#include <src/libslic3r/Arachne/SkeletalTrapezoidation.hpp>

Collaboration diagram for Slic3r::Arachne::SkeletalTrapezoidation:

Classes
struct	TransitionMidRef

Public Types
using	Segment = PolygonsSegmentIndex

using	PointMap = ankerl::unordered_dense::map< Point, Point, PointHash >

using	NodeSet = ankerl::unordered_dense::set< node_t * >

Public Member Functions
	SkeletalTrapezoidation (const Polygons &polys, const BeadingStrategy &beading_strategy, double transitioning_angle, coord_t discretization_step_size, coord_t transition_filter_dist, coord_t allowed_filter_deviation, coord_t beading_propagation_transition_dist)

void	generateToolpaths (std::vector< VariableWidthLines > &generated_toolpaths, bool filter_outermost_central_edges=false)

Public Attributes
graph_t	graph

Protected Member Functions
void	constructFromPolygons (const Polygons &polys)

node_t &	makeNode (vd_t::vertex_type &vd_node, Point p)
	Get the node which the VD node maps to, or create a new mapping if there wasn't any yet.

void	transferEdge (Point from, Point to, vd_t::edge_type &vd_edge, edge_t *&prev_edge, Point &start_source_point, Point &end_source_point, const std::vector< Segment > &segments)

Points	discretize (const vd_t::edge_type &segment, const std::vector< Segment > &segments)

void	separatePointyQuadEndNodes ()

void	updateIsCentral ()

void	filterCentral (coord_t max_length)

bool	filterCentral (edge_t *starting_edge, coord_t traveled_dist, coord_t max_length)

void	filterOuterCentral ()

void	updateBeadCount ()

void	filterNoncentralRegions ()

bool	filterNoncentralRegions (edge_t *to_edge, coord_t bead_count, coord_t traveled_dist, coord_t max_dist)

void	generateTransitionMids (ptr_vector_t< std::list< TransitionMiddle > > &edge_transitions)

void	filterTransitionMids ()

std::list< TransitionMidRef >	dissolveNearbyTransitions (edge_t *edge_to_start, TransitionMiddle &origin_transition, coord_t traveled_dist, coord_t max_dist, bool going_up)

void	dissolveBeadCountRegion (edge_t *edge_to_start, coord_t from_bead_count, coord_t to_bead_count)

bool	filterEndOfCentralTransition (edge_t *edge_to_start, coord_t traveled_dist, coord_t max_dist, coord_t replacing_bead_count)

void	generateAllTransitionEnds (ptr_vector_t< std::list< TransitionEnd > > &edge_transition_ends)

void	applyTransitions (ptr_vector_t< std::list< TransitionEnd > > &edge_transition_ends)

void	generateTransitioningRibs ()

void	generateTransitionEnds (edge_t &edge, coord_t mid_R, coord_t transition_lower_bead_count, ptr_vector_t< std::list< TransitionEnd > > &edge_transition_ends)

bool	generateTransitionEnd (edge_t &edge, coord_t start_pos, coord_t end_pos, coord_t transition_half_length, double start_rest, double end_rest, coord_t transition_lower_bead_count, ptr_vector_t< std::list< TransitionEnd > > &edge_transition_ends)

bool	isGoingDown (edge_t *outgoing, coord_t traveled_dist, coord_t transition_half_length, coord_t lower_bead_count) const

bool	isEndOfCentral (const edge_t &edge) const

void	generateExtraRibs ()

void	generateSegments ()

edge_t *	getQuadMaxRedgeTo (edge_t *quad_start_edge)

void	propagateBeadingsUpward (std::vector< edge_t * > &upward_quad_mids, ptr_vector_t< BeadingPropagation > &node_beadings)

void	propagateBeadingsDownward (std::vector< edge_t * > &upward_quad_mids, ptr_vector_t< BeadingPropagation > &node_beadings)

void	propagateBeadingsDownward (edge_t *edge_to_peak, ptr_vector_t< BeadingPropagation > &node_beadings)

Beading	interpolate (const Beading &left, double ratio_left_to_whole, const Beading &right, coord_t switching_radius) const

Beading	interpolate (const Beading &left, double ratio_left_to_whole, const Beading &right) const

std::shared_ptr< BeadingPropagation >	getOrCreateBeading (node_t *node, ptr_vector_t< BeadingPropagation > &node_beadings)

std::shared_ptr< BeadingPropagation >	getNearestBeading (node_t *node, coord_t max_dist)

void	generateJunctions (ptr_vector_t< BeadingPropagation > &node_beadings, ptr_vector_t< LineJunctions > &edge_junctions)

void	addToolpathSegment (const ExtrusionJunction &from, const ExtrusionJunction &to, bool is_odd, bool force_new_path, bool from_is_3way, bool to_is_3way)

void	connectJunctions (ptr_vector_t< LineJunctions > &edge_junctions)

void	generateLocalMaximaSingleBeads ()

Static Protected Member Functions
static bool	computePointCellRange (vd_t::cell_type &cell, Point &start_source_point, Point &end_source_point, vd_t::edge_type &starting_vd_edge, vd_t::edge_type &ending_vd_edge, const std::vector< Segment > &segments)

static void	computeSegmentCellRange (vd_t::cell_type &cell, Point &start_source_point, Point &end_source_point, vd_t::edge_type &starting_vd_edge, vd_t::edge_type &ending_vd_edge, const std::vector< Segment > &segments)

Protected Attributes
ankerl::unordered_dense::map< vd_t::edge_type , edge_t >	vd_edge_to_he_edge

ankerl::unordered_dense::map< vd_t::vertex_type , node_t >	vd_node_to_he_node

std::vector< VariableWidthLines > *	p_generated_toolpaths

Private Types
using	pos_t = double

using	vd_t = boost::polygon::voronoi_diagram< pos_t >

using	graph_t = SkeletalTrapezoidationGraph

using	edge_t = STHalfEdge

using	node_t = STHalfEdgeNode

using	Beading = BeadingStrategy::Beading

using	BeadingPropagation = SkeletalTrapezoidationJoint::BeadingPropagation

using	TransitionMiddle = SkeletalTrapezoidationEdge::TransitionMiddle

using	TransitionEnd = SkeletalTrapezoidationEdge::TransitionEnd

template<typename T >
using	ptr_vector_t = std::vector< std::shared_ptr< T > >

Private Attributes
double	transitioning_angle
	How pointy a region should be before we apply the method. Equals 180* - limit_bisector_angle.

coord_t	discretization_step_size
	approximate size of segments when parabolic VD edges get discretized (and vertex-vertex edges)

coord_t	transition_filter_dist
	Filter transition mids (i.e. anchors) closer together than this.

coord_t	allowed_filter_deviation
	The allowed line width deviation induced by filtering.

coord_t	beading_propagation_transition_dist
	When there are different beadings propagated from below and from above, use this transitioning distance.

const BeadingStrategy &	beading_strategy

Static Private Attributes
static constexpr coord_t	central_filter_dist = scaled<coord_t>(0.02)
	Filter areas marked as 'central' smaller than this.

static constexpr coord_t	snap_dist = scaled<coord_t>(0.02)
	Generic arithmatic inaccuracy. Only used to determine whether a transition really needs to insert an extra edge.

Friends
bool	detect_voronoi_edge_intersecting_input_segment (const Geometry::VoronoiDiagram &voronoi_diagram, const std::vector< VoronoiUtils::Segment > &segments)

Detailed Description

Main class of the dynamic beading strategies.

The input polygon region is decomposed into trapezoids and represented as a half-edge data-structure.

We determine which edges are 'central' accordinding to the transitioning_angle of the beading strategy, and determine the bead count for these central regions and apply them outward when generating toolpaths. [oversimplified]

The method can be visually explained as generating the 3D union of cones surface on the outline polygons, and changing the heights along central regions of that surface so that they are flat. For more info, please consult the paper "A framework for adaptive width control of dense contour-parallel toolpaths in fused deposition modeling" by Kuipers et al. This visual explanation aid explains the use of "upward", "lower" etc, i.e. the radial distance and/or the bead count are used as heights of this visualization, there is no coordinate called 'Z'.

TODO: split this class into two:

Class for generating the decomposition and aux functions for performing updates
Class for editing the structure for our purposes.

Member Typedef Documentation

◆ Beading

using Slic3r::Arachne::SkeletalTrapezoidation::Beading = BeadingStrategy::Beading

private

◆ BeadingPropagation

using Slic3r::Arachne::SkeletalTrapezoidation::BeadingPropagation = SkeletalTrapezoidationJoint::BeadingPropagation

private

◆ edge_t

using Slic3r::Arachne::SkeletalTrapezoidation::edge_t = STHalfEdge

private

◆ graph_t

using Slic3r::Arachne::SkeletalTrapezoidation::graph_t = SkeletalTrapezoidationGraph

private

◆ node_t

using Slic3r::Arachne::SkeletalTrapezoidation::node_t = STHalfEdgeNode

private

◆ NodeSet

using Slic3r::Arachne::SkeletalTrapezoidation::NodeSet = ankerl::unordered_dense::set<node_t*>

◆ PointMap

using Slic3r::Arachne::SkeletalTrapezoidation::PointMap = ankerl::unordered_dense::map<Point, Point, PointHash>

◆ pos_t

using Slic3r::Arachne::SkeletalTrapezoidation::pos_t = double

private

◆ ptr_vector_t

template<typename T >

using Slic3r::Arachne::SkeletalTrapezoidation::ptr_vector_t = std::vector<std::shared_ptr<T> >

private

◆ Segment

using Slic3r::Arachne::SkeletalTrapezoidation::Segment = PolygonsSegmentIndex

◆ TransitionEnd

using Slic3r::Arachne::SkeletalTrapezoidation::TransitionEnd = SkeletalTrapezoidationEdge::TransitionEnd

private

◆ TransitionMiddle

using Slic3r::Arachne::SkeletalTrapezoidation::TransitionMiddle = SkeletalTrapezoidationEdge::TransitionMiddle

private

◆ vd_t

using Slic3r::Arachne::SkeletalTrapezoidation::vd_t = boost::polygon::voronoi_diagram<pos_t>

private

Constructor & Destructor Documentation

◆ SkeletalTrapezoidation()

Slic3r::Arachne::SkeletalTrapezoidation::SkeletalTrapezoidation	(	const Polygons &	polys,
		const BeadingStrategy &	beading_strategy,
		double	transitioning_angle,
		coord_t	discretization_step_size,
		coord_t	transition_filter_dist,
		coord_t	allowed_filter_deviation,
		coord_t	beading_propagation_transition_dist
	)

Construct a new trapezoidation problem to solve.

Parameters

polys	The shapes to fill with walls.
beading_strategy	The strategy to use to fill these shapes.
transitioning_angle	Where we transition to a different number of walls, how steep should this transition be? A lower angle means that the transition will be longer.
discretization_step_size	Since g-code can't represent smooth transitions in line width, the line width must change with discretized steps. This indicates how long the line segments between those steps will be.
transition_filter_dist	The minimum length of transitions. Transitions shorter than this will be considered for dissolution.
beading_propagation_transition_dist	When there are different beadings propagated from below and from above, use this transitioning distance.

     : transitioning_angle(transitioning_angle),
    discretization_step_size(discretization_step_size),
    transition_filter_dist(transition_filter_dist),
    allowed_filter_deviation(allowed_filter_deviation),
    beading_propagation_transition_dist(beading_propagation_transition_dist),
    beading_strategy(beading_strategy)
{
    constructFromPolygons(polys);
}

References constructFromPolygons().

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Member Function Documentation

◆ addToolpathSegment()

void Slic3r::Arachne::SkeletalTrapezoidation::addToolpathSegment	(	const ExtrusionJunction &	from,
		const ExtrusionJunction &	to,
		bool	is_odd,
		bool	force_new_path,
		bool	from_is_3way,
		bool	to_is_3way
	)

protected

Add a new toolpath segment, defined between two extrusion-juntions.

Parameters

from	The junction from which to add a segment.
to	The junction to which to add a segment.
is_odd	Whether this segment is an odd gap filler along the middle of the skeleton.
force_new_path	Whether to prevent adding this path to an existing path which ends in `from`
from_is_3way	Whether the `from` junction is a splitting junction where two normal wall lines and a gap filler line come together.
to_is_3way	Whether the `to` junction is a splitting junction where two normal wall lines and a gap filler line come together.

{
    if (from == to) return;
 
    std::vector<VariableWidthLines> &generated_toolpaths = *p_generated_toolpaths;
 
    size_t inset_idx = from.perimeter_index;
    if (inset_idx >= generated_toolpaths.size())
    {
        generated_toolpaths.resize(inset_idx + 1);
    }
    assert((generated_toolpaths[inset_idx].empty() || !generated_toolpaths[inset_idx].back().junctions.empty()) && "empty extrusion lines should never have been generated");
    if (generated_toolpaths[inset_idx].empty()
        || generated_toolpaths[inset_idx].back().is_odd != is_odd
        || generated_toolpaths[inset_idx].back().junctions.back().perimeter_index != inset_idx // inset_idx should always be consistent
    )
    {
        force_new_path = true;
    }
    if (!force_new_path
        && shorter_then(generated_toolpaths[inset_idx].back().junctions.back().p - from.p, scaled<coord_t>(0.010))
        && std::abs(generated_toolpaths[inset_idx].back().junctions.back().w - from.w) < scaled<coord_t>(0.010)
        && ! from_is_3way // force new path at 3way intersection
    )
    {
        generated_toolpaths[inset_idx].back().junctions.push_back(to);
    }
    else if (!force_new_path
             && shorter_then(generated_toolpaths[inset_idx].back().junctions.back().p - to.p, scaled<coord_t>(0.010))
             && std::abs(generated_toolpaths[inset_idx].back().junctions.back().w - to.w) < scaled<coord_t>(0.010)
             && ! to_is_3way // force new path at 3way intersection
    )
    {
        if ( ! is_odd)
        {
            BOOST_LOG_TRIVIAL(error) << "Reversing even wall line causes it to be printed CCW instead of CW!";
        }
        generated_toolpaths[inset_idx].back().junctions.push_back(from);
    }
    else
    {
        generated_toolpaths[inset_idx].emplace_back(inset_idx, is_odd);
        generated_toolpaths[inset_idx].back().junctions.push_back(from);
        generated_toolpaths[inset_idx].back().junctions.push_back(to);
    }
};

References Slic3r::empty(), error, Slic3r::Arachne::ExtrusionJunction::p, Slic3r::Arachne::ExtrusionJunction::perimeter_index, Slic3r::shorter_then(), and Slic3r::Arachne::ExtrusionJunction::w.

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◆ applyTransitions()

void Slic3r::Arachne::SkeletalTrapezoidation::applyTransitions ( ptr_vector_t< std::list< TransitionEnd > > & edge_transition_ends )

protected

Also set the rest values at nodes in between the transition ends

{
    for (edge_t& edge : graph.edges)
    {
        if (edge.twin->data.hasTransitionEnds())
        {
            coord_t length = (edge.from->p - edge.to->p).cast<int64_t>().norm();
            auto& twin_transition_ends = *edge.twin->data.getTransitionEnds();
            if (! edge.data.hasTransitionEnds())
            {
                edge_transition_ends.emplace_back(std::make_shared<std::list<TransitionEnd>>());
                edge.data.setTransitionEnds(edge_transition_ends.back());
            }
            auto& transition_ends = *edge.data.getTransitionEnds();
            for (TransitionEnd& end : twin_transition_ends)
            {
                transition_ends.emplace_back(length - end.pos, end.lower_bead_count, end.is_lower_end);
            }
            twin_transition_ends.clear();
        }
    }
    
    for (edge_t& edge : graph.edges)
    {
        if (! edge.data.hasTransitionEnds())
        {
            continue;
        }
 
        assert(edge.data.isCentral());
 
        auto& transitions = *edge.data.getTransitionEnds();
        transitions.sort([](const TransitionEnd& a, const TransitionEnd& b) { return a.pos < b.pos; } );
 
        node_t* from = edge.from;
        node_t* to = edge.to;
        Point a = from->p;
        Point b = to->p;
        Point ab = b - a;
        coord_t ab_size = (ab).cast<int64_t>().norm();
 
        edge_t* last_edge_replacing_input = &edge;
        for (TransitionEnd& transition_end : transitions)
        {
            coord_t new_node_bead_count = transition_end.is_lower_end? transition_end.lower_bead_count : transition_end.lower_bead_count + 1;
            coord_t end_pos = transition_end.pos;
            node_t* close_node = (end_pos < ab_size / 2)? from : to;
            if ((end_pos < snap_dist || end_pos > ab_size - snap_dist)
                && close_node->data.bead_count == new_node_bead_count
            )
            {
                assert(end_pos <= ab_size);
                close_node->data.transition_ratio = 0;
                continue;
            }
            Point mid = a + normal(ab, end_pos);
            
            assert(last_edge_replacing_input->data.isCentral());
            assert(last_edge_replacing_input->data.type != SkeletalTrapezoidationEdge::EdgeType::EXTRA_VD);
            last_edge_replacing_input = graph.insertNode(last_edge_replacing_input, mid, new_node_bead_count);
            assert(last_edge_replacing_input->data.type != SkeletalTrapezoidationEdge::EdgeType::EXTRA_VD);
            assert(last_edge_replacing_input->data.isCentral());
        }
    }
}

References Slic3r::Arachne::SkeletalTrapezoidationJoint::bead_count, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, Slic3r::Arachne::HalfEdgeGraph< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::edges, Slic3r::Arachne::SkeletalTrapezoidationEdge::EXTRA_VD, graph, Slic3r::Arachne::SkeletalTrapezoidationGraph::insertNode(), Slic3r::Arachne::SkeletalTrapezoidationEdge::isCentral(), Slic3r::length(), Slic3r::Arachne::normal(), Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::p, snap_dist, Slic3r::Arachne::SkeletalTrapezoidationJoint::transition_ratio, and Slic3r::Arachne::SkeletalTrapezoidationEdge::type.

