bool
BridgeDetector::detect_angle()
{
    if (this->_edges.empty() || this->_anchors.empty()) return false;

    /*  Outset the bridge expolygon by half the amount we used for detecting anchors;
        we'll use this one to clip our test lines and be sure that their endpoints
        are inside the anchors and not on their contours leading to false negatives. */
    Polygons clip_area;
    offset(this->expolygon, &clip_area, +this->extrusion_width/2);

    /*  we'll now try several directions using a rudimentary visibility check:
        bridge in several directions and then sum the length of lines having both
        endpoints within anchors */

    // we test angles according to configured resolution
    std::vector<double> angles;
    for (int i = 0; i <= PI/this->resolution; ++i)
        angles.push_back(i * this->resolution);

    // we also test angles of each bridge contour
    {
        Polygons pp = this->expolygon;
        for (Polygons::const_iterator p = pp.begin(); p != pp.end(); ++p) {
            Lines lines = p->lines();
            for (Lines::const_iterator line = lines.begin(); line != lines.end(); ++line)
                angles.push_back(line->direction());
        }
    }

    /*  we also test angles of each open supporting edge
        (this finds the optimal angle for C-shaped supports) */
    for (Polylines::const_iterator edge = this->_edges.begin(); edge != this->_edges.end(); ++edge) {
        if (edge->first_point().coincides_with(edge->last_point())) continue;
        angles.push_back(Line(edge->first_point(), edge->last_point()).direction());
    }

    // remove duplicates
    double min_resolution = PI/180.0;  // 1 degree
    std::sort(angles.begin(), angles.end());
    for (size_t i = 1; i < angles.size(); ++i) {
        if (xd::Geometry::directions_parallel(angles[i], angles[i-1], min_resolution)) {
            angles.erase(angles.begin() + i);
            --i;
        }
    }
    /*  compare first value with last one and remove the greatest one (PI)
        in case they are parallel (PI, 0) */
    if (xd::Geometry::directions_parallel(angles.front(), angles.back(), min_resolution))
        angles.pop_back();

    BridgeDirectionComparator bdcomp(this->extrusion_width);
    double line_increment = this->extrusion_width;
    bool have_coverage = false;
    for (std::vector<double>::const_iterator angle = angles.begin(); angle != angles.end(); ++angle) {
        Polygons my_clip_area = clip_area;
        ExPolygons my_anchors = this->_anchors;

        // rotate everything - the center point doesn't matter
        for (Polygons::iterator it = my_clip_area.begin(); it != my_clip_area.end(); ++it)
            it->rotate(-*angle, Point(0,0));
        for (ExPolygons::iterator it = my_anchors.begin(); it != my_anchors.end(); ++it)
            it->rotate(-*angle, Point(0,0));

        // generate lines in this direction
        BoundingBox bb;
        for (ExPolygons::const_iterator it = my_anchors.begin(); it != my_anchors.end(); ++it)
            bb.merge((Points)*it);

        Lines lines;
        for (coord_t y = bb.min.y; y <= bb.max.y; y += line_increment)
            lines.push_back(Line(Point(bb.min.x, y), Point(bb.max.x, y)));

        Lines clipped_lines;
        intersection(lines, my_clip_area, &clipped_lines);

        // remove any line not having both endpoints within anchors
        for (size_t i = 0; i < clipped_lines.size(); ++i) {
            Line &line = clipped_lines[i];
            if (!xd::Geometry::contains(my_anchors, line.a)
                    || !xd::Geometry::contains(my_anchors, line.b)) {
                clipped_lines.erase(clipped_lines.begin() + i);
                --i;
            }
        }

        std::vector<double> lengths;
        double total_length = 0;
        for (Lines::const_iterator line = clipped_lines.begin(); line != clipped_lines.end(); ++line) {
            double len = line->length();
            lengths.push_back(len);
            total_length += len;
        }
        if (total_length) have_coverage = true;

        // sum length of bridged lines
        bdcomp.dir_coverage[*angle] = total_length;

        /*  The following produces more correct results in some cases and more broken in others.
            TODO: investigate, as it looks more reliable than line clipping. */
        // $directions_coverage{$angle} = sum(map $_->area, @{$self->coverage($angle)}) // 0;

        // max length of bridged lines
        bdcomp.dir_avg_length[*angle] = !lengths.empty()
                                        ? *std::max_element(lengths.begin(), lengths.end())
                                        : 0;
    }

    // if no direction produced coverage, then there's no bridge direction
    if (!have_coverage) return false;

    // sort directions by score
    std::sort(angles.begin(), angles.end(), bdcomp);

    this->angle = angles.front();
    if (this->angle >= PI) this->angle -= PI;

//    #ifdef SLIC3R_DEBUG
//    printf("  Optimal infill angle is %d degrees\n", (int)Slic3r::Geometry::rad2deg(this->angle));
//    #endif

    return true;
}
MotionPlannerGraph*
MotionPlanner::init_graph(int island_idx)
{
    if (this->graphs[island_idx + 1] == NULL) {
        Polygons pp;
        if (island_idx == -1) {
            pp = this->outer;
        } else {
            pp = this->inner[island_idx];
        }
        
        MotionPlannerGraph* graph = this->graphs[island_idx + 1] = new MotionPlannerGraph();
        
