cubic_function#General_formula_for_roots // delta = 18abcd - 4 b^3 d + b^2 c^2 - 4ac^3 - 27 a^2 d^2 - /* + Real discriminant = Real(18) * a * b * c * d - Real(4) * (b * b * b) * d + (b * b) * (c * c) - Real(4) * a * (c * c * c) - Real(27) * (a * a) * (d * d); - */ + + Debug("Trying to solve %fx^3 + %fx^2 + %fx + %f (Discriminant: %f)", a,b,c,d, discriminant); // discriminant > 0 => 3 distinct, real roots. // discriminant = 0 => a multiple root (1 or 2 real roots) // discriminant < 0 => 1 real root, 2 complex conjugate roots + Real delta0 = (b*b) - Real(3) * a * c; + Real delta1 = Real(2) * (b * b * b) - Real(9) * a * b * c + Real(27) * (a * a) * d; + + std::vector roots; + + Real C = pow((delta1 + Sqrt((delta1 * delta1) - 4 * (delta0 * delta0 * delta0)) ) / Real(2), 1/3); + + if (false && discriminant < 0) + { + Real real_root = (Real(-1) / (Real(3) * a)) * (b + C + delta0 / C); + + roots.push_back(real_root); + + return roots; + + } + ////HACK: We know any roots we care about will be between 0 and 1, so... - Debug("Trying to solve %fx^3 + %fx^2 + %fx + %f", a,b,c,d); Real maxi(100); Real prevRes(d); - std::vector roots; for(int i = -1; i <= 100; ++i) { Real x(i); @@ -227,32 +243,32 @@ namespace IPDF Debug("Clipping Bezier to Rect %s", r.Str().c_str()); // Convert bezier coefficients -> cubic coefficients - Real xa = x0-x1+x2-x3; - Real xb = x1 - Real(2)*x2 + Real(3)*x3; - Real xc = x2 - Real(3)*x3; - Real xd = x3 - r.x; + Real xd = x0 - r.x; + Real xc = Real(3)*(x1 - x0); + Real xb = Real(3)*(x2 - x1) - xc; + Real xa = x3 - x0 - xc - xb; // Find its roots. std::vector x_intersection = SolveCubic(xa, xb, xc, xd); // And for the other side. - xd = x3 - r.x - r.w; + xd = x0 - r.x - r.w; std::vector x_intersection_pt2 = SolveCubic(xa, xb, xc, xd); x_intersection.insert(x_intersection.end(), x_intersection_pt2.begin(), x_intersection_pt2.end()); // Similarly for y-coordinates. // Convert bezier coefficients -> cubic coefficients - Real ya = y0-y1+y2-y3; - Real yb = y1 - Real(2)*y2 + Real(3)*y3; - Real yc = y2 - Real(3)*y3; - Real yd = y3 - r.y; + Real yd = y0 - r.y; + Real yc = Real(3)*(y1 - y0); + Real yb = Real(3)*(y2 - y1) - yc; + Real ya = y3 - y0 - yc - yb; // Find its roots. std::vector y_intersection = SolveCubic(ya, yb, yc, yd); // And for the other side. - yd = y3 - r.y - r.h; + yd = y0 - r.y - r.h; std::vector y_intersection_pt2 = SolveCubic(ya, yb, yc, yd); y_intersection.insert(y_intersection.end(), y_intersection_pt2.begin(), y_intersection_pt2.end()); @@ -283,6 +299,10 @@ namespace IPDF { all_beziers.push_back(this->ReParametrise(t0, t1)); } + else + { + Debug("Segment removed (point at %f, %f)", ptx, pty); + } t0 = t1; } return all_beziers; diff --git a/src/document.cpp b/src/document.cpp index ead1b8e..ba5a0f7 100644 --- a/src/document.cpp +++ b/src/document.cpp @@ -132,19 +132,38 @@ int Document::ClipObjectToQuadChild(int object_id, QuadTreeNodeChildren type) } case BEZIER: { - Rect child_node_bounds = TransformFromQuadChild({0,0,1,1}, type); + Rect obj_bounds = TransformToQuadChild(m_objects.bounds[object_id], type); + if (obj_bounds.x < 0) + { + obj_bounds.w += obj_bounds.x; + obj_bounds.x = 0; + } + if (obj_bounds.y < 0) + { + obj_bounds.h += obj_bounds.y; + obj_bounds.y = 0; + } + if (obj_bounds.x + obj_bounds.w > 1) + { + obj_bounds.w += (1 - (obj_bounds.x + obj_bounds.w)); + } + if (obj_bounds.y + obj_bounds.h > 1) + { + obj_bounds.h += (1 - (obj_bounds.y + obj_bounds.h)); + } + Rect child_node_bounds = TransformFromQuadChild(obj_bounds, 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); + std::vector new_curves = Bezier(m_objects.beziers[m_objects.data_indices[object_id]], child_node_bounds).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]); + new_bounds = TransformToQuadChild(new_curves[i].SolveBounds(), type); + Bezier new_curve_data = new_curves[i].ToRelative(new_bounds); + unsigned index = AddBezierData(new_curve_data); m_objects.bounds.push_back(new_bounds); m_objects.types.push_back(BEZIER); m_objects.data_indices.push_back(index); -- 2.20.1