Referenced by generateTransitioningRibs().

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◆ computePointCellRange()

bool Slic3r::Arachne::SkeletalTrapezoidation::computePointCellRange	(	vd_t::cell_type &	cell,
		Point &	start_source_point,
		Point &	end_source_point,
		vd_t::edge_type *&	starting_vd_edge,
		vd_t::edge_type *&	ending_vd_edge,
		const std::vector< Segment > &	segments
	)

staticprotected

Compute the range of line segments that surround a cell of the skeletal graph that belongs to a point on the medial axis.

This should only be used on cells that belong to a corner in the skeletal graph, e.g. triangular cells, not trapezoid cells.

The resulting line segments is just the first and the last segment. They are linked to the neighboring segments, so you can iterate over the segments until you reach the last segment.

Parameters

	cell	The cell to compute the range of line segments for.
[out]	start_source_point	The start point of the source segment of this cell.
[out]	end_source_point	The end point of the source segment of this cell.
[out]	starting_vd_edge	The edge of the Voronoi diagram where the loop around the cell starts.
[out]	ending_vd_edge	The edge of the Voronoi diagram where the loop around the cell ends.
	points	All vertices of the input Polygons.
	segments	All edges of the input Polygons. /return Whether the cell is inside of the polygon. If it's outside of the polygon we should skip processing it altogether.

{
    if (cell.incident_edge()->is_infinite())
        return false; //Infinite edges only occur outside of the polygon. Don't copy any part of this cell.
 
    // Check if any point of the cell is inside or outside polygon
    // Copy whole cell into graph or not at all
 
    // If the cell.incident_edge()->vertex0() is far away so much that it doesn't even fit into Vec2i64, then there is no way that it will be inside the input polygon.
    if (const vd_t::vertex_type &vert = *cell.incident_edge()->vertex0();
        vert.x() >= double(std::numeric_limits<int64_t>::max()) || vert.x() <= double(std::numeric_limits<int64_t>::lowest()) ||
        vert.y() >= double(std::numeric_limits<int64_t>::max()) || vert.y() <= double(std::numeric_limits<int64_t>::lowest()))
        return false; // Don't copy any part of this cell
 
    const Point source_point = VoronoiUtils::getSourcePoint(cell, segments);
    const PolygonsPointIndex source_point_index = VoronoiUtils::getSourcePointIndex(cell, segments);
    Vec2i64 some_point = VoronoiUtils::p(cell.incident_edge()->vertex0());
    if (some_point == source_point.cast<int64_t>())
        some_point = VoronoiUtils::p(cell.incident_edge()->vertex1());
 
    //Test if the some_point is even inside the polygon.
    //The edge leading out of a polygon must have an endpoint that's not in the corner following the contour of the polygon at that vertex.
    //So if it's inside the corner formed by the polygon vertex, it's all fine.
    //But if it's outside of the corner, it must be a vertex of the Voronoi diagram that goes outside of the polygon towards infinity.
    if (!LinearAlg2D::isInsideCorner(source_point_index.prev().p(), source_point_index.p(), source_point_index.next().p(), some_point))
        return false; // Don't copy any part of this cell
 
    vd_t::edge_type* vd_edge = cell.incident_edge();
    do {
        assert(vd_edge->is_finite());
        if (Vec2i64 p1 = VoronoiUtils::p(vd_edge->vertex1()); p1 == source_point.cast<int64_t>()) {
            start_source_point = source_point;
            end_source_point = source_point;
            starting_vd_edge = vd_edge->next();
            ending_vd_edge = vd_edge;
        } else {
            assert((VoronoiUtils::p(vd_edge->vertex0()) == source_point.cast<int64_t>() || !vd_edge->is_secondary()) && "point cells must end in the point! They cannot cross the point with an edge, because collinear edges are not allowed in the input.");
        }
    }
    while (vd_edge = vd_edge->next(), vd_edge != cell.incident_edge());
    assert(starting_vd_edge && ending_vd_edge);
    assert(starting_vd_edge != ending_vd_edge);
    return true;
}

References Slic3r::Arachne::VoronoiUtils::getSourcePoint(), Slic3r::Arachne::VoronoiUtils::getSourcePointIndex(), Slic3r::Arachne::LinearAlg2D::isInsideCorner(), Slic3r::Arachne::PathsPointIndex< Paths >::next(), Slic3r::Arachne::PathsPointIndex< Paths >::p(), Slic3r::Arachne::VoronoiUtils::p(), and Slic3r::Arachne::PathsPointIndex< Paths >::prev().

Referenced by constructFromPolygons().

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◆ computeSegmentCellRange()

void Slic3r::Arachne::SkeletalTrapezoidation::computeSegmentCellRange	(	vd_t::cell_type &	cell,
		Point &	start_source_point,
		Point &	end_source_point,
		vd_t::edge_type *&	starting_vd_edge,
		vd_t::edge_type *&	ending_vd_edge,
		const std::vector< Segment > &	segments
	)

staticprotected

Compute the range of line segments that surround a cell of the skeletal graph that belongs to a line segment of the medial axis.

This should only be used on cells that belong to a central line segment of the skeletal graph, e.g. trapezoid cells, not triangular cells.

The resulting line segments is just the first and the last segment. They are linked to the neighboring segments, so you can iterate over the segments until you reach the last segment.

Parameters

	cell	The cell to compute the range of line segments for.
[out]	start_source_point	The start point of the source segment of this cell.
[out]	end_source_point	The end point of the source segment of this cell.
[out]	starting_vd_edge	The edge of the Voronoi diagram where the loop around the cell starts.
[out]	ending_vd_edge	The edge of the Voronoi diagram where the loop around the cell ends.
	points	All vertices of the input Polygons.
	segments	All edges of the input Polygons. /return Whether the cell is inside of the polygon. If it's outside of the polygon we should skip processing it altogether.

{
    const Segment &source_segment = VoronoiUtils::getSourceSegment(cell, segments);
    const Point    from           = source_segment.from();
    const Point    to             = source_segment.to();
 
    // Find starting edge
    // Find end edge
    bool seen_possible_start = false;
    bool after_start = false;
    bool ending_edge_is_set_before_start = false;
    vd_t::edge_type* edge = cell.incident_edge();
    do {
        if (edge->is_infinite())
            continue;
 
        Vec2i64 v0 = VoronoiUtils::p(edge->vertex0());
        Vec2i64 v1 = VoronoiUtils::p(edge->vertex1());
 
        assert(!(v0 == to.cast<int64_t>() && v1 == from.cast<int64_t>() ));
        if (v0 == to.cast<int64_t>()  && !after_start) { // Use the last edge which starts in source_segment.to
            starting_vd_edge = edge;
            seen_possible_start = true;
        }
        else if (seen_possible_start) {
            after_start = true;
        }
 
        if (v1 == from.cast<int64_t>()  && (!ending_vd_edge || ending_edge_is_set_before_start)) {
            ending_edge_is_set_before_start = !after_start;
            ending_vd_edge = edge;
        }
    } while (edge = edge->next(), edge != cell.incident_edge());
    
    assert(starting_vd_edge && ending_vd_edge);
    assert(starting_vd_edge != ending_vd_edge);
    
    start_source_point = source_segment.to();
    end_source_point = source_segment.from();
}

References Slic3r::Arachne::PolygonsSegmentIndex::from(), Slic3r::Arachne::VoronoiUtils::getSourceSegment(), Slic3r::Arachne::VoronoiUtils::p(), and Slic3r::Arachne::PolygonsSegmentIndex::to().

Referenced by constructFromPolygons().

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◆ connectJunctions()

void Slic3r::Arachne::SkeletalTrapezoidation::connectJunctions ( ptr_vector_t< LineJunctions > & edge_junctions )

protected

connect junctions in each quad

{
    using EdgeSet = ankerl::unordered_dense::set<edge_t*>;
 
    EdgeSet unprocessed_quad_starts(graph.edges.size() * 5 / 2);
    for (edge_t& edge : graph.edges)
    {
        if (!edge.prev)
        {
            unprocessed_quad_starts.emplace(&edge);
        }
    }
 
    EdgeSet passed_odd_edges;
 
    while (!unprocessed_quad_starts.empty())
    {
        edge_t* poly_domain_start = *unprocessed_quad_starts.begin();
        edge_t* quad_start = poly_domain_start;
        bool new_domain_start = true;
        do
        {
            edge_t* quad_end = quad_start;
            while (quad_end->next)
            {
                quad_end = quad_end->next;
            }
 
            edge_t* edge_to_peak = getQuadMaxRedgeTo(quad_start);
            // walk down on both sides and connect junctions
            edge_t* edge_from_peak = edge_to_peak->next; assert(edge_from_peak);
 
            unprocessed_quad_starts.erase(quad_start);
 
            if (! edge_to_peak->data.hasExtrusionJunctions())
            {
                edge_junctions.emplace_back(std::make_shared<LineJunctions>());
                edge_to_peak->data.setExtrusionJunctions(edge_junctions.back());
            }
            // The junctions on the edge(s) from the start of the quad to the node with highest R
            LineJunctions from_junctions = *edge_to_peak->data.getExtrusionJunctions();
            if (! edge_from_peak->twin->data.hasExtrusionJunctions())
            {
                edge_junctions.emplace_back(std::make_shared<LineJunctions>());
                edge_from_peak->twin->data.setExtrusionJunctions(edge_junctions.back());
            }
            // The junctions on the edge(s) from the end of the quad to the node with highest R
            LineJunctions to_junctions = *edge_from_peak->twin->data.getExtrusionJunctions();
            if (edge_to_peak->prev)
            {
                LineJunctions from_prev_junctions = *edge_to_peak->prev->data.getExtrusionJunctions();
                while (!from_junctions.empty() && !from_prev_junctions.empty() && from_junctions.back().perimeter_index <= from_prev_junctions.front().perimeter_index)
                {
                    from_junctions.pop_back();
                }
                from_junctions.reserve(from_junctions.size() + from_prev_junctions.size());
                from_junctions.insert(from_junctions.end(), from_prev_junctions.begin(), from_prev_junctions.end());
                assert(!edge_to_peak->prev->prev);
                if(edge_to_peak->prev->prev)
                {
                    BOOST_LOG_TRIVIAL(warning) << "The edge we're about to connect is already connected.";
                }
            }
            if (edge_from_peak->next)
            {
                LineJunctions to_next_junctions = *edge_from_peak->next->twin->data.getExtrusionJunctions();
                while (!to_junctions.empty() && !to_next_junctions.empty() && to_junctions.back().perimeter_index <= to_next_junctions.front().perimeter_index)
                {
                    to_junctions.pop_back();
                }
                to_junctions.reserve(to_junctions.size() + to_next_junctions.size());
                to_junctions.insert(to_junctions.end(), to_next_junctions.begin(), to_next_junctions.end());
                assert(!edge_from_peak->next->next);
                if(edge_from_peak->next->next)
                {
                    BOOST_LOG_TRIVIAL(warning) << "The edge we're about to connect is already connected!";
                }
            }
            assert(std::abs(int(from_junctions.size()) - int(to_junctions.size())) <= 1); // at transitions one end has more beads
            if(std::abs(int(from_junctions.size()) - int(to_junctions.size())) > 1)
            {
                BOOST_LOG_TRIVIAL(warning) << "Can't create a transition when connecting two perimeters where the number of beads differs too much! " << from_junctions.size() << " vs. " << to_junctions.size();
            }
 
            size_t segment_count = std::min(from_junctions.size(), to_junctions.size());
            for (size_t junction_rev_idx = 0; junction_rev_idx < segment_count; junction_rev_idx++)
            {
                ExtrusionJunction& from = from_junctions[from_junctions.size() - 1 - junction_rev_idx];
                ExtrusionJunction& to = to_junctions[to_junctions.size() - 1 - junction_rev_idx];
                assert(from.perimeter_index == to.perimeter_index);
                if(from.perimeter_index != to.perimeter_index)
                {
                    BOOST_LOG_TRIVIAL(warning) << "Connecting two perimeters with different indices! Perimeter " << from.perimeter_index << " and " << to.perimeter_index;
                }
                const bool from_is_odd =
                    quad_start->to->data.bead_count > 0 && quad_start->to->data.bead_count % 2 == 1 // quad contains single bead segment
                    && quad_start->to->data.transition_ratio == 0 // We're not in a transition
                    && junction_rev_idx == segment_count - 1 // Is single bead segment
                    && shorter_then(from.p - quad_start->to->p, scaled<coord_t>(0.005));
                const bool to_is_odd =
                    quad_end->from->data.bead_count > 0 && quad_end->from->data.bead_count % 2 == 1 // quad contains single bead segment
                    && quad_end->from->data.transition_ratio == 0 // We're not in a transition
                    && junction_rev_idx == segment_count - 1 // Is single bead segment
                    && shorter_then(to.p - quad_end->from->p, scaled<coord_t>(0.005));
                const bool is_odd_segment = from_is_odd && to_is_odd;
                if (is_odd_segment
                    && passed_odd_edges.count(quad_start->next->twin) > 0) // Only generate toolpath for odd segments once
                {
                    continue; // Prevent duplication of single bead segments
                }
                bool from_is_3way = from_is_odd && quad_start->to->isMultiIntersection();
                bool to_is_3way = to_is_odd && quad_end->from->isMultiIntersection();
                passed_odd_edges.emplace(quad_start->next);
 
                addToolpathSegment(from, to, is_odd_segment, new_domain_start, from_is_3way, to_is_3way);
            }
            new_domain_start = false;
        }
        while(quad_start = quad_start->getNextUnconnected(), quad_start != poly_domain_start);
    }
}

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◆ constructFromPolygons()

void Slic3r::Arachne::SkeletalTrapezoidation::constructFromPolygons ( const Polygons & polys )

protected

Compute the skeletal trapezoidation decomposition of the input shape.

Compute the Voronoi Diagram (VD) and transfer all inside edges into our half-edge (HE) datastructure.

The algorithm is currently a bit overcomplicated, because the discretization of parabolic edges is performed at the same time as all edges are being transfered, which means that there is no one-to-one mapping from VD edges to HE edges. Instead we map from a VD edge to the last HE edge. This could be cimplified by recording the edges which should be discretized and discretizing the mafterwards.

Another complication arises because the VD uses floating logic, which can result in zero-length segments after rounding to integers. We therefore collapse edges and their whole cells afterwards.

{
#ifdef ARACHNE_DEBUG
    this->outline = polys;
#endif
 
    // Check self intersections.
    assert([&polys]() -> bool {
        EdgeGrid::Grid grid;
        grid.set_bbox(get_extents(polys));
        grid.create(polys, scaled<coord_t>(10.));
        return !grid.has_intersecting_edges();
    }());
 
    vd_edge_to_he_edge.clear();
    vd_node_to_he_node.clear();
 
    std::vector<Segment> segments;
    for (size_t poly_idx = 0; poly_idx < polys.size(); poly_idx++)
        for (size_t point_idx = 0; point_idx < polys[poly_idx].size(); point_idx++)
            segments.emplace_back(&polys, poly_idx, point_idx);
 
#ifdef ARACHNE_DEBUG
    {
        static int iRun = 0;
        BoundingBox bbox = get_extents(polys);
        SVG svg(debug_out_path("arachne_voronoi-input-%d.svg", iRun++).c_str(), bbox);
        svg.draw_outline(polys, "black", scaled<coordf_t>(0.03f));
    }
#endif
 
    Geometry::VoronoiDiagram voronoi_diagram;
    construct_voronoi(segments.begin(), segments.end(), &voronoi_diagram);
 
#ifdef ARACHNE_DEBUG_VORONOI
    {
        static int iRun = 0;
        dump_voronoi_to_svg(debug_out_path("arachne_voronoi-diagram-%d.svg", iRun++).c_str(), voronoi_diagram, to_points(polys), to_lines(polys));
    }
#endif
 
    // When any Voronoi vertex is missing, the Voronoi diagram is not planar, or some voronoi edge is
    // intersecting input segment, rotate the input polygon and try again.
    VoronoiDiagramStatus      status         = detect_voronoi_diagram_known_issues(voronoi_diagram, segments);
    const std::vector<double> fix_angles     = {PI / 6, PI / 5, PI / 7, PI / 11};
    double                    fixed_by_angle = fix_angles.front();
 
    PointMap vertex_mapping;
    // polys_copy is referenced through items stored in the std::vector segments.
    Polygons                                    polys_copy = polys;
    if (status != VoronoiDiagramStatus::NO_ISSUE_DETECTED) {
        if (status == VoronoiDiagramStatus::MISSING_VORONOI_VERTEX)
            BOOST_LOG_TRIVIAL(warning) << "Detected missing Voronoi vertex, input polygons will be rotated back and forth.";
        else if (status == VoronoiDiagramStatus::NON_PLANAR_VORONOI_DIAGRAM)
            BOOST_LOG_TRIVIAL(warning) << "Detected non-planar Voronoi diagram, input polygons will be rotated back and forth.";
        else if (status == VoronoiDiagramStatus::VORONOI_EDGE_INTERSECTING_INPUT_SEGMENT)
            BOOST_LOG_TRIVIAL(warning) << "Detected Voronoi edge intersecting input segment, input polygons will be rotated back and forth.";
 
        std::tie(vertex_mapping, fixed_by_angle) = try_to_fix_degenerated_voronoi_diagram_by_rotation(voronoi_diagram, polys, polys_copy, segments, fix_angles);
 
        VoronoiDiagramStatus status_after_fix = detect_voronoi_diagram_known_issues(voronoi_diagram, segments);
        assert(status_after_fix == VoronoiDiagramStatus::NO_ISSUE_DETECTED);
        if (status_after_fix == VoronoiDiagramStatus::MISSING_VORONOI_VERTEX)
            BOOST_LOG_TRIVIAL(error) << "Detected missing Voronoi vertex even after the rotation of input.";
        else if (status_after_fix == VoronoiDiagramStatus::NON_PLANAR_VORONOI_DIAGRAM)
            BOOST_LOG_TRIVIAL(error) << "Detected non-planar Voronoi diagram even after the rotation of input.";
        else if (status_after_fix == VoronoiDiagramStatus::VORONOI_EDGE_INTERSECTING_INPUT_SEGMENT)
            BOOST_LOG_TRIVIAL(error) << "Detected Voronoi edge intersecting input segment even after the rotation of input.";
    }
 
process_voronoi_diagram:
    assert(this->graph.edges.empty() && this->graph.nodes.empty() && this->vd_edge_to_he_edge.empty() && this->vd_node_to_he_node.empty());
    for (vd_t::cell_type cell : voronoi_diagram.cells()) {
        if (!cell.incident_edge())
            continue; // There is no spoon
 
        Point start_source_point;
        Point end_source_point;
        vd_t::edge_type* starting_voronoi_edge = nullptr;
        vd_t::edge_type* ending_voronoi_edge   = nullptr;
        // Compute and store result in above variables
 
        if (cell.contains_point()) {
            const bool keep_going = computePointCellRange(cell, start_source_point, end_source_point, starting_voronoi_edge, ending_voronoi_edge, segments);
            if (!keep_going)
                continue;
        } else {
            assert(cell.contains_segment());
            computeSegmentCellRange(cell, start_source_point, end_source_point, starting_voronoi_edge, ending_voronoi_edge, segments);
        }
 
        if (!starting_voronoi_edge || !ending_voronoi_edge) {
            assert(false && "Each cell should start / end in a polygon vertex");
            continue;
        }
 
        // Copy start to end edge to graph
        edge_t* prev_edge = nullptr;
        assert(VoronoiUtils::p(starting_voronoi_edge->vertex1()).x() <= std::numeric_limits<coord_t>::max() && VoronoiUtils::p(starting_voronoi_edge->vertex1()).x() >= std::numeric_limits<coord_t>::lowest());
        assert(VoronoiUtils::p(starting_voronoi_edge->vertex1()).y() <= std::numeric_limits<coord_t>::max() && VoronoiUtils::p(starting_voronoi_edge->vertex1()).y() >= std::numeric_limits<coord_t>::lowest());
        transferEdge(start_source_point, VoronoiUtils::p(starting_voronoi_edge->vertex1()).cast<coord_t>(), *starting_voronoi_edge, prev_edge, start_source_point, end_source_point, segments);
        node_t* starting_node = vd_node_to_he_node[starting_voronoi_edge->vertex0()];
        starting_node->data.distance_to_boundary = 0;
 
        constexpr bool is_next_to_start_or_end = true;
        graph.makeRib(prev_edge, start_source_point, end_source_point, is_next_to_start_or_end);
        for (vd_t::edge_type* vd_edge = starting_voronoi_edge->next(); vd_edge != ending_voronoi_edge; vd_edge = vd_edge->next()) {
            assert(vd_edge->is_finite());
 
            assert(VoronoiUtils::p(vd_edge->vertex0()).x() <= std::numeric_limits<coord_t>::max() && VoronoiUtils::p(vd_edge->vertex0()).x() >= std::numeric_limits<coord_t>::lowest());
            assert(VoronoiUtils::p(vd_edge->vertex0()).y() <= std::numeric_limits<coord_t>::max() && VoronoiUtils::p(vd_edge->vertex0()).y() >= std::numeric_limits<coord_t>::lowest());
            assert(VoronoiUtils::p(vd_edge->vertex1()).x() <= std::numeric_limits<coord_t>::max() && VoronoiUtils::p(vd_edge->vertex1()).x() >= std::numeric_limits<coord_t>::lowest());
            assert(VoronoiUtils::p(vd_edge->vertex1()).y() <= std::numeric_limits<coord_t>::max() && VoronoiUtils::p(vd_edge->vertex1()).y() >= std::numeric_limits<coord_t>::lowest());
 
            Point v1 = VoronoiUtils::p(vd_edge->vertex0()).cast<coord_t>();
            Point v2 = VoronoiUtils::p(vd_edge->vertex1()).cast<coord_t>();
            transferEdge(v1, v2, *vd_edge, prev_edge, start_source_point, end_source_point, segments);
 
            graph.makeRib(prev_edge, start_source_point, end_source_point, vd_edge->next() == ending_voronoi_edge);
        }
 
        assert(VoronoiUtils::p(starting_voronoi_edge->vertex0()).x() <= std::numeric_limits<coord_t>::max() && VoronoiUtils::p(starting_voronoi_edge->vertex0()).x() >= std::numeric_limits<coord_t>::lowest());
        assert(VoronoiUtils::p(starting_voronoi_edge->vertex0()).y() <= std::numeric_limits<coord_t>::max() && VoronoiUtils::p(starting_voronoi_edge->vertex0()).y() >= std::numeric_limits<coord_t>::lowest());
        transferEdge(VoronoiUtils::p(ending_voronoi_edge->vertex0()).cast<coord_t>(), end_source_point, *ending_voronoi_edge, prev_edge, start_source_point, end_source_point, segments);
        prev_edge->to->data.distance_to_boundary = 0;
    }
 
    // For some input polygons, as in GH issues #8474 and #8514 resulting Voronoi diagram is degenerated because it is not planar.
    // When this degenerated Voronoi diagram is processed, the resulting half-edge structure contains some edges that don't have
    // a twin edge. Based on this, we created a fast mechanism that detects those causes and tries to recompute the Voronoi
    // diagram on slightly rotated input polygons that usually make the Voronoi generator generate a non-degenerated Voronoi diagram.
    if (status == VoronoiDiagramStatus::NO_ISSUE_DETECTED && has_missing_twin_edge(this->graph)) {
        BOOST_LOG_TRIVIAL(warning) << "Detected degenerated Voronoi diagram, input polygons will be rotated back and forth.";
        status                                   = VoronoiDiagramStatus::OTHER_TYPE_OF_VORONOI_DIAGRAM_DEGENERATION;
        std::tie(vertex_mapping, fixed_by_angle) = try_to_fix_degenerated_voronoi_diagram_by_rotation(voronoi_diagram, polys, polys_copy, segments, fix_angles);
 
        assert(!detect_missing_voronoi_vertex(voronoi_diagram, segments));
        if (detect_missing_voronoi_vertex(voronoi_diagram, segments))
            BOOST_LOG_TRIVIAL(error) << "Detected missing Voronoi vertex after the rotation of input.";
 
        assert(Geometry::VoronoiUtilsCgal::is_voronoi_diagram_planar_intersection(voronoi_diagram));
 
        this->graph.edges.clear();
        this->graph.nodes.clear();
        this->vd_edge_to_he_edge.clear();
        this->vd_node_to_he_node.clear();
 
        goto process_voronoi_diagram;
    }
 
    if (status != VoronoiDiagramStatus::NO_ISSUE_DETECTED) {
        assert(!has_missing_twin_edge(this->graph));
 
        if (has_missing_twin_edge(this->graph))
            BOOST_LOG_TRIVIAL(error) << "Detected degenerated Voronoi diagram even after the rotation of input.";
    }
 
    if (status != VoronoiDiagramStatus::NO_ISSUE_DETECTED)
        rotate_back_skeletal_trapezoidation_graph_after_fix(this->graph, fixed_by_angle, vertex_mapping);
 
#ifdef ARACHNE_DEBUG
    assert(Geometry::VoronoiUtilsCgal::is_voronoi_diagram_planar_intersection(voronoi_diagram));
#endif
 
    separatePointyQuadEndNodes();
 
    graph.collapseSmallEdges();
 
    // Set [incident_edge] the first possible edge that way we can iterate over all reachable edges from node.incident_edge,
    // without needing to iterate backward
    for (edge_t& edge : graph.edges)
        if (!edge.prev)
            edge.from->incident_edge = &edge;
}

Referenced by SkeletalTrapezoidation().

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◆ discretize()

Points Slic3r::Arachne::SkeletalTrapezoidation::discretize	(	const vd_t::edge_type &	segment,
		const std::vector< Segment > &	segments
	)

protected

Discretize a Voronoi edge that represents the medial axis of a vertex- line region or vertex-vertex region into small segments that can be considered to have a straight medial axis and a linear line width transition.

The medial axis between a point and a line is a parabola. The rest of the algorithm doesn't want to have to deal with parabola, so this discretises the parabola into straight line segments. This is necessary if there is a sharp inner corner (acts as a point) that comes close to a straight edge.

The medial axis between a point and a point is a straight line segment. However the distance from the medial axis to either of those points draws a parabola as you go along the medial axis. That means that the resulting line width along the medial axis would not be linearly increasing or linearly decreasing, but needs to take the shape of a parabola. Instead, we'll break this edge up into tiny line segments that can approximate the parabola with tiny linear increases or decreases in line width.

Parameters

segment	The variable-width Voronoi edge to discretize.
points	All vertices of the original Polygons to fill with beads.
segments	All line segments of the original Polygons to fill with beads.

Returns: A number of coordinates along the edge where the edge is broken up into discrete pieces.

{
    /*Terminology in this function assumes that the edge moves horizontally from
    left to right. This is not necessarily the case; the edge can go in any
    direction, but it helps to picture it in a certain direction in your head.*/
 
    const vd_t::cell_type* left_cell = vd_edge.cell();
    const vd_t::cell_type* right_cell = vd_edge.twin()->cell();
 
    assert(VoronoiUtils::p(vd_edge.vertex0()).x() <= std::numeric_limits<coord_t>::max() && VoronoiUtils::p(vd_edge.vertex0()).x() >= std::numeric_limits<coord_t>::lowest());
    assert(VoronoiUtils::p(vd_edge.vertex0()).y() <= std::numeric_limits<coord_t>::max() && VoronoiUtils::p(vd_edge.vertex0()).y() >= std::numeric_limits<coord_t>::lowest());
    assert(VoronoiUtils::p(vd_edge.vertex1()).x() <= std::numeric_limits<coord_t>::max() && VoronoiUtils::p(vd_edge.vertex1()).x() >= std::numeric_limits<coord_t>::lowest());
    assert(VoronoiUtils::p(vd_edge.vertex1()).y() <= std::numeric_limits<coord_t>::max() && VoronoiUtils::p(vd_edge.vertex1()).y() >= std::numeric_limits<coord_t>::lowest());
 
    Point start = VoronoiUtils::p(vd_edge.vertex0()).cast<coord_t>();
    Point end = VoronoiUtils::p(vd_edge.vertex1()).cast<coord_t>();
    
    bool point_left = left_cell->contains_point();
    bool point_right = right_cell->contains_point();
    if ((!point_left && !point_right) || vd_edge.is_secondary()) // Source vert is directly connected to source segment
    {
        return Points({ start, end });
    }
    else if (point_left != point_right) //This is a parabolic edge between a point and a line.
    {
        Point p = VoronoiUtils::getSourcePoint(*(point_left ? left_cell : right_cell), segments);
        const Segment& s = VoronoiUtils::getSourceSegment(*(point_left ? right_cell : left_cell), segments);
        return VoronoiUtils::discretizeParabola(p, s, start, end, discretization_step_size, transitioning_angle);
    }
    else //This is a straight edge between two points.
    {
        /*While the edge is straight, it is still discretized since the part
        becomes narrower between the two points. As such it may need different
        beadings along the way.*/
        Point left_point = VoronoiUtils::getSourcePoint(*left_cell, segments);
        Point right_point = VoronoiUtils::getSourcePoint(*right_cell, segments);
        coord_t d = (right_point - left_point).cast<int64_t>().norm();
        Point middle = (left_point + right_point) / 2;
        Point x_axis_dir = perp(Point(right_point - left_point));
        coord_t x_axis_length = x_axis_dir.cast<int64_t>().norm();
 
        const auto projected_x = [x_axis_dir, x_axis_length, middle](Point from) //Project a point on the edge.
        {
            Point vec = from - middle;
            assert(( vec.cast<int64_t>().dot(x_axis_dir.cast<int64_t>())/ int64_t(x_axis_length)) <= std::numeric_limits<coord_t>::max());
            coord_t x = vec.cast<int64_t>().dot(x_axis_dir.cast<int64_t>()) / int64_t(x_axis_length);
            return x;
        };
        
        coord_t start_x = projected_x(start);
        coord_t end_x = projected_x(end);
 
        //Part of the edge will be bound to the markings on the endpoints of the edge. Calculate how far that is.
        float bound = 0.5 / tan((M_PI - transitioning_angle) * 0.5);
        int64_t marking_start_x = - int64_t(d) * bound;
        int64_t marking_end_x = int64_t(d) * bound;
 
        assert((middle.cast<int64_t>() + x_axis_dir.cast<int64_t>() * marking_start_x / int64_t(x_axis_length)).x() <= std::numeric_limits<coord_t>::max());
        assert((middle.cast<int64_t>() + x_axis_dir.cast<int64_t>() * marking_start_x / int64_t(x_axis_length)).y() <= std::numeric_limits<coord_t>::max());
        assert((middle.cast<int64_t>() + x_axis_dir.cast<int64_t>() * marking_end_x / int64_t(x_axis_length)).x() <= std::numeric_limits<coord_t>::max());
        assert((middle.cast<int64_t>() + x_axis_dir.cast<int64_t>() * marking_end_x / int64_t(x_axis_length)).y() <= std::numeric_limits<coord_t>::max());
        Point marking_start = middle + (x_axis_dir.cast<int64_t>() * marking_start_x / int64_t(x_axis_length)).cast<coord_t>();
        Point marking_end = middle + (x_axis_dir.cast<int64_t>() * marking_end_x / int64_t(x_axis_length)).cast<coord_t>();
        int64_t direction = 1;
        
        if (start_x > end_x) //Oops, the Voronoi edge is the other way around.
        {
            direction = -1;
            std::swap(marking_start, marking_end);
            std::swap(marking_start_x, marking_end_x);
        }
 
        //Start generating points along the edge.
        Point a = start;
        Point b = end;
        Points ret;
        ret.emplace_back(a);
 
        //Introduce an extra edge at the borders of the markings?
        bool add_marking_start = marking_start_x * direction > int64_t(start_x) * direction;
        bool add_marking_end = marking_end_x * direction > int64_t(start_x) * direction;
 
        //The edge's length may not be divisible by the step size, so calculate an integer step count and evenly distribute the vertices among those.
        Point ab = b - a;
        coord_t ab_size = ab.cast<int64_t>().norm();
        coord_t step_count = (ab_size + discretization_step_size / 2) / discretization_step_size;
        if (step_count % 2 == 1)
        {
            step_count++; // enforce a discretization point being added in the middle
        }
        for (coord_t step = 1; step < step_count; step++)
        {
            Point here = a + (ab.cast<int64_t>() * int64_t(step) / int64_t(step_count)).cast<coord_t>(); //Now simply interpolate the coordinates to get the new vertices!
            coord_t x_here = projected_x(here); //If we've surpassed the position of the extra markings, we may need to insert them first.
            if (add_marking_start && marking_start_x * direction < int64_t(x_here) * direction)
            {
                ret.emplace_back(marking_start);
                add_marking_start = false;
            }
            if (add_marking_end && marking_end_x * direction < int64_t(x_here) * direction)
            {
                ret.emplace_back(marking_end);
                add_marking_end = false;
            }
            ret.emplace_back(here);
        }
        if (add_marking_end && marking_end_x * direction < int64_t(end_x) * direction)
        {
            ret.emplace_back(marking_end);
        }
        ret.emplace_back(b);
        return ret;
    }
}

References discretization_step_size, Slic3r::Arachne::VoronoiUtils::discretizeParabola(), Slic3r::dot(), Slic3r::Arachne::VoronoiUtils::getSourcePoint(), Slic3r::Arachne::VoronoiUtils::getSourceSegment(), M_PI, Slic3r::Arachne::VoronoiUtils::p(), Slic3r::perp(), tan(), and transitioning_angle.

Referenced by transferEdge().

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◆ dissolveBeadCountRegion()

void Slic3r::Arachne::SkeletalTrapezoidation::dissolveBeadCountRegion	(	edge_t *	edge_to_start,
		coord_t	from_bead_count,
		coord_t	to_bead_count
	)

protected

Spread a certain bead count over a region in the graph.

Parameters

edge_to_start	One edge of the region to spread the bead count in.
from_bead_count	All edges with this bead count will be changed.
to_bead_count	The new bead count for those edges.

{
    assert(from_bead_count != to_bead_count);
    if (edge_to_start->to->data.bead_count != from_bead_count)
        return;
 
    edge_to_start->to->data.bead_count = to_bead_count;
    for (edge_t* edge = edge_to_start->next; edge && edge != edge_to_start->twin; edge = edge->twin->next)
    {
        if (!edge->data.isCentral())
        {
            continue;
        }
        dissolveBeadCountRegion(edge, from_bead_count, to_bead_count);
    }
}

References Slic3r::Arachne::SkeletalTrapezoidationJoint::bead_count, Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, dissolveBeadCountRegion(), Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::next, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::to, and Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::twin.

Referenced by dissolveBeadCountRegion(), and filterTransitionMids().

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◆ dissolveNearbyTransitions()

std::list< SkeletalTrapezoidation::TransitionMidRef > Slic3r::Arachne::SkeletalTrapezoidation::dissolveNearbyTransitions	(	edge_t *	edge_to_start,
		TransitionMiddle &	origin_transition,
		coord_t	traveled_dist,
		coord_t	max_dist,
		bool	going_up
	)

protected

Merge transitions that are too close together.

Parameters

edge_to_start	Edge pointing to the node from which to start traveling in all directions except along `edge_to_start` .
origin_transition	The transition for which we are checking nearby transitions.
traveled_dist	The distance traveled before we came to `edge_to_start.to` .
going_up	Whether we are traveling in the upward direction as seen from the `origin_transition`. If this doesn't align with the direction according to the R diff on a consecutive edge we know there was a local optimum.

Returns: Whether the origin transition should be dissolved.

{
    std::list<TransitionMidRef> to_be_dissolved;
    if (traveled_dist > max_dist)
        return to_be_dissolved;
 
    bool should_dissolve = true;
    for (edge_t* edge = edge_to_start->next; edge && edge != edge_to_start->twin; edge = edge->twin->next){
        if (!edge->data.isCentral())
            continue;
 
        Point a = edge->from->p;
        Point b = edge->to->p;
        Point ab = b - a;
        coord_t ab_size = ab.cast<int64_t>().norm();
        bool is_aligned = edge->isUpward();
        edge_t* aligned_edge = is_aligned? edge : edge->twin;
        bool seen_transition_on_this_edge = false;
 
        const coord_t origin_radius          = origin_transition.feature_radius;
        const coord_t radius_here            = edge->from->data.distance_to_boundary;
        const bool    dissolve_result_is_odd = bool(origin_transition.lower_bead_count % 2) == going_up;
        const coord_t width_deviation        = std::abs(origin_radius - radius_here) * 2; // times by two because the deviation happens at both sides of the significant edge
        const coord_t line_width_deviation = dissolve_result_is_odd ? width_deviation : width_deviation / 2; // assume the deviation will be split over either 1 or 2 lines, i.e. assume wall_distribution_count = 1
        if (line_width_deviation > allowed_filter_deviation)
            should_dissolve = false;
 
        if (should_dissolve && aligned_edge->data.hasTransitions()) {
            auto& transitions = *aligned_edge->data.getTransitions();
            for (auto transition_it = transitions.begin(); transition_it != transitions.end(); ++ transition_it) { // Note: this is not necessarily iterating in the traveling direction!
                // Check whether we should dissolve
                coord_t pos = is_aligned? transition_it->pos : ab_size - transition_it->pos;
                if (traveled_dist + pos < max_dist && transition_it->lower_bead_count == origin_transition.lower_bead_count) { // Only dissolve local optima
                    if (traveled_dist + pos < beading_strategy.getTransitioningLength(transition_it->lower_bead_count)) {
                        // Consecutive transitions both in/decreasing in bead count should never be closer together than the transition distance
                        assert(going_up != is_aligned || transition_it->lower_bead_count == 0); 
                    }
                    to_be_dissolved.emplace_back(aligned_edge, transition_it);
                    seen_transition_on_this_edge = true;
                }
            }
        }
        if (should_dissolve && !seen_transition_on_this_edge) {
            std::list<SkeletalTrapezoidation::TransitionMidRef> to_be_dissolved_here = dissolveNearbyTransitions(edge, origin_transition, traveled_dist + ab_size, max_dist, going_up);
            if (to_be_dissolved_here.empty()) { // The region is too long to be dissolved in this direction, so it cannot be dissolved in any direction.
                to_be_dissolved.clear();
                return to_be_dissolved;
            }
            to_be_dissolved.splice(to_be_dissolved.end(), to_be_dissolved_here); // Transfer to_be_dissolved_here into to_be_dissolved
            should_dissolve = should_dissolve && !to_be_dissolved.empty();
        }
    }
 
    if (!should_dissolve)
        to_be_dissolved.clear();
 
    return to_be_dissolved;
}

References allowed_filter_deviation, beading_strategy, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, dissolveNearbyTransitions(), Slic3r::Arachne::SkeletalTrapezoidationEdge::TransitionMiddle::feature_radius, Slic3r::Arachne::BeadingStrategy::getTransitioningLength(), Slic3r::Arachne::SkeletalTrapezoidationEdge::getTransitions(), Slic3r::Arachne::SkeletalTrapezoidationEdge::hasTransitions(), Slic3r::Arachne::SkeletalTrapezoidationEdge::TransitionMiddle::lower_bead_count, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::next, and Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::twin.

Referenced by dissolveNearbyTransitions(), and filterTransitionMids().

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◆ filterCentral() [1/2]

void Slic3r::Arachne::SkeletalTrapezoidation::filterCentral ( coord_t max_length )

protected

Filter out small central areas.

Only used to get rid of small edges which get marked as central because of rounding errors because the region is so small.

{
    for (edge_t& edge : graph.edges)
    {
        if (isEndOfCentral(edge) && edge.to->isLocalMaximum() && !edge.to->isLocalMaximum())
        {
            filterCentral(edge.twin, 0, max_length);
        }
    }
}

References Slic3r::Arachne::HalfEdgeGraph< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::edges, filterCentral(), graph, and isEndOfCentral().

Referenced by filterCentral(), filterCentral(), and generateToolpaths().

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◆ filterCentral() [2/2]

bool Slic3r::Arachne::SkeletalTrapezoidation::filterCentral	(	edge_t *	starting_edge,
		coord_t	traveled_dist,
		coord_t	max_length
	)

protected

Filter central areas connected to starting_edge recursively.

Returns: Whether we should unmark this section marked as central, on the way back out of the recursion.

{
    coord_t length = (starting_edge->from->p - starting_edge->to->p).cast<int64_t>().norm();
    if (traveled_dist + length > max_length)
    {
        return false;
    }
    
    bool should_dissolve = true; //Should we unmark this as central and propagate that?
    for (edge_t* next_edge = starting_edge->next; next_edge && next_edge != starting_edge->twin; next_edge = next_edge->twin->next)
    {
        if (next_edge->data.isCentral())
        {
            should_dissolve &= filterCentral(next_edge, traveled_dist + length, max_length);
        }
    }
 
    should_dissolve &= !starting_edge->to->isLocalMaximum(); // Don't filter central regions with a local maximum!
    if (should_dissolve)
    {
        starting_edge->data.setIsCentral(false);
        starting_edge->twin->data.setIsCentral(false);
    }
    return should_dissolve;
}

References Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, filterCentral(), Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::from, Slic3r::Arachne::STHalfEdgeNode::isLocalMaximum(), Slic3r::length(), Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::next, Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::p, Slic3r::Arachne::SkeletalTrapezoidationEdge::setIsCentral(), Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::to, and Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::twin.

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◆ filterEndOfCentralTransition()

bool Slic3r::Arachne::SkeletalTrapezoidation::filterEndOfCentralTransition	(	edge_t *	edge_to_start,
		coord_t	traveled_dist,
		coord_t	max_dist,
		coord_t	replacing_bead_count
	)

protected

Change the bead count if the given edge is at the end of a central region.

This is necessary to provide a transitioning bead count to the edges of a central region to transition more smoothly from a high bead count in the central region to a lower bead count at the edge.

Parameters

edge_to_start	One edge from a zone that needs to be filtered.
traveled_dist	The distance along the edges we've traveled so far.
max_distance	Don't filter beyond this range.
replacing_bead_count	The new bead count for this region.

Returns: true if the bead count of this edge was changed.

{
    if (traveled_dist > max_dist)
    {
        return false;
    }
    
    bool is_end_of_central = true;
    bool should_dissolve = false;
    for (edge_t* next_edge = edge_to_start->next; next_edge && next_edge != edge_to_start->twin; next_edge = next_edge->twin->next)
    {
        if (next_edge->data.isCentral())
        {
            coord_t length = (next_edge->to->p - next_edge->from->p).cast<int64_t>().norm();
            should_dissolve |= filterEndOfCentralTransition(next_edge, traveled_dist + length, max_dist, replacing_bead_count);
            is_end_of_central = false;
        }
    }
    if (is_end_of_central && traveled_dist < max_dist)
    {
        should_dissolve = true;
    }
    
    if (should_dissolve)
    {
        edge_to_start->to->data.bead_count = replacing_bead_count;
    }
    return should_dissolve;
}

References Slic3r::Arachne::SkeletalTrapezoidationJoint::bead_count, Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, filterEndOfCentralTransition(), Slic3r::length(), Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::next, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::to, and Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::twin.

Referenced by filterEndOfCentralTransition(), and filterTransitionMids().

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◆ filterNoncentralRegions() [1/2]

void Slic3r::Arachne::SkeletalTrapezoidation::filterNoncentralRegions ( )

protected

Add central regions and set bead counts where there is an end of the central area and when traveling upward we get to another region with the same bead count.

{
    for (edge_t& edge : graph.edges)
    {
        if (!isEndOfCentral(edge))
        {
            continue;
        }
        if(edge.to->data.bead_count < 0 && edge.to->data.distance_to_boundary != 0)
        {
            BOOST_LOG_TRIVIAL(warning) << "Encountered an uninitialized bead at the boundary!";
        }
        assert(edge.to->data.bead_count >= 0 || edge.to->data.distance_to_boundary == 0);
        constexpr coord_t max_dist = scaled<coord_t>(0.4);
        filterNoncentralRegions(&edge, edge.to->data.bead_count, 0, max_dist);
    }
}

References Slic3r::Arachne::HalfEdgeGraph< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::edges, filterNoncentralRegions(), graph, and isEndOfCentral().

Referenced by filterNoncentralRegions(), filterNoncentralRegions(), and generateToolpaths().

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◆ filterNoncentralRegions() [2/2]

bool Slic3r::Arachne::SkeletalTrapezoidation::filterNoncentralRegions	(	edge_t *	to_edge,
		coord_t	bead_count,
		coord_t	traveled_dist,
		coord_t	max_dist
	)

protected

Add central regions and set bead counts for a particular edge and all of its adjacent edges.

Recursive subroutine for filterNoncentralRegions().

Returns: Whether to set the bead count on the way back

{
    coord_t r = to_edge->to->data.distance_to_boundary;
 
    edge_t* next_edge = to_edge->next;
    for (; next_edge && next_edge != to_edge->twin; next_edge = next_edge->twin->next)
    {
        if (next_edge->to->data.distance_to_boundary >= r || shorter_then(next_edge->to->p - next_edge->from->p, scaled<coord_t>(0.01)))
        {
            break; // Only walk upward
        }
    }
    if (next_edge == to_edge->twin || ! next_edge)
    {
        return false;
    }
 
    const coord_t length = (next_edge->to->p - next_edge->from->p).cast<int64_t>().norm();
 
    bool dissolve = false;
    if (next_edge->to->data.bead_count == bead_count)
    {
        dissolve = true;
    }
    else if (next_edge->to->data.bead_count < 0)
    {
        dissolve = filterNoncentralRegions(next_edge, bead_count, traveled_dist + length, max_dist);
    }
    else // Upward bead count is different
    {
        // Dissolve if two central regions with different bead count are closer together than the max_dist (= transition distance)
        dissolve = (traveled_dist + length < max_dist) && std::abs(next_edge->to->data.bead_count - bead_count) == 1;
    }
 
    if (dissolve)
    {
        next_edge->data.setIsCentral(true);
        next_edge->twin->data.setIsCentral(true);
        next_edge->to->data.bead_count = beading_strategy.getOptimalBeadCount(next_edge->to->data.distance_to_boundary * 2);
        next_edge->to->data.transition_ratio = 0;
    }
    return dissolve; // Dissolving only depend on the one edge going upward. There cannot be multiple edges going upward.
}

References Slic3r::Arachne::SkeletalTrapezoidationJoint::bead_count, beading_strategy, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, Slic3r::Arachne::SkeletalTrapezoidationJoint::distance_to_boundary, filterNoncentralRegions(), Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::from, Slic3r::Arachne::BeadingStrategy::getOptimalBeadCount(), Slic3r::length(), Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::next, Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::p, Slic3r::Arachne::SkeletalTrapezoidationEdge::setIsCentral(), Slic3r::shorter_then(), Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::to, Slic3r::Arachne::SkeletalTrapezoidationJoint::transition_ratio, and Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::twin.

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◆ filterOuterCentral()

void Slic3r::Arachne::SkeletalTrapezoidation::filterOuterCentral ( )

protected

Unmark the outermost edges directly connected to the outline, as not being central.

Only used to emulate some related literature.

The paper shows that this function is bad for the stability of the framework.

{
    for (edge_t& edge : graph.edges)
    {
        if (!edge.prev)
        {
            edge.data.setIsCentral(false);
            edge.twin->data.setIsCentral(false);
        }
    }
}

References Slic3r::Arachne::HalfEdgeGraph< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::edges, and graph.

Referenced by generateToolpaths().

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◆ filterTransitionMids()

void Slic3r::Arachne::SkeletalTrapezoidation::filterTransitionMids ( )

protected

Removes some transition middle points.

Transitions can be removed if there are multiple intersecting transitions that are too close together. If transitions have opposite effects, both are removed.

{
    for (edge_t& edge : graph.edges)
    {
        if (! edge.data.hasTransitions())
        {
            continue;
        }
        auto& transitions = *edge.data.getTransitions();
 
        // This is how stuff should be stored in transitions
        assert(transitions.front().lower_bead_count <= transitions.back().lower_bead_count);
        assert(edge.from->data.distance_to_boundary <= edge.to->data.distance_to_boundary);
        
        const Point a = edge.from->p;
        const Point b = edge.to->p;
        Point ab = b - a;
        coord_t ab_size = ab.cast<int64_t>().norm();
 
        bool going_up = true;
        std::list<TransitionMidRef> to_be_dissolved_back = dissolveNearbyTransitions(&edge, transitions.back(), ab_size - transitions.back().pos, transition_filter_dist, going_up);
        bool should_dissolve_back = !to_be_dissolved_back.empty();
        for (TransitionMidRef& ref : to_be_dissolved_back)
        {
            dissolveBeadCountRegion(&edge, transitions.back().lower_bead_count + 1, transitions.back().lower_bead_count);
            ref.edge->data.getTransitions()->erase(ref.transition_it);
        }
 
        {
            coord_t trans_bead_count = transitions.back().lower_bead_count;
            coord_t upper_transition_half_length = (1.0 - beading_strategy.getTransitionAnchorPos(trans_bead_count)) * beading_strategy.getTransitioningLength(trans_bead_count);
            should_dissolve_back |= filterEndOfCentralTransition(&edge, ab_size - transitions.back().pos, upper_transition_half_length, trans_bead_count);
        }
        
        if (should_dissolve_back)
        {
            transitions.pop_back();
        }
        if (transitions.empty())
        { // FilterEndOfCentralTransition gives inconsistent new bead count when executing for the same transition in two directions.
            continue;
        }
 
        going_up = false;
        std::list<TransitionMidRef> to_be_dissolved_front = dissolveNearbyTransitions(edge.twin, transitions.front(), transitions.front().pos, transition_filter_dist, going_up);
        bool should_dissolve_front = !to_be_dissolved_front.empty();
        for (TransitionMidRef& ref : to_be_dissolved_front)
        {
            dissolveBeadCountRegion(edge.twin, transitions.front().lower_bead_count, transitions.front().lower_bead_count + 1);
            ref.edge->data.getTransitions()->erase(ref.transition_it);
        }
 
        {
            coord_t trans_bead_count = transitions.front().lower_bead_count;
            coord_t lower_transition_half_length = beading_strategy.getTransitionAnchorPos(trans_bead_count) * beading_strategy.getTransitioningLength(trans_bead_count);
            should_dissolve_front |= filterEndOfCentralTransition(edge.twin, transitions.front().pos, lower_transition_half_length, trans_bead_count + 1);
        }
        
        if (should_dissolve_front)
        {
            transitions.pop_front();
        }
        if (transitions.empty())
        { // FilterEndOfCentralTransition gives inconsistent new bead count when executing for the same transition in two directions.
            continue;
        }
    }
}

References beading_strategy, dissolveBeadCountRegion(), dissolveNearbyTransitions(), Slic3r::Arachne::HalfEdgeGraph< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::edges, filterEndOfCentralTransition(), Slic3r::Arachne::BeadingStrategy::getTransitionAnchorPos(), Slic3r::Arachne::BeadingStrategy::getTransitioningLength(), graph, and transition_filter_dist.

Referenced by generateTransitioningRibs().

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◆ generateAllTransitionEnds()

void Slic3r::Arachne::SkeletalTrapezoidation::generateAllTransitionEnds ( ptr_vector_t< std::list< TransitionEnd > > & edge_transition_ends )

protected

Generate the endpoints of all transitions for all edges in the graph.

Parameters

[out] edge_transition_ends The resulting transition endpoints.

{
    for (edge_t& edge : graph.edges)
    {
        if (! edge.data.hasTransitions())
        {
            continue;
        }
        auto& transition_positions = *edge.data.getTransitions();
 
        assert(edge.from->data.distance_to_boundary <= edge.to->data.distance_to_boundary);
        for (TransitionMiddle& transition_middle : transition_positions)
        {
            assert(transition_positions.front().pos <= transition_middle.pos);
            assert(transition_middle.pos <= transition_positions.back().pos);
            generateTransitionEnds(edge, transition_middle.pos, transition_middle.lower_bead_count, edge_transition_ends);
        }
    }
}

References Slic3r::Arachne::HalfEdgeGraph< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::edges, generateTransitionEnds(), and graph.

Referenced by generateTransitioningRibs().

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◆ generateExtraRibs()

void Slic3r::Arachne::SkeletalTrapezoidation::generateExtraRibs ( )

protected

Create extra ribs in the graph where the graph contains a parabolic arc or a straight between two inner corners.

There might be transitions there as the beads go through a narrow bottleneck in the polygon.

{
    for (auto edge_it = graph.edges.begin(); edge_it != graph.edges.end(); ++edge_it)
    {
        edge_t& edge = *edge_it;
        
        if (!edge.data.isCentral() 
            || shorter_then(edge.to->p - edge.from->p, discretization_step_size)
            || edge.from->data.distance_to_boundary >= edge.to->data.distance_to_boundary) 
        {
            continue;
        }
 
 
        std::vector<coord_t> rib_thicknesses = beading_strategy.getNonlinearThicknesses(edge.from->data.bead_count);
 
        if (rib_thicknesses.empty()) continue;
 
        // Preload some variables before [edge] gets changed
        node_t* from = edge.from;
        node_t* to = edge.to;
        Point a = from->p;
        Point b = to->p;
        Point ab = b - a;
        coord_t ab_size = ab.cast<int64_t>().norm();
        coord_t a_R = edge.from->data.distance_to_boundary;
        coord_t b_R = edge.to->data.distance_to_boundary;
        
        edge_t* last_edge_replacing_input = &edge;
        for (coord_t rib_thickness : rib_thicknesses)
        {
            if (rib_thickness / 2 <= a_R) 
            {
                continue;
            }
            if (rib_thickness / 2 >= b_R) 
            {
                break;
            }
            
            coord_t new_node_bead_count = std::min(edge.from->data.bead_count, edge.to->data.bead_count);
            coord_t end_pos = int64_t(ab_size) * int64_t(rib_thickness / 2 - a_R) / int64_t(b_R - a_R);
            assert(end_pos > 0);
            assert(end_pos < ab_size);
            node_t* close_node = (end_pos < ab_size / 2)? from : to;
            if ((end_pos < snap_dist || end_pos > ab_size - snap_dist)
                && close_node->data.bead_count == new_node_bead_count
            )
            {
                assert(end_pos <= ab_size);
                close_node->data.transition_ratio = 0;
                continue;
            }
            Point mid = a + normal(ab, end_pos);
            
            assert(last_edge_replacing_input->data.isCentral());
            assert(last_edge_replacing_input->data.type != SkeletalTrapezoidationEdge::EdgeType::EXTRA_VD);
            last_edge_replacing_input = graph.insertNode(last_edge_replacing_input, mid, new_node_bead_count);
            assert(last_edge_replacing_input->data.type != SkeletalTrapezoidationEdge::EdgeType::EXTRA_VD);
            assert(last_edge_replacing_input->data.isCentral());
        }
    }
}

References Slic3r::Arachne::SkeletalTrapezoidationJoint::bead_count, beading_strategy, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, discretization_step_size, Slic3r::Arachne::SkeletalTrapezoidationJoint::distance_to_boundary, Slic3r::Arachne::HalfEdgeGraph< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::edges, Slic3r::Arachne::SkeletalTrapezoidationEdge::EXTRA_VD, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::from, Slic3r::Arachne::BeadingStrategy::getNonlinearThicknesses(), graph, Slic3r::Arachne::SkeletalTrapezoidationGraph::insertNode(), Slic3r::Arachne::SkeletalTrapezoidationEdge::isCentral(), Slic3r::Arachne::normal(), Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::p, Slic3r::shorter_then(), snap_dist, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::to, Slic3r::Arachne::SkeletalTrapezoidationJoint::transition_ratio, and Slic3r::Arachne::SkeletalTrapezoidationEdge::type.

Referenced by generateToolpaths().

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◆ generateJunctions()

void Slic3r::Arachne::SkeletalTrapezoidation::generateJunctions	(	ptr_vector_t< BeadingPropagation > &	node_beadings,
		ptr_vector_t< LineJunctions > &	edge_junctions
	)

protected

generate junctions for each bone

Parameters

edge_to_junctions junctions ordered high R to low R

{
    for (edge_t& edge_ : graph.edges)
    {
        edge_t* edge = &edge_;
        if (edge->from->data.distance_to_boundary > edge->to->data.distance_to_boundary)
        { // Only consider the upward half-edges
            continue;
        }
 
        coord_t start_R = edge->to->data.distance_to_boundary; // higher R
        coord_t end_R = edge->from->data.distance_to_boundary; // lower R
 
        if ((edge->from->data.bead_count == edge->to->data.bead_count && edge->from->data.bead_count >= 0)
            || end_R >= start_R)
        { // No beads to generate
            continue;
        }
 
        Beading* beading = &getOrCreateBeading(edge->to, node_beadings)->beading;
        edge_junctions.emplace_back(std::make_shared<LineJunctions>());
        edge_.data.setExtrusionJunctions(edge_junctions.back());  // initialization
        LineJunctions& ret = *edge_junctions.back();
 
        assert(beading->total_thickness >= edge->to->data.distance_to_boundary * 2);
        if(beading->total_thickness < edge->to->data.distance_to_boundary * 2)
        {
            BOOST_LOG_TRIVIAL(warning) << "Generated junction is beyond the center of total width.";
        }
 
        Point a = edge->to->p;
        Point b = edge->from->p;
        Point ab = b - a;
 
        const size_t num_junctions = beading->toolpath_locations.size();
        size_t junction_idx;
        // Compute starting junction_idx for this segment
        for (junction_idx = (std::max(size_t(1), beading->toolpath_locations.size()) - 1) / 2; junction_idx < num_junctions; junction_idx--)
        {
            coord_t bead_R = beading->toolpath_locations[junction_idx];
            // toolpath_locations computed inside DistributedBeadingStrategy could be off by 1 because of rounding errors.
            // In GH issue #8472, these roundings errors caused missing the middle extrusion.
            // Adding small epsilon should help resolve those cases.
            if (bead_R <= start_R + 1)
            { // Junction coinciding with start node is used in this function call
                break;
            }
        }
 
        // Robustness against odd segments which might lie just slightly outside of the range due to rounding errors
        // not sure if this is really needed (TODO)
        if (junction_idx + 1 < num_junctions
            && beading->toolpath_locations[junction_idx + 1] <= start_R + scaled<coord_t>(0.005)
            && beading->total_thickness < start_R + scaled<coord_t>(0.005)
        )
        {
            junction_idx++;
        }
 
        for (; junction_idx < num_junctions; junction_idx--) //When junction_idx underflows, it'll be more than num_junctions too.
        {
            coord_t bead_R = beading->toolpath_locations[junction_idx];
            assert(bead_R >= 0);
            if (bead_R < end_R)
            { // Junction coinciding with a node is handled by the next segment
                break;
            }
            Point junction(a + (ab.cast<int64_t>() * int64_t(bead_R - start_R) / int64_t(end_R - start_R)).cast<coord_t>());
            if (bead_R > start_R - scaled<coord_t>(0.005))
            { // Snap to start node if it is really close, in order to be able to see 3-way intersection later on more robustly
                junction = a;
            }
            ret.emplace_back(junction, beading->bead_widths[junction_idx], junction_idx);
        }
    }
}

References Slic3r::Arachne::SkeletalTrapezoidationJoint::bead_count, Slic3r::Arachne::BeadingStrategy::Beading::bead_widths, Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, Slic3r::Arachne::SkeletalTrapezoidationJoint::distance_to_boundary, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::from, Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::p, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::to, Slic3r::Arachne::BeadingStrategy::Beading::toolpath_locations, and Slic3r::Arachne::BeadingStrategy::Beading::total_thickness.

◆ generateLocalMaximaSingleBeads()

void Slic3r::Arachne::SkeletalTrapezoidation::generateLocalMaximaSingleBeads ( )

protected

Genrate small segments for local maxima where the beading would only result in a single bead

{
    std::vector<VariableWidthLines> &generated_toolpaths = *p_generated_toolpaths;
 
    for (auto& node : graph.nodes)
    {
        if (! node.data.hasBeading())
        {
            continue;
        }
        Beading& beading = node.data.getBeading()->beading;
        if (beading.bead_widths.size() % 2 == 1 && node.isLocalMaximum(true) && !node.isCentral())
        {
            const size_t inset_index = beading.bead_widths.size() / 2;
            constexpr bool is_odd = true;
            if (inset_index >= generated_toolpaths.size())
            {
                generated_toolpaths.resize(inset_index + 1);
            }
            generated_toolpaths[inset_index].emplace_back(inset_index, is_odd);
            ExtrusionLine& line = generated_toolpaths[inset_index].back();
            const coord_t width = beading.bead_widths[inset_index];
            // total area to be extruded is pi*(w/2)^2 = pi*w*w/4
            // Width a constant extrusion width w, that would be a length of pi*w/4
            // If we make a small circle to fill up the hole, then that circle would have a circumference of 2*pi*r
            // So our circle needs to be such that r=w/8
            const coord_t     r          = width / 8;
            constexpr coord_t n_segments = 6;
            for (coord_t segment = 0; segment < n_segments; segment++) {
                float a = 2.0 * M_PI / n_segments * segment;
                line.junctions.emplace_back(node.p + Point(r * cos(a), r * sin(a)), width, inset_index);
            }
        }
    }
}

References Slic3r::Arachne::ExtrusionLine::back(), Slic3r::Arachne::BeadingStrategy::Beading::bead_widths, cos(), Slic3r::Arachne::ExtrusionLine::junctions, M_PI, segment(), and sin().

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◆ generateSegments()

void Slic3r::Arachne::SkeletalTrapezoidation::generateSegments ( )

protected

Parameters

[out] segments the generated segments

{
    std::vector<edge_t*> upward_quad_mids;
    for (edge_t& edge : graph.edges)
    {
        if (edge.prev && edge.next && edge.isUpward())
        {
            upward_quad_mids.emplace_back(&edge);
        }
    }
    
    std::sort(upward_quad_mids.begin(), upward_quad_mids.end(), [](edge_t* a, edge_t* b)
    {
        if (a->to->data.distance_to_boundary == b->to->data.distance_to_boundary)
        { // Ordering between two 'upward' edges of the same distance is important when one of the edges is flat and connected to the other
            if (a->from->data.distance_to_boundary == a->to->data.distance_to_boundary
                && b->from->data.distance_to_boundary == b->to->data.distance_to_boundary)
            {
                coord_t max = std::numeric_limits<coord_t>::max();
                coord_t a_dist_from_up = std::min(a->distToGoUp().value_or(max), a->twin->distToGoUp().value_or(max)) - (a->to->p - a->from->p).cast<int64_t>().norm();
                coord_t b_dist_from_up = std::min(b->distToGoUp().value_or(max), b->twin->distToGoUp().value_or(max)) - (b->to->p - b->from->p).cast<int64_t>().norm();
                return a_dist_from_up < b_dist_from_up;
            }
            else if (a->from->data.distance_to_boundary == a->to->data.distance_to_boundary)
            {
                return true; // Edge a might be 'above' edge b
            }
            else if (b->from->data.distance_to_boundary == b->to->data.distance_to_boundary)
            {
                return false; // Edge b might be 'above' edge a
            }
            else
            {
                // Ordering is not important
            }
        }
        return a->to->data.distance_to_boundary > b->to->data.distance_to_boundary;
    });
 
    ptr_vector_t<BeadingPropagation> node_beadings;
    { // Store beading
        for (node_t& node : graph.nodes)
        {
            if (node.data.bead_count <= 0)
            {
                continue;
            }
            if (node.data.transition_ratio == 0)
            {
                node_beadings.emplace_back(new BeadingPropagation(beading_strategy.compute(node.data.distance_to_boundary * 2, node.data.bead_count)));
                node.data.setBeading(node_beadings.back());
                assert(node_beadings.back()->beading.total_thickness == node.data.distance_to_boundary * 2);
                if(node_beadings.back()->beading.total_thickness != node.data.distance_to_boundary * 2)
                {
                    BOOST_LOG_TRIVIAL(warning) << "If transitioning to an endpoint (ratio 0), the node should be exactly in the middle.";
                }
            }
            else
            {
                Beading low_count_beading = beading_strategy.compute(node.data.distance_to_boundary * 2, node.data.bead_count);
                Beading high_count_beading = beading_strategy.compute(node.data.distance_to_boundary * 2, node.data.bead_count + 1);
                Beading merged = interpolate(low_count_beading, 1.0 - node.data.transition_ratio, high_count_beading);
                node_beadings.emplace_back(new BeadingPropagation(merged));
                node.data.setBeading(node_beadings.back());
                assert(merged.total_thickness == node.data.distance_to_boundary * 2);
                if(merged.total_thickness != node.data.distance_to_boundary * 2)
                {
                    BOOST_LOG_TRIVIAL(warning) << "If merging two beads, the new bead must be exactly in the middle.";
                }
            }
        }
    }
 
#ifdef ARACHNE_DEBUG
    static int iRun = 0;
    export_graph_to_svg(debug_out_path("ST-generateSegments-before-propagation-%d.svg", iRun), this->graph, this->outline);
#endif
 
    propagateBeadingsUpward(upward_quad_mids, node_beadings);
 
#ifdef ARACHNE_DEBUG
    export_graph_to_svg(debug_out_path("ST-generateSegments-upward-propagation-%d.svg", iRun), this->graph, this->outline);
#endif
 
    propagateBeadingsDownward(upward_quad_mids, node_beadings);
 
#ifdef ARACHNE_DEBUG
    export_graph_to_svg(debug_out_path("ST-generateSegments-downward-propagation-%d.svg", iRun), this->graph, this->outline);
#endif
 
    ptr_vector_t<LineJunctions> edge_junctions; // junctions ordered high R to low R
    generateJunctions(node_beadings, edge_junctions);
 
#ifdef ARACHNE_DEBUG
    export_graph_to_svg(debug_out_path("ST-generateSegments-junctions-%d.svg", iRun), this->graph, this->outline, edge_junctions);
#endif
 
    connectJunctions(edge_junctions);
 
    generateLocalMaximaSingleBeads();
 
#ifdef ARACHNE_DEBUG
    ++iRun;
#endif
}

References Slic3r::Arachne::HalfEdgeGraph< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::edges, and graph.

Referenced by generateToolpaths().

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◆ generateToolpaths()

void Slic3r::Arachne::SkeletalTrapezoidation::generateToolpaths	(	std::vector< VariableWidthLines > &	generated_toolpaths,
		bool	filter_outermost_central_edges = `false`
	)

Generate the paths that the printer must extrude, to print the outlines in the input polygons.

Parameters

filter_outermost_central_edges Some edges are "central" but still touch the outside of the polygon. If enabled, don't treat these as "central" but as if it's a obtuse corner. As a result, sharp corners will no longer end in a single line but will just loop.

{
#ifdef ARACHNE_DEBUG
    static int iRun = 0;
#endif
 
    p_generated_toolpaths = &generated_toolpaths;
 
    updateIsCentral();
 
#ifdef ARACHNE_DEBUG
    export_graph_to_svg(debug_out_path("ST-updateIsCentral-final-%d.svg", iRun), this->graph, this->outline);
#endif
 
    filterCentral(central_filter_dist);
 
#ifdef ARACHNE_DEBUG
    export_graph_to_svg(debug_out_path("ST-filterCentral-final-%d.svg", iRun), this->graph, this->outline);
#endif
 
    if (filter_outermost_central_edges)
        filterOuterCentral();
 
    updateBeadCount();
 
#ifdef ARACHNE_DEBUG
    export_graph_to_svg(debug_out_path("ST-updateBeadCount-final-%d.svg", iRun), this->graph, this->outline);
#endif
 
    filterNoncentralRegions();
 
#ifdef ARACHNE_DEBUG
    export_graph_to_svg(debug_out_path("ST-filterNoncentralRegions-final-%d.svg", iRun), this->graph, this->outline);
#endif
 
    generateTransitioningRibs();
 
#ifdef ARACHNE_DEBUG
    export_graph_to_svg(debug_out_path("ST-generateTransitioningRibs-final-%d.svg", iRun), this->graph, this->outline);
#endif
 
    generateExtraRibs();
 
#ifdef ARACHNE_DEBUG
    export_graph_to_svg(debug_out_path("ST-generateExtraRibs-final-%d.svg", iRun), this->graph, this->outline);
#endif
 
    generateSegments();
 
#ifdef ARACHNE_DEBUG
    export_graph_to_svg(debug_out_path("ST-generateSegments-final-%d.svg", iRun), this->graph, this->outline);
#endif
 
#ifdef ARACHNE_DEBUG
    ++iRun;
#endif
}

References central_filter_dist, Slic3r::debug_out_path(), filterCentral(), filterNoncentralRegions(), filterOuterCentral(), generateExtraRibs(), generateSegments(), generateTransitioningRibs(), p_generated_toolpaths, updateBeadCount(), and updateIsCentral().

Referenced by Slic3r::Arachne::WallToolPaths::generate().

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◆ generateTransitionEnd()

bool Slic3r::Arachne::SkeletalTrapezoidation::generateTransitionEnd	(	edge_t &	edge,
		coord_t	start_pos,
		coord_t	end_pos,
		coord_t	transition_half_length,
		double	start_rest,
		double	end_rest,
		coord_t	transition_lower_bead_count,
		ptr_vector_t< std::list< TransitionEnd > > &	edge_transition_ends
	)

protected

Compute a single endpoint of a transition.

Parameters

	edge	The edge to generate the endpoint for.
	start_pos	The position where the transition starts.
	end_pos	The position where the transition ends on the other side.
	transition_half_length	The distance to the transition middle point.
	start_rest	The gap between the start of the transition and the starting endpoint, as ratio of the inner bead width at the high end of the transition.
	end_rest	The gap between the end of the transition and the ending endpoint, as ratio of the inner bead width at the high end of the transition.
	transition_lower_bead_count	The bead count at the lower end of the transition.
[out]	edge_transition_ends	The list to put the resulting endpoints in.

Returns: Whether the given edge is going downward (i.e. towards a thinner region of the polygon).

{
    Point a = edge.from->p;
    Point b = edge.to->p;
    Point ab = b - a;
    coord_t ab_size = ab.cast<int64_t>().norm(); // TODO: prevent recalculation of these values
 
    assert(start_pos <= ab_size);
    if(start_pos > ab_size)
    {
        BOOST_LOG_TRIVIAL(warning) << "Start position of edge is beyond edge range.";
    }
 
    bool going_up = end_rest > start_rest;
 
    assert(edge.data.isCentral());
    if (!edge.data.isCentral())
    {
        BOOST_LOG_TRIVIAL(warning) << "This function shouldn't generate ends in or beyond non-central regions.";
        return false;
    }
 
    if (end_pos > ab_size)
    { // Recurse on all further edges
        float rest = end_rest - (start_rest - end_rest) * (end_pos - ab_size) / (start_pos - end_pos);
        assert(rest >= 0);
        assert(rest <= std::max(end_rest, start_rest));
        assert(rest >= std::min(end_rest, start_rest));
 
        coord_t central_edge_count = 0;
        for (edge_t* outgoing = edge.next; outgoing && outgoing != edge.twin; outgoing = outgoing->twin->next)
        {
            if (!outgoing->data.isCentral()) continue;
            central_edge_count++;
        }
 
        bool is_only_going_down = true;
        bool has_recursed = false;
        for (edge_t* outgoing = edge.next; outgoing && outgoing != edge.twin;)
        {
            edge_t* next = outgoing->twin->next; // Before we change the outgoing edge itself
            if (!outgoing->data.isCentral())
            {
                outgoing = next;
                continue; // Don't put transition ends in non-central regions
            }
            if (central_edge_count > 1 && going_up && isGoingDown(outgoing, 0, end_pos - ab_size + transition_half_length, lower_bead_count))
            { // We're after a 3-way_all-central_junction-node and going in the direction of lower bead count
                // don't introduce a transition end along this central direction, because this direction is the downward direction
                // while we are supposed to be [going_up]
                outgoing = next;
                continue;
            }
            bool is_going_down = generateTransitionEnd(*outgoing, 0, end_pos - ab_size, transition_half_length, rest, end_rest, lower_bead_count, edge_transition_ends);
            is_only_going_down &= is_going_down;
            outgoing = next;
            has_recursed = true;
        }
        if (!going_up || (has_recursed && !is_only_going_down))
        {
            edge.to->data.transition_ratio = rest;
            edge.to->data.bead_count = lower_bead_count;
        }
        return is_only_going_down;
    }
    else // end_pos < ab_size
    { // Add transition end point here
        bool is_lower_end = end_rest == 0; // TODO collapse this parameter into the bool for which it is used here!
        coord_t pos = -1;
 
        edge_t* upward_edge = nullptr;
        if (edge.isUpward())
        {
            upward_edge = &edge;
            pos = end_pos;
        }
        else
        {
            upward_edge = edge.twin;
            pos = ab_size - end_pos;
        }
 
        if(!upward_edge->data.hasTransitionEnds())
        {
            //This edge doesn't have a data structure yet for the transition ends. Make one.
            edge_transition_ends.emplace_back(std::make_shared<std::list<TransitionEnd>>());
            upward_edge->data.setTransitionEnds(edge_transition_ends.back());
        }
        auto transitions = upward_edge->data.getTransitionEnds();
 
        //Add a transition to it (on the correct side).
        assert(ab_size == (edge.twin->from->p - edge.twin->to->p).cast<int64_t>().norm());
        assert(pos <= ab_size);
        if (transitions->empty() || pos < transitions->front().pos)
        { // Preorder so that sorting later on is faster
            transitions->emplace_front(pos, lower_bead_count, is_lower_end);
        }
        else
        {
            transitions->emplace_back(pos, lower_bead_count, is_lower_end);
        }
        return false;
    }
}

References Slic3r::Arachne::SkeletalTrapezoidationJoint::bead_count, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::from, generateTransitionEnd(), Slic3r::Arachne::SkeletalTrapezoidationEdge::getTransitionEnds(), Slic3r::Arachne::SkeletalTrapezoidationEdge::hasTransitionEnds(), Slic3r::Arachne::SkeletalTrapezoidationEdge::isCentral(), isGoingDown(), Slic3r::Arachne::STHalfEdge::isUpward(), Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::next, Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::p, Slic3r::Arachne::SkeletalTrapezoidationEdge::setTransitionEnds(), Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::to, Slic3r::Arachne::SkeletalTrapezoidationJoint::transition_ratio, and Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::twin.

Referenced by generateTransitionEnd(), and generateTransitionEnds().

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◆ generateTransitionEnds()

void Slic3r::Arachne::SkeletalTrapezoidation::generateTransitionEnds	(	edge_t &	edge,
		coord_t	mid_R,
		coord_t	transition_lower_bead_count,
		ptr_vector_t< std::list< TransitionEnd > > &	edge_transition_ends
	)

protected

Generate the endpoints of a specific transition midpoint.

Parameters

	edge	The edge to create transitions on.
	mid_R	The radius of the transition middle point.
	transition_lower_bead_count	The bead count at the lower end of the transition.
[out]	edge_transition_ends	A list of endpoints to add the new endpoints to.

{
    const Point a = edge.from->p;
    const Point b = edge.to->p;
    const Point ab = b - a;
    const coord_t ab_size = ab.cast<int64_t>().norm();
 
    const coord_t transition_length = beading_strategy.getTransitioningLength(lower_bead_count);
    const float transition_mid_position = beading_strategy.getTransitionAnchorPos(lower_bead_count);
    constexpr float inner_bead_width_ratio_after_transition = 1.0;
 
    constexpr coord_t start_rest = 0;
    const float mid_rest = transition_mid_position * inner_bead_width_ratio_after_transition;
    constexpr float end_rest = inner_bead_width_ratio_after_transition;
 
    { // Lower bead count transition end
        const coord_t start_pos = ab_size - mid_pos;
        const coord_t transition_half_length = transition_mid_position * int64_t(transition_length);
        const coord_t end_pos = start_pos + transition_half_length;
        generateTransitionEnd(*edge.twin, start_pos, end_pos, transition_half_length, mid_rest, start_rest, lower_bead_count, edge_transition_ends);
    }
 
    { // Upper bead count transition end
        const coord_t start_pos = mid_pos;
        const coord_t transition_half_length = (1.0 - transition_mid_position) * transition_length;
        const coord_t end_pos = mid_pos + transition_half_length;
#ifdef DEBUG
        if (! generateTransitionEnd(edge, start_pos, end_pos, transition_half_length, mid_rest, end_rest, lower_bead_count, edge_transition_ends))
        {
            BOOST_LOG_TRIVIAL(warning) << "There must have been at least one direction in which the bead count is increasing enough for the transition to happen!";
        }
#else
        generateTransitionEnd(edge, start_pos, end_pos, transition_half_length, mid_rest, end_rest, lower_bead_count, edge_transition_ends);
#endif
    }
}

References beading_strategy, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::from, generateTransitionEnd(), Slic3r::Arachne::BeadingStrategy::getTransitionAnchorPos(), Slic3r::Arachne::BeadingStrategy::getTransitioningLength(), Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::p, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::to, and Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::twin.

Referenced by generateAllTransitionEnds().

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◆ generateTransitioningRibs()

void Slic3r::Arachne::SkeletalTrapezoidation::generateTransitioningRibs ( )

protected

Create extra edges along all edges, where it needs to transition from one bead count to another.

For example, if an edge of the graph goes from a bead count of 6 to a bead count of 1, it needs to generate 5 places where the beads around this line transition to a lower bead count. These are the "ribs". They reach from the edge to the border of the polygon. Where the beads hit those ribs the beads know to make a transition.

{
    // Store the upward edges to the transitions.
    // We only store the halfedge for which the distance_to_boundary is higher at the end than at the beginning.
    ptr_vector_t<std::list<TransitionMiddle>> edge_transitions;
    generateTransitionMids(edge_transitions);
 
    for (edge_t& edge : graph.edges)
    { // Check if there is a transition in between nodes with different bead counts
        if (edge.data.isCentral() && edge.from->data.bead_count != edge.to->data.bead_count)
        {
            assert(edge.data.hasTransitions() || edge.twin->data.hasTransitions());
        }
    }
 
    filterTransitionMids();
 
#ifdef ARACHNE_DEBUG
    static int iRun = 0;
    export_graph_to_svg(debug_out_path("ST-generateTransitioningRibs-mids-%d.svg", iRun++), this->graph, this->outline);
#endif
 
    ptr_vector_t<std::list<TransitionEnd>> edge_transition_ends; // We only map the half edge in the upward direction. mapped items are not sorted
    generateAllTransitionEnds(edge_transition_ends);
 
#ifdef ARACHNE_DEBUG
    export_graph_to_svg(debug_out_path("ST-generateTransitioningRibs-ends-%d.svg", iRun++), this->graph, this->outline);
#endif
 
    applyTransitions(edge_transition_ends);
    // Note that the shared pointer lists will be out of scope and thus destroyed here, since the remaining refs are weak_ptr.
 
#ifdef ARACHNE_DEBUG
    ++iRun;
#endif
}

References applyTransitions(), Slic3r::debug_out_path(), Slic3r::Arachne::HalfEdgeGraph< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::edges, filterTransitionMids(), generateAllTransitionEnds(), generateTransitionMids(), and graph.

Referenced by generateToolpaths().

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◆ generateTransitionMids()

void Slic3r::Arachne::SkeletalTrapezoidation::generateTransitionMids ( ptr_vector_t< std::list< TransitionMiddle > > & edge_transitions )

protected

Generate middle points of all transitions on edges.

The transition middle points are saved in the graph itself. They are also returned via the output parameter.

Parameters

[out] edge_transitions A list of transitions that were generated.

{
    for (edge_t& edge : graph.edges)
    {
        assert(edge.data.centralIsSet());
        if (!edge.data.isCentral())
        { // Only central regions introduce transitions
            continue;
        }
        coord_t start_R = edge.from->data.distance_to_boundary;
        coord_t end_R = edge.to->data.distance_to_boundary;
        int start_bead_count = edge.from->data.bead_count;
        int end_bead_count = edge.to->data.bead_count;
 
        if (start_R == end_R)
        { // No transitions occur when both end points have the same distance_to_boundary
            assert(edge.from->data.bead_count == edge.to->data.bead_count);
            if(edge.from->data.bead_count != edge.to->data.bead_count)
            {
                BOOST_LOG_TRIVIAL(warning) << "Bead count " << edge.from->data.bead_count << " is different from " << edge.to->data.bead_count << " even though distance to boundary is the same.";
            }
            continue;
        }
        else if (start_R > end_R)
        { // Only consider those half-edges which are going from a lower to a higher distance_to_boundary
            continue;
        }
 
        if (edge.from->data.bead_count == edge.to->data.bead_count)
        { // No transitions should occur according to the enforced bead counts
            continue;
        }
 
        if (start_bead_count > beading_strategy.getOptimalBeadCount(start_R * 2)
            || end_bead_count > beading_strategy.getOptimalBeadCount(end_R * 2))
        { // Wasn't the case earlier in this function because of already introduced transitions
            BOOST_LOG_TRIVIAL(error) << "transitioning segment overlap! (?)";
        }
        assert(start_R < end_R);
        if(start_R >= end_R)
        {
            BOOST_LOG_TRIVIAL(warning) << "Transitioning the wrong way around! This function expects to transition from small R to big R, but was transitioning from " << start_R << " to " << end_R;
        }
        coord_t edge_size = (edge.from->p - edge.to->p).cast<int64_t>().norm();
        for (int transition_lower_bead_count = start_bead_count; transition_lower_bead_count < end_bead_count; transition_lower_bead_count++)
        {
            coord_t mid_R = beading_strategy.getTransitionThickness(transition_lower_bead_count) / 2;
            if (mid_R > end_R)
            {
                BOOST_LOG_TRIVIAL(error) << "transition on segment lies outside of segment!";
                mid_R = end_R;
            }
            if (mid_R < start_R)
            {
                BOOST_LOG_TRIVIAL(error) << "transition on segment lies outside of segment!";
                mid_R = start_R;
            }
            coord_t mid_pos = int64_t(edge_size) * int64_t(mid_R - start_R) / int64_t(end_R - start_R);
 
            assert(mid_pos >= 0);
            assert(mid_pos <= edge_size);
            if(mid_pos < 0 || mid_pos > edge_size)
            {
                BOOST_LOG_TRIVIAL(warning) << "Transition mid is out of bounds of the edge.";
            }
            auto transitions = edge.data.getTransitions();
            constexpr bool ignore_empty = true;
            assert((! edge.data.hasTransitions(ignore_empty)) || mid_pos >= transitions->back().pos);
            if (! edge.data.hasTransitions(ignore_empty))
            {
                edge_transitions.emplace_back(std::make_shared<std::list<TransitionMiddle>>());
                edge.data.setTransitions(edge_transitions.back());  // initialization
                transitions = edge.data.getTransitions();
            }
            transitions->emplace_back(mid_pos, transition_lower_bead_count, mid_R);
        }
        assert((edge.from->data.bead_count == edge.to->data.bead_count) || edge.data.hasTransitions());
    }
}

References beading_strategy, Slic3r::Arachne::HalfEdgeGraph< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::edges, error, Slic3r::Arachne::BeadingStrategy::getOptimalBeadCount(), Slic3r::Arachne::BeadingStrategy::getTransitionThickness(), and graph.

Referenced by generateTransitioningRibs().

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◆ getNearestBeading()

std::shared_ptr< SkeletalTrapezoidationJoint::BeadingPropagation > Slic3r::Arachne::SkeletalTrapezoidation::getNearestBeading	(	node_t *	node,
		coord_t	max_dist
	)

protected

In case we cannot find the beading of a node, get a beading from the nearest node.

Parameters

node	The node to attempt to get a beading from. The actual node that the returned beading is from may be a different, nearby node.
max_dist	The maximum distance to search for.

Returns: A beading for the node, or nullptr if there is no node nearby with a beading.

{
    struct DistEdge
    {
        edge_t* edge_to;
        coord_t dist;
        DistEdge(edge_t* edge_to, coord_t dist)
        : edge_to(edge_to), dist(dist)
        {}
    };
 
    auto compare = [](const DistEdge& l, const DistEdge& r) -> bool { return l.dist > r.dist; };
    std::priority_queue<DistEdge, std::vector<DistEdge>, decltype(compare)> further_edges(compare);
    bool first = true;
    for (edge_t* outgoing = node->incident_edge; outgoing && (first || outgoing != node->incident_edge); outgoing = outgoing->twin->next)
    {
        further_edges.emplace(outgoing, (outgoing->to->p - outgoing->from->p).cast<int64_t>().norm());
        first = false;
    }
 
    for (coord_t counter = 0; counter < SKELETAL_TRAPEZOIDATION_BEAD_SEARCH_MAX; counter++)
    { // Prevent endless recursion
        if (further_edges.empty()) return nullptr;
        DistEdge here = further_edges.top();
        further_edges.pop();
        if (here.dist > max_dist) return nullptr;
        if (here.edge_to->to->data.hasBeading())
        {
            return here.edge_to->to->data.getBeading();
        }
        else
        { // recurse
            for (edge_t* further_edge = here.edge_to->next; further_edge && further_edge != here.edge_to->twin; further_edge = further_edge->twin->next)
            {
                further_edges.emplace(further_edge, here.dist + (further_edge->to->p - further_edge->from->p).cast<int64_t>().norm());
            }
        }
    }
    return nullptr;
}

References Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::incident_edge, and SKELETAL_TRAPEZOIDATION_BEAD_SEARCH_MAX.

◆ getOrCreateBeading()

std::shared_ptr< SkeletalTrapezoidationJoint::BeadingPropagation > Slic3r::Arachne::SkeletalTrapezoidation::getOrCreateBeading	(	node_t *	node,
		ptr_vector_t< BeadingPropagation > &	node_beadings
	)

protected

Get the beading at a certain node of the skeletal graph, or create one if it doesn't have one yet.

This is a lazy get.

Parameters

node	The node to get the beading from.
node_beadings	A list of all beadings for nodes.

Returns: The beading of that node.

{
    if (! node->data.hasBeading())
    {
        if (node->data.bead_count == -1)
        { // This bug is due to too small central edges
            constexpr coord_t nearby_dist = scaled<coord_t>(0.1);
            auto nearest_beading = getNearestBeading(node, nearby_dist);
            if (nearest_beading)
            {
                return nearest_beading;
            }
            
            // Else make a new beading:
            bool has_central_edge = false;
            bool first = true;
            coord_t dist = std::numeric_limits<coord_t>::max();
            for (edge_t* edge = node->incident_edge; edge && (first || edge != node->incident_edge); edge = edge->twin->next)
            {
                if (edge->data.isCentral())
                {
                    has_central_edge = true;
                }
                assert(edge->to->data.distance_to_boundary >= 0);
                dist = std::min(dist, edge->to->data.distance_to_boundary + coord_t((edge->to->p - edge->from->p).cast<int64_t>().norm()));
                first = false;
            }
            if (!has_central_edge)
            {
                BOOST_LOG_TRIVIAL(error) << "Unknown beading for non-central node!";
            }
            assert(dist != std::numeric_limits<coord_t>::max());
            node->data.bead_count = beading_strategy.getOptimalBeadCount(dist * 2);
        }
        assert(node->data.bead_count != -1);
        node_beadings.emplace_back(new BeadingPropagation(beading_strategy.compute(node->data.distance_to_boundary * 2, node->data.bead_count)));
        node->data.setBeading(node_beadings.back());
    }
    assert(node->data.hasBeading());
    return node->data.getBeading();
}

References Slic3r::Arachne::SkeletalTrapezoidationJoint::bead_count, Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, Slic3r::Arachne::SkeletalTrapezoidationJoint::distance_to_boundary, error, Slic3r::Arachne::SkeletalTrapezoidationJoint::getBeading(), Slic3r::Arachne::SkeletalTrapezoidationJoint::hasBeading(), Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::incident_edge, and Slic3r::Arachne::SkeletalTrapezoidationJoint::setBeading().

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◆ getQuadMaxRedgeTo()

SkeletalTrapezoidation::edge_t * Slic3r::Arachne::SkeletalTrapezoidation::getQuadMaxRedgeTo ( edge_t * quad_start_edge )

protected

From a quad (a group of linked edges in one cell of the Voronoi), find the edge pointing to the node that is furthest away from the border of the polygon.

Parameters

quad_start_edge The first edge of the quad.

Returns: The edge of the quad that is furthest away from the border.

{
    assert(quad_start_edge->prev == nullptr);
    assert(quad_start_edge->from->data.distance_to_boundary == 0);
    coord_t max_R = -1;
    edge_t* ret = nullptr;
    for (edge_t* edge = quad_start_edge; edge; edge = edge->next)
    {
        coord_t r = edge->to->data.distance_to_boundary;
        if (r > max_R)
        {
            max_R = r;
            ret = edge;
        }
    }
 
    if (!ret->next && ret->to->data.distance_to_boundary - scaled<coord_t>(0.005) < ret->from->data.distance_to_boundary)
    {
        ret = ret->prev;
    }
    assert(ret);
    assert(ret->next);
    return ret;
}

References Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, Slic3r::Arachne::SkeletalTrapezoidationJoint::distance_to_boundary, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::from, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::next, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::prev, and Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::to.

◆ interpolate() [1/2]

SkeletalTrapezoidation::Beading Slic3r::Arachne::SkeletalTrapezoidation::interpolate	(	const Beading &	left,
		double	ratio_left_to_whole,
		const Beading &	right
	)		const

protected

Subroutine of interpolate(const Beading&, Ratio, const Beading&, coord_t)

This creates a new Beading between two beadings, assuming that both have the same number of beads.

Parameters

left	One of the beadings to interpolate between.
ratio_left_to_whole	The position within the two beadings to sample an interpolation. Should be a ratio between 0 and 1.
right	One of the beadings to interpolate between.

Returns: The beading at the interpolated location.

{
    assert(ratio_left_to_whole >= 0.0 && ratio_left_to_whole <= 1.0);
    float ratio_right_to_whole = 1.0 - ratio_left_to_whole;
 
    Beading ret = (left.total_thickness > right.total_thickness)? left : right;
    for (size_t inset_idx = 0; inset_idx < std::min(left.bead_widths.size(), right.bead_widths.size()); inset_idx++)
    {
        if(left.bead_widths[inset_idx] == 0 || right.bead_widths[inset_idx] == 0)
        {
            ret.bead_widths[inset_idx] = 0; //0-width wall markers stay 0-width.
        }
        else
        {
            ret.bead_widths[inset_idx] = ratio_left_to_whole * left.bead_widths[inset_idx] + ratio_right_to_whole * right.bead_widths[inset_idx];
        }
        ret.toolpath_locations[inset_idx] = ratio_left_to_whole * left.toolpath_locations[inset_idx] + ratio_right_to_whole * right.toolpath_locations[inset_idx];
    }
    return ret;
}

References Slic3r::Arachne::BeadingStrategy::Beading::bead_widths, and Slic3r::Arachne::BeadingStrategy::Beading::toolpath_locations.

◆ interpolate() [2/2]

SkeletalTrapezoidation::Beading Slic3r::Arachne::SkeletalTrapezoidation::interpolate	(	const Beading &	left,
		double	ratio_left_to_whole,
		const Beading &	right,
		coord_t	switching_radius
	)		const

protected

Find a beading in between two other beadings.

This creates a new beading. With this we can find the coordinates of the endpoints of the actual line segments to draw.

The parameters left and right are not actually always left or right but just arbitrary directions to visually indicate the difference.

Parameters

left	One of the beadings to interpolate between.
ratio_left_to_whole	The position within the two beadings to sample an interpolation. Should be a ratio between 0 and 1.
right	One of the beadings to interpolate between.
switching_radius	The bead radius at which we switch from the left beading to the merged beading, if the beadings have a different number of beads.

Returns: The beading at the interpolated location.

{
    assert(ratio_left_to_whole >= 0.0 && ratio_left_to_whole <= 1.0);
    Beading ret = interpolate(left, ratio_left_to_whole, right);
 
    // TODO: don't use toolpath locations past the middle!
    // TODO: stretch bead widths and locations of the higher bead count beading to fit in the left over space
    coord_t next_inset_idx;
    for (next_inset_idx = left.toolpath_locations.size() - 1; next_inset_idx >= 0; next_inset_idx--)
    {
        if (switching_radius > left.toolpath_locations[next_inset_idx])
        {
            break;
        }
    }
    if (next_inset_idx < 0)
    { // There is no next inset, because there is only one
        assert(left.toolpath_locations.empty() || left.toolpath_locations.front() >= switching_radius);
        return ret;
    }
    if (next_inset_idx + 1 == coord_t(left.toolpath_locations.size()))
    { // We cant adjust to fit the next edge because there is no previous one?!
        return ret;
    }
    assert(next_inset_idx < coord_t(left.toolpath_locations.size()));
    assert(left.toolpath_locations[next_inset_idx] <= switching_radius);
    assert(left.toolpath_locations[next_inset_idx + 1] >= switching_radius);
    if (ret.toolpath_locations[next_inset_idx] > switching_radius)
    { // One inset disappeared between left and the merged one
        // solve for ratio f:
        // f*l + (1-f)*r = s
        // f*l + r - f*r = s
        // f*(l-r) + r = s
        // f*(l-r) = s - r
        // f = (s-r) / (l-r)
        float new_ratio = static_cast<float>(switching_radius - right.toolpath_locations[next_inset_idx]) / static_cast<float>(left.toolpath_locations[next_inset_idx] - right.toolpath_locations[next_inset_idx]);
        new_ratio = std::min(1.0, new_ratio + 0.1);
        return interpolate(left, new_ratio, right);
    }
    return ret;
}

References Slic3r::Arachne::BeadingStrategy::Beading::toolpath_locations.

◆ isEndOfCentral()

bool Slic3r::Arachne::SkeletalTrapezoidation::isEndOfCentral ( const edge_t & edge ) const

protected

Determines whether this edge marks the end of the central region.

Parameters

edge	The edge to check.

Returns: true if this edge goes from a central region to a non-central region, or false in every other case (central to central, non-central to non-central, non-central to central, or end-of-the-line).

{
    if (!edge_to.data.isCentral())
    {
        return false;
    }
    if (!edge_to.next)
    {
        return true;
    }
    for (const edge_t* edge = edge_to.next; edge && edge != edge_to.twin; edge = edge->twin->next)
    {
        if (edge->data.isCentral())
        {
            return false;
        }
        assert(edge->twin);
    }
    return true;
}

References Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, Slic3r::Arachne::SkeletalTrapezoidationEdge::isCentral(), Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::next, and Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::twin.

Referenced by filterCentral(), and filterNoncentralRegions().

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◆ isGoingDown()

bool Slic3r::Arachne::SkeletalTrapezoidation::isGoingDown	(	edge_t *	outgoing,
		coord_t	traveled_dist,
		coord_t	transition_half_length,
		coord_t	lower_bead_count
	)		const

protected

Determines whether an edge is going downwards or upwards in the graph.

An edge is said to go "downwards" if it's going towards a narrower part of the polygon. The notion of "downwards" comes from the conical representation of the graph, where the polygon is filled with a cone of maximum radius.

This function works by recursively checking adjacent edges until the edge is reached.

Parameters

outgoing	The edge to check.
traveled_dist	The distance traversed so far.
transition_half_length	The radius of the transition width.
lower_bead_count	The bead count at the lower end of the edge.

Returns: true if this edge is going down, or false if it's going up.

{
    // NOTE: the logic below is not fully thought through.
    // TODO: take transition mids into account
    if (outgoing->to->data.distance_to_boundary == 0)
    {
        return true;
    }
    bool is_upward = outgoing->to->data.distance_to_boundary >= outgoing->from->data.distance_to_boundary;
    edge_t* upward_edge = is_upward? outgoing : outgoing->twin;
    if (outgoing->to->data.bead_count > lower_bead_count + 1)
    {
        assert(upward_edge->data.hasTransitions() && "If the bead count is going down there has to be a transition mid!");
        if(!upward_edge->data.hasTransitions())
        {
            BOOST_LOG_TRIVIAL(warning) << "If the bead count is going down there has to be a transition mid!";
        }
        return false;
    }
    coord_t length = (outgoing->to->p - outgoing->from->p).cast<int64_t>().norm();
    if (upward_edge->data.hasTransitions())
    {
        auto& transition_mids = *upward_edge->data.getTransitions();
        TransitionMiddle& mid = is_upward? transition_mids.front() : transition_mids.back();
        if (
            mid.lower_bead_count == lower_bead_count &&
            ((is_upward && mid.pos + traveled_dist < max_dist)
                || (!is_upward && length - mid.pos + traveled_dist < max_dist))
        )
        {
            return true;
        }
    }
    if (traveled_dist + length > max_dist)
    {
        return false;
    }
    if (outgoing->to->data.bead_count <= lower_bead_count
        && !(outgoing->to->data.bead_count == lower_bead_count && outgoing->to->data.transition_ratio > 0.0))
    {
        return true;
    }
    
    bool is_only_going_down = true;
    bool has_recursed = false;
    for (edge_t* next = outgoing->next; next && next != outgoing->twin; next = next->twin->next)
    {
        if (!next->data.isCentral())
        {
            continue;
        }
        bool is_going_down = isGoingDown(next, traveled_dist + length, max_dist, lower_bead_count);
        is_only_going_down &= is_going_down;
        has_recursed = true;
    }
    return has_recursed && is_only_going_down;
}

References Slic3r::Arachne::SkeletalTrapezoidationJoint::bead_count, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::data, Slic3r::Arachne::SkeletalTrapezoidationJoint::distance_to_boundary, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::from, Slic3r::Arachne::SkeletalTrapezoidationEdge::getTransitions(), Slic3r::Arachne::SkeletalTrapezoidationEdge::hasTransitions(), isGoingDown(), Slic3r::length(), Slic3r::Arachne::SkeletalTrapezoidationEdge::TransitionMiddle::lower_bead_count, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::next, Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::p, Slic3r::Arachne::SkeletalTrapezoidationEdge::TransitionMiddle::pos, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::to, Slic3r::Arachne::SkeletalTrapezoidationJoint::transition_ratio, and Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::twin.

Referenced by generateTransitionEnd(), and isGoingDown().

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◆ makeNode()

SkeletalTrapezoidation::node_t & Slic3r::Arachne::SkeletalTrapezoidation::makeNode	(	vd_t::vertex_type &	vd_node,
		Point	p
	)

protected

Get the node which the VD node maps to, or create a new mapping if there wasn't any yet.

{
    auto he_node_it = vd_node_to_he_node.find(&vd_node);
    if (he_node_it == vd_node_to_he_node.end())
    {
        graph.nodes.emplace_front(SkeletalTrapezoidationJoint(), p);
        node_t& node = graph.nodes.front();
        vd_node_to_he_node.emplace(&vd_node, &node);
        return node;
    }
    else
    {
        return *he_node_it->second;
    }
}

References graph, Slic3r::Arachne::HalfEdgeGraph< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::nodes, and vd_node_to_he_node.

Referenced by transferEdge().

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◆ propagateBeadingsDownward() [1/2]

void Slic3r::Arachne::SkeletalTrapezoidation::propagateBeadingsDownward	(	edge_t *	edge_to_peak,
		ptr_vector_t< BeadingPropagation > &	node_beadings
	)

protected

Subroutine of propagateBeadingsDownward(std::vector<edge_t*>&, ptr_vector_t<BeadingPropagation>&)

{
    coord_t length = (edge_to_peak->to->p - edge_to_peak->from->p).cast<int64_t>().norm();
    BeadingPropagation& top_beading = *getOrCreateBeading(edge_to_peak->to, node_beadings);
    assert(top_beading.beading.total_thickness >= edge_to_peak->to->data.distance_to_boundary * 2);
    if(top_beading.beading.total_thickness < edge_to_peak->to->data.distance_to_boundary * 2)
    {
        BOOST_LOG_TRIVIAL(warning) << "Top bead is beyond the center of the total width.";
    }
    assert(!top_beading.is_upward_propagated_only);
 
    if(!edge_to_peak->from->data.hasBeading())
    { // Set new beading if there is no beading associated with the node yet
        BeadingPropagation propagated_beading = top_beading;
        propagated_beading.dist_from_top_source += length;
        node_beadings.emplace_back(new BeadingPropagation(propagated_beading));
        edge_to_peak->from->data.setBeading(node_beadings.back());
        assert(propagated_beading.beading.total_thickness >= edge_to_peak->from->data.distance_to_boundary * 2);
        if(propagated_beading.beading.total_thickness < edge_to_peak->from->data.distance_to_boundary * 2)
        {
            BOOST_LOG_TRIVIAL(warning) << "Propagated bead is beyond the center of the total width.";
        }
    }
    else
    {
        BeadingPropagation& bottom_beading = *edge_to_peak->from->data.getBeading();
        coord_t total_dist = top_beading.dist_from_top_source + length + bottom_beading.dist_to_bottom_source;
        double ratio_of_top = static_cast<float>(bottom_beading.dist_to_bottom_source) / std::min(total_dist, beading_propagation_transition_dist);
        ratio_of_top = std::max(0.0, ratio_of_top);
        if (ratio_of_top >= 1.0)
        {
            bottom_beading = top_beading;
            bottom_beading.dist_from_top_source += length;
        }
        else
        {
            Beading merged_beading = interpolate(top_beading.beading, ratio_of_top, bottom_beading.beading, edge_to_peak->from->data.distance_to_boundary);
            bottom_beading = BeadingPropagation(merged_beading);
            bottom_beading.is_upward_propagated_only = false;
            assert(merged_beading.total_thickness >= edge_to_peak->from->data.distance_to_boundary * 2);
            if(merged_beading.total_thickness < edge_to_peak->from->data.distance_to_boundary * 2)
            {
                BOOST_LOG_TRIVIAL(warning) << "Merged bead is beyond the center of the total width.";
            }
        }
    }
}

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◆ propagateBeadingsDownward() [2/2]

void Slic3r::Arachne::SkeletalTrapezoidation::propagateBeadingsDownward	(	std::vector< edge_t * > &	upward_quad_mids,
		ptr_vector_t< BeadingPropagation > &	node_beadings
	)

protected

propagate beading info from higher R nodes to lower R nodes

merge with upward propagated beadings if they are encountered

don't transfer to nodes which lie on the outline polygon

edges are sorted so that we can do a depth-first walk without employing a recursive algorithm

Parameters

upward_quad_mids all upward halfedges of the inner skeletal edges (not directly connected to the outline) sorted on their highest [distance_to_boundary]. Higher dist first.

{
    for (edge_t* upward_quad_mid : upward_quad_mids)
    {
        // Transfer beading information to lower nodes
        if (!upward_quad_mid->data.isCentral())
        {
            // for equidistant edge: propagate from known beading to node with unknown beading
            if (upward_quad_mid->from->data.distance_to_boundary == upward_quad_mid->to->data.distance_to_boundary
                && upward_quad_mid->from->data.hasBeading()
                && ! upward_quad_mid->to->data.hasBeading()
            )
            {
                propagateBeadingsDownward(upward_quad_mid->twin, node_beadings);
            }
            else
            {
                propagateBeadingsDownward(upward_quad_mid, node_beadings);
            }
        }
    }
}

◆ propagateBeadingsUpward()

void Slic3r::Arachne::SkeletalTrapezoidation::propagateBeadingsUpward	(	std::vector< edge_t * > &	upward_quad_mids,
		ptr_vector_t< BeadingPropagation > &	node_beadings
	)

protected

Propagate beading information from nodes that are closer to the edge (low radius R) to nodes that are farther from the edge (high R).

only propagate from nodes with beading info upward to nodes without beading info

Edges are sorted by their radius, so that we can do a depth-first walk without employing a recursive algorithm.

In upward propagated beadings we store the distance traveled, so that we can merge these beadings with the downward propagated beadings in propagateBeadingsDownward(.)

Parameters

upward_quad_mids all upward halfedges of the inner skeletal edges (not directly connected to the outline) sorted on their highest [distance_to_boundary]. Higher dist first.

{
    for (auto upward_quad_mids_it = upward_quad_mids.rbegin(); upward_quad_mids_it != upward_quad_mids.rend(); ++upward_quad_mids_it)
    {
        edge_t* upward_edge = *upward_quad_mids_it;
        if (upward_edge->to->data.bead_count >= 0)
        { // Don't override local beading
            continue;
        }
        if (! upward_edge->from->data.hasBeading())
        { // Only propagate if we have something to propagate
            continue;
        }
        BeadingPropagation& lower_beading = *upward_edge->from->data.getBeading();
        if (upward_edge->to->data.hasBeading())
        { // Only propagate to places where there is place
            continue;
        }
        assert((upward_edge->from->data.distance_to_boundary != upward_edge->to->data.distance_to_boundary || shorter_then(upward_edge->to->p - upward_edge->from->p, central_filter_dist)) && "zero difference R edges should always be central");
        coord_t length = (upward_edge->to->p - upward_edge->from->p).cast<int64_t>().norm();
        BeadingPropagation upper_beading = lower_beading;
        upper_beading.dist_to_bottom_source += length;
        upper_beading.is_upward_propagated_only = true;
        node_beadings.emplace_back(new BeadingPropagation(upper_beading));
        upward_edge->to->data.setBeading(node_beadings.back());
        assert(upper_beading.beading.total_thickness <= upward_edge->to->data.distance_to_boundary * 2);
    }
}

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◆ separatePointyQuadEndNodes()

void Slic3r::Arachne::SkeletalTrapezoidation::separatePointyQuadEndNodes ( )

protected

For VD cells associated with an input polygon vertex, we need to separate the node at the end and start of the cell into two That way we can reach both the quad_start and the quad_end from the [incident_edge] of the two new nodes Otherwise if node.incident_edge = quad_start you couldnt reach quad_end.twin by normal iteration (i.e. it = it.twin.next)

{
    NodeSet visited_nodes;
    for (edge_t& edge : graph.edges)
    {
        if (edge.prev) 
        {
            continue;
        }
        edge_t* quad_start = &edge;
        if (visited_nodes.find(quad_start->from) == visited_nodes.end())
        {
            visited_nodes.emplace(quad_start->from);
        }
        else
        { // Needs to be duplicated
            graph.nodes.emplace_back(*quad_start->from);
            node_t* new_node = &graph.nodes.back();
            new_node->incident_edge = quad_start;
            quad_start->from = new_node;
            quad_start->twin->to = new_node;
        }
    }
}

References Slic3r::Arachne::HalfEdgeGraph< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::edges, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::from, graph, Slic3r::Arachne::HalfEdgeNode< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::incident_edge, Slic3r::Arachne::HalfEdgeGraph< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::nodes, Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::to, and Slic3r::Arachne::HalfEdge< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::twin.

Referenced by constructFromPolygons().

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◆ transferEdge()

void Slic3r::Arachne::SkeletalTrapezoidation::transferEdge	(	Point	from,
		Point	to,
		vd_t::edge_type &	vd_edge,
		edge_t *&	prev_edge,
		Point &	start_source_point,
		Point &	end_source_point,
		const std::vector< Segment > &	segments
	)

protected

Transfer an edge from the VD to the HE and perform discretization of parabolic edges (and vertex-vertex edges) prev_edge serves as input and output. May be null as input.

{
    auto he_edge_it = vd_edge_to_he_edge.find(vd_edge.twin());
    if (he_edge_it != vd_edge_to_he_edge.end())
    { // Twin segment(s) have already been made
        edge_t* source_twin = he_edge_it->second;
        assert(source_twin);
        auto end_node_it = vd_node_to_he_node.find(vd_edge.vertex1());
        assert(end_node_it != vd_node_to_he_node.end());
        node_t* end_node = end_node_it->second;
        for (edge_t* twin = source_twin; ;twin = twin->prev->twin->prev)
        {
            if(!twin)
            {
                BOOST_LOG_TRIVIAL(warning) << "Encountered a voronoi edge without twin.";
                continue; //Prevent reading unallocated memory.
            }
            assert(twin);
            graph.edges.emplace_front(SkeletalTrapezoidationEdge());
            edge_t* edge = &graph.edges.front();
            edge->from = twin->to;
            edge->to = twin->from;
            edge->twin = twin;
            twin->twin = edge;
            edge->from->incident_edge = edge;
            
            if (prev_edge)
            {
                edge->prev = prev_edge;
                prev_edge->next = edge;
            }
 
            prev_edge = edge;
 
            if (prev_edge->to == end_node)
            {
                return;
            }
            
            if (!twin->prev || !twin->prev->twin || !twin->prev->twin->prev)
            {
                BOOST_LOG_TRIVIAL(error) << "Discretized segment behaves oddly!";
                return;
            }
            
            assert(twin->prev); // Forth rib
            assert(twin->prev->twin); // Back rib
            assert(twin->prev->twin->prev); // Prev segment along parabola
            
            constexpr bool is_not_next_to_start_or_end = false; // Only ribs at the end of a cell should be skipped
            graph.makeRib(prev_edge, start_source_point, end_source_point, is_not_next_to_start_or_end);
        }
        assert(prev_edge);
    }
    else
    {
        Points discretized = discretize(vd_edge, segments);
        assert(discretized.size() >= 2);
        if(discretized.size() < 2)
        {
            BOOST_LOG_TRIVIAL(warning) << "Discretized Voronoi edge is degenerate.";
        }
        
        assert(!prev_edge || prev_edge->to);
        if(prev_edge && !prev_edge->to)
        {
            BOOST_LOG_TRIVIAL(warning) << "Previous edge doesn't go anywhere.";
        }
        node_t* v0 = (prev_edge)? prev_edge->to : &makeNode(*vd_edge.vertex0(), from); // TODO: investigate whether boost:voronoi can produce multiple verts and violates consistency
        Point p0 = discretized.front();
        for (size_t p1_idx = 1; p1_idx < discretized.size(); p1_idx++)
        {
            Point p1 = discretized[p1_idx];
            node_t* v1;
            if (p1_idx < discretized.size() - 1)
            {
                graph.nodes.emplace_front(SkeletalTrapezoidationJoint(), p1);
                v1 = &graph.nodes.front();
            }
            else
            {
                v1 = &makeNode(*vd_edge.vertex1(), to);
            }
 
            graph.edges.emplace_front(SkeletalTrapezoidationEdge());
            edge_t* edge = &graph.edges.front();
            edge->from = v0;
            edge->to = v1;
            edge->from->incident_edge = edge;
            
            if (prev_edge)
            {
                edge->prev = prev_edge;
                prev_edge->next = edge;
            }
            
            prev_edge = edge;
            p0 = p1;
            v0 = v1;
            
            if (p1_idx < discretized.size() - 1)
            { // Rib for last segment gets introduced outside this function!
                constexpr bool is_not_next_to_start_or_end = false; // Only ribs at the end of a cell should be skipped
                graph.makeRib(prev_edge, start_source_point, end_source_point, is_not_next_to_start_or_end);
            }
        }
        assert(prev_edge);
        vd_edge_to_he_edge.emplace(&vd_edge, prev_edge);
    }
}

Referenced by constructFromPolygons().

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◆ updateBeadCount()

void Slic3r::Arachne::SkeletalTrapezoidation::updateBeadCount ( )

protected

Set bead count in central regions based on the optimal_bead_count of the beading strategy.

{
    for (edge_t& edge : graph.edges)
    {
        if (edge.data.isCentral())
        {
            edge.to->data.bead_count = beading_strategy.getOptimalBeadCount(edge.to->data.distance_to_boundary * 2);
        }
    }
 
    // Fix bead count at locally maximal R, also for central regions!! See TODO s in generateTransitionEnd(.)
    for (node_t& node : graph.nodes)
    {
        if (node.isLocalMaximum())
        {
            if (node.data.distance_to_boundary < 0)
            {
                BOOST_LOG_TRIVIAL(warning) << "Distance to boundary not yet computed for local maximum!";
                node.data.distance_to_boundary = std::numeric_limits<coord_t>::max();
                edge_t* edge = node.incident_edge;
                do
                {
                    node.data.distance_to_boundary = std::min(node.data.distance_to_boundary, edge->to->data.distance_to_boundary + coord_t((edge->from->p - edge->to->p).cast<int64_t>().norm()));
                } while (edge = edge->twin->next, edge != node.incident_edge);
            }
            coord_t bead_count = beading_strategy.getOptimalBeadCount(node.data.distance_to_boundary * 2);
            node.data.bead_count = bead_count;
        }
    }
}

Referenced by generateToolpaths().

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◆ updateIsCentral()

void Slic3r::Arachne::SkeletalTrapezoidation::updateIsCentral ( )

protected

{
    //                                            _.-'^`      A and B are the endpoints of an edge we're checking.
    //                                      _.-'^`            Part of the line AB will be used as a cap,
    //                                _.-'^` \                because the polygon is too narrow there.
    //                          _.-'^`        \               If |AB| minus the cap is still bigger than dR,
    //                    _.-'^`               \ R2           the edge AB is considered central. It's then
    //              _.-'^` \              _.-'\`\             significant compared to the edges around it.
    //        _.-'^`        \R1     _.-'^`     '`\ dR
    //  _.-'^`a/2            \_.-'^`a             \           Line AR2 is parallel to the polygon contour.
    //  `^'-._````````````````A```````````v````````B```````   dR is the remaining diameter at B.
    //        `^'-._                     dD = |AB|            As a result, AB is less often central if the polygon
    //              `^'-._                                    corner is obtuse.
    //                             sin a = dR / dD
 
    coord_t outer_edge_filter_length = beading_strategy.getTransitionThickness(0) / 2;
 
    float cap = sin(beading_strategy.getTransitioningAngle() * 0.5); // = cos(bisector_angle / 2)
    for (edge_t& edge: graph.edges)
    {
        assert(edge.twin);
        if(!edge.twin)
        {
            BOOST_LOG_TRIVIAL(warning) << "Encountered a Voronoi edge without twin!";
            continue;
        }
        if(edge.twin->data.centralIsSet())
        {
            edge.data.setIsCentral(edge.twin->data.isCentral());
        }
        else if(edge.data.type == SkeletalTrapezoidationEdge::EdgeType::EXTRA_VD)
        {
            edge.data.setIsCentral(false);
        }
        else if(std::max(edge.from->data.distance_to_boundary, edge.to->data.distance_to_boundary) < outer_edge_filter_length)
        {
            edge.data.setIsCentral(false);
        }
        else
        {
            Point a = edge.from->p;
            Point b = edge.to->p;
            Point ab = b - a;
            coord_t dR = std::abs(edge.to->data.distance_to_boundary - edge.from->data.distance_to_boundary);
            coord_t dD = ab.cast<int64_t>().norm();
            edge.data.setIsCentral(dR < dD * cap);
        }
    }
}

References beading_strategy, Slic3r::Arachne::HalfEdgeGraph< node_data_t, edge_data_t, derived_node_t, derived_edge_t >::edges, Slic3r::Arachne::SkeletalTrapezoidationEdge::EXTRA_VD, Slic3r::Arachne::BeadingStrategy::getTransitioningAngle(), Slic3r::Arachne::BeadingStrategy::getTransitionThickness