=== modified file 'src/helper/geom-pathstroke.cpp'--- src/helper/geom-pathstroke.cpp 2016-08-03 13:29:38 +0000+++ src/helper/geom-pathstroke.cpp 2016-11-28 20:42:57 +0000@@ -1,6 +1,7 @@/* Authors:* Liam P. White* Tavmjong Bah+ * Alexander Brock** Copyright (C) 2014-2015 Authors*@@ -746,33 +747,36 @@len = l;}-void offset_cubic(Geom::Path& p, Geom::CubicBezier const& bez, double width, double tol, size_t levels)-{+double _offset_cubic_stable_sub(+ Geom::CubicBezier const& bez,+ Geom::CubicBezier& c,+ const Geom::Point& start_normal,+ const Geom::Point& end_normal,+ const Geom::Point& start_new,+ const Geom::Point& end_new,+ const double start_rad,+ const double end_rad,+ const double start_len,+ const double end_len,+ const double width,+ const double width_correction) {using Geom::X;using Geom::Y;- Geom::Point start_pos = bez.initialPoint();- Geom::Point end_pos = bez.finalPoint();-- Geom::Point start_normal = Geom::rot90(bez.unitTangentAt(0));- Geom::Point end_normal = -Geom::rot90(Geom::unitTangentAt(Geom::reverse(bez.toSBasis()), 0.));-- // offset the start and end control points out by the width- Geom::Point start_new = start_pos + start_normal*width;- Geom::Point end_new = end_pos + end_normal*width;-- // --------- double start_rad, end_rad;- double start_len, end_len; // tangent lengths- get_cubic_data(bez, 0, start_len, start_rad);- get_cubic_data(bez, 1, end_len, end_rad);-double start_off = 1, end_off = 1;// correction of the lengths of the tangent to the offsetif (!Geom::are_near(start_rad, 0))- start_off += width / start_rad;+ start_off += (width + width_correction) / start_rad;if (!Geom::are_near(end_rad, 0))- end_off += width / end_rad;+ end_off += (width + width_correction) / end_rad;++ // We don't change the direction of the control points+ if (start_off < 0) {+ start_off = 0;+ }+ if (end_off < 0) {+ end_off = 0;+ }start_off *= start_len;end_off *= end_len;// --------@@ -783,23 +787,137 @@mid2_new = Geom::Point(end_new[X] - mid2_new[X]/3., end_new[Y] - mid2_new[Y]/3.);// create the estimate curve- Geom::CubicBezier c = Geom::CubicBezier(start_new, mid1_new, mid2_new, end_new);+ c = Geom::CubicBezier(start_new, mid1_new, mid2_new, end_new);++ // check the tolerance for our estimate to be a parallel curve++ double worst_residual = 0;+ for (size_t ii = 3; ii <= 7; ii+=2) {+ const double t = static_cast<double>(ii) / 10;+ const Geom::Point req = bez.pointAt(t);+ const Geom::Point chk = c.pointAt(c.nearestTime(req));+ const double current_residual = (chk-req).length() - std::abs(width);+ if (std::abs(current_residual) > std::abs(worst_residual)) {+ worst_residual = current_residual;+ }+ }+ return worst_residual;+}++void offset_cubic(Geom::Path& p, Geom::CubicBezier const& bez, double width, double tol, size_t levels)+{+ using Geom::X;+ using Geom::Y;++ const Geom::Point start_pos = bez.initialPoint();+ const Geom::Point end_pos = bez.finalPoint();++ const Geom::Point start_normal = Geom::rot90(bez.unitTangentAt(0));+ const Geom::Point end_normal = -Geom::rot90(Geom::unitTangentAt(Geom::reverse(bez.toSBasis()), 0.));++ // offset the start and end control points out by the width+ const Geom::Point start_new = start_pos + start_normal*width;+ const Geom::Point end_new = end_pos + end_normal*width;++ // --------+ double start_rad, end_rad;+ double start_len, end_len; // tangent lengths+ get_cubic_data(bez, 0, start_len, start_rad);+ get_cubic_data(bez, 1, end_len, end_rad);+++ Geom::CubicBezier c;++ double best_width_correction = 0;+ double best_residual = _offset_cubic_stable_sub(+ bez, c,+ start_normal, end_normal,+ start_new, end_new,+ start_rad, end_rad,+ start_len, end_len,+ width, best_width_correction);+ double stepsize = std::abs(width)/2;+ bool seen_success = false;+ double stepsize_threshold = 0;+ // std::cout << "Residual from " << best_residual << " ";+ size_t ii = 0;+ for (; ii < 100 && stepsize > stepsize_threshold; ++ii) {+ bool success = false;+ const double width_correction = best_width_correction - (best_residual > 0 ? 1 : -1) * stepsize;+ Geom::CubicBezier current_curve;+ const double residual = _offset_cubic_stable_sub(+ bez, current_curve,+ start_normal, end_normal,+ start_new, end_new,+ start_rad, end_rad,+ start_len, end_len,+ width, width_correction);+ if (std::abs(residual) < std::abs(best_residual)) {+ best_residual = residual;+ best_width_correction = width_correction;+ c = current_curve;+ success = true;+ if (std::abs(best_residual) < tol/4) {+ break;+ }+ }++ if (success) {+ if (!seen_success) {+ seen_success = true;+ //std::cout << "Stepsize factor: " << std::abs(width) / stepsize << std::endl;+ stepsize_threshold = stepsize / 1000;+ }+ }+ else {+ stepsize /= 2;+ }+ if (std::abs(best_width_correction) >= std::abs(width)/2) {+ //break; // Seems to prevent some numerical instabilities, not clear if useful+ }+ }// reached maximum recursive depth// don't bother with any more correctionif (levels == 0) {- p.append(c);+ try {+ p.append(c);+ }+ catch (...) {+ if ((p.finalPoint() - c.initialPoint()).length() < 1e-6) {+ c.setInitial(p.finalPoint());+ }+ else {+ auto line = Geom::LineSegment(p.finalPoint(), c.initialPoint());+ p.append(line);+ }+ p.append(c);+ }+return;}- // check the tolerance for our estimate to be a parallel curve- Geom::Point chk = c.pointAt(.5);- Geom::Point req = bez.pointAt(.5) + Geom::rot90(bez.unitTangentAt(.5))*width; // required accuracy-- Geom::Point const diff = req - chk;- double const err = Geom::dot(diff, diff);-- if (err < tol) {+ // We find the point on our new curve (c) for which the distance between+ // (c) and (bez) differs the most from the desired distance (width).+ double worst_err = std::abs(best_residual);+ double worst_time = .5;+ for (size_t ii = 1; ii <= 9; ++ii) {+ const double t = static_cast<double>(ii) / 10;+ const Geom::Point req = bez.pointAt(t);+ // We use the exact solution with nearestTime because it is numerically+ // much more stable than simply assuming that the point on (c) closest+ // to bez.pointAt(t) is given by c.pointAt(t)+ const Geom::Point chk = c.pointAt(c.nearestTime(req));++ Geom::Point const diff = req - chk;+ const double err = std::abs(diff.length() - std::abs(width));+ if (err > worst_err) {+ worst_err = err;+ worst_time = t;+ }+ }++ if (worst_err < tol) {if (Geom::are_near(start_new, p.finalPoint())) {p.setFinal(start_new); // if it isn't near, we throw}@@ -809,7 +927,7 @@return;} else {// split the curve in two- std::pair<Geom::CubicBezier, Geom::CubicBezier> s = bez.subdivide(.5);+ std::pair<Geom::CubicBezier, Geom::CubicBezier> s = bez.subdivide(worst_time);offset_cubic(p, s.first, width, tol, levels - 1);offset_cubic(p, s.second, width, tol, levels - 1);}@@ -827,9 +945,8 @@offset_cubic(p, cub, width, tol, levels);}-void offset_curve(Geom::Path& res, Geom::Curve const* current, double width)+void offset_curve(Geom::Path& res, Geom::Curve const* current, double width, double tolerance){- double const tolerance = 0.0025;size_t levels = 8;if (current->isDegenerate()) return; // don't do anything@@ -855,14 +972,14 @@default: {Geom::Path sbasis_path = Geom::cubicbezierpath_from_sbasis(current->toSBasis(), tolerance);for (size_t i = 0; i < sbasis_path.size(); ++i)- offset_curve(res, &sbasis_path[i], width);+ offset_curve(res, &sbasis_path[i], width, tolerance);break;}}} else {Geom::Path sbasis_path = Geom::cubicbezierpath_from_sbasis(current->toSBasis(), 0.1);for (size_t i = 0; i < sbasis_path.size(); ++i)- offset_curve(res, &sbasis_path[i], width);+ offset_curve(res, &sbasis_path[i], width, tolerance);}}@@ -949,6 +1066,7 @@Geom::Path half_outline(Geom::Path const& input, double width, double miter, LineJoinType join){+ double const tolerance = 5.0 * (width/100); // Tolerance is 5%Geom::Path res;if (input.size() == 0) return res;@@ -963,12 +1081,13 @@res.start(start);// Do two curves at a time for efficiency, since the join function needs to know the outgoing curve as well- const size_t k = (input.back_closed().isDegenerate() && input.closed())- ?input.size_default()-1:input.size_default();+ const Geom::Curve &closingline = input.back_closed();+ const size_t k = (are_near(closingline.initialPoint(), closingline.finalPoint()) && input.closed() )+ ?input.size_open():input.size_default();for (size_t u = 0; u < k; u += 2) {temp.clear();- offset_curve(temp, &input[u], width);+ offset_curve(temp, &input[u], width, tolerance);// on the first run through, there isn't a joinif (u == 0) {@@ -981,12 +1100,11 @@// odd number of pathsif (u < k - 1) {temp.clear();- offset_curve(temp, &input[u+1], width);+ offset_curve(temp, &input[u+1], width, tolerance);tangents(tang, input[u], input[u+1]);outline_join(res, temp, tang[0], tang[1], width, miter, join);}}-if (input.closed()) {Geom::Curve const &c1 = res.back();Geom::Curve const &c2 = res.front();@@ -998,7 +1116,6 @@outline_join(temp, temp2, tang[0], tang[1], width, miter, join);res.erase(res.begin());res.erase_last();- //res.append(temp);res.close();}@@ -1010,9 +1127,8 @@{if (res.size() == 0 || temp.size() == 0)return;-Geom::Curve const& outgoing = temp.front();- if (Geom::are_near(res.finalPoint(), outgoing.initialPoint())) {+ if (Geom::are_near(res.finalPoint(), outgoing.initialPoint(), 0.01)) {// if the points are /that/ close, just ignore this oneres.setFinal(temp.initialPoint());res.append(temp);
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