        // add polygon boundaries as edges
        size_t node_idx = 0;
        Lines lines;
        for (Polygons::const_iterator polygon = pp.begin(); polygon != pp.end(); ++polygon) {
            graph->nodes.push_back(polygon->points.back());
            node_idx++;
            for (Points::const_iterator p = polygon->points.begin(); p != polygon->points.end(); ++p) {
                graph->nodes.push_back(*p);
                double dist = graph->nodes[node_idx-1].distance_to(*p);
                graph->add_edge(node_idx-1, node_idx, dist);
                graph->add_edge(node_idx, node_idx-1, dist);
                node_idx++;
            }
            polygon->lines(&lines);
        }
        
        // add Voronoi edges as internal edges
        {
            typedef voronoi_diagram<double> VD;
            typedef std::map<const VD::vertex_type*,size_t> t_vd_vertices;
            VD vd;
            t_vd_vertices vd_vertices;
            
            boost::polygon::construct_voronoi(lines.begin(), lines.end(), &vd);
            for (VD::const_edge_iterator edge = vd.edges().begin(); edge != vd.edges().end(); ++edge) {
                if (edge->is_infinite()) continue;
                
                const VD::vertex_type* v0 = edge->vertex0();
                const VD::vertex_type* v1 = edge->vertex1();
                Point p0 = Point(v0->x(), v0->y());
                Point p1 = Point(v1->x(), v1->y());
                // contains() should probably be faster than contains(),
                // and should it fail on any boundary points it's not a big problem
                if (island_idx == -1) {
                    if (!this->outer.contains(p0) || !this->outer.contains(p1)) continue;
                } else {
                    if (!this->inner[island_idx].contains(p0) || !this->inner[island_idx].contains(p1)) continue;
                }
                
                t_vd_vertices::const_iterator i_v0 = vd_vertices.find(v0);
                size_t v0_idx;
                if (i_v0 == vd_vertices.end()) {
                    graph->nodes.push_back(p0);
                    v0_idx = node_idx;
                    vd_vertices[v0] = node_idx;
                    node_idx++;
                } else {
                    v0_idx = i_v0->second;
                }
                
                t_vd_vertices::const_iterator i_v1 = vd_vertices.find(v1);
                size_t v1_idx;
                if (i_v1 == vd_vertices.end()) {
                    graph->nodes.push_back(p1);
                    v1_idx = node_idx;
                    vd_vertices[v1] = node_idx;
                    node_idx++;
                } else {
                    v1_idx = i_v1->second;
                }
                
                double dist = graph->nodes[v0_idx].distance_to(graph->nodes[v1_idx]);
                graph->add_edge(v0_idx, v1_idx, dist);
            }
        }
        
        return graph;
    }
    return this->graphs[island_idx + 1];
}
void
BridgeDetector::coverage(double angle, Polygons* coverage) const
{
    // Clone our expolygon and rotate it so that we work with vertical lines.
    ExPolygon expolygon = this->expolygon;
    expolygon.rotate(PI/2.0 - angle, Point(0,0));

    /*  Outset the bridge expolygon by half the amount we used for detecting anchors;
        we'll use this one to generate our trapezoids and be sure that their vertices
        are inside the anchors and not on their contours leading to false negatives. */
    ExPolygons grown;
    offset(expolygon, &grown, this->extrusion_width/2.0);

    // Compute trapezoids according to a vertical orientation
    Polygons trapezoids;
    for (ExPolygons::const_iterator it = grown.begin(); it != grown.end(); ++it)
        it->get_trapezoids2(&trapezoids, PI/2.0);

    // get anchors, convert them to Polygons and rotate them too
    Polygons anchors;
    for (ExPolygons::const_iterator anchor = this->_anchors.begin(); anchor != this->_anchors.end(); ++anchor) {
        Polygons pp = *anchor;
        for (Polygons::iterator p = pp.begin(); p != pp.end(); ++p)
            p->rotate(PI/2.0 - angle, Point(0,0));
        anchors.insert(anchors.end(), pp.begin(), pp.end());
    }

    Polygons covered;
    for (Polygons::const_iterator trapezoid = trapezoids.begin(); trapezoid != trapezoids.end(); ++trapezoid) {
        Lines lines = trapezoid->lines();
        Lines supported;
        intersection(lines, anchors, &supported);

        // not nice, we need a more robust non-numeric check
        for (size_t i = 0; i < supported.size(); ++i) {
            if (supported[i].length() < this->extrusion_width) {
                supported.erase(supported.begin() + i);
                i--;
            }
        }

        if (supported.size() >= 2) covered.push_back(*trapezoid);
    }

    // merge trapezoids and rotate them back
    Polygons _coverage;
    union_(covered, &_coverage);
    for (Polygons::iterator p = _coverage.begin(); p != _coverage.end(); ++p)
        p->rotate(-(PI/2.0 - angle), Point(0,0));

    // intersect trapezoids with actual bridge area to remove extra margins
    // and append it to result
    intersection(_coverage, this->expolygon, coverage);

    /*
    if (0) {
        my @lines = map @{$_->lines}, @$trapezoids;
        $_->rotate(-(PI/2 - $angle), [0,0]) for @lines;

        require "Slic3r/SVG.pm";
        Slic3r::SVG::output(
            "coverage_" . rad2deg($angle) . ".svg",
            expolygons          => [$self->expolygon],
            green_expolygons    => $self->_anchors,
            red_expolygons      => $coverage,
            lines               => \@lines,
        );
    }
    */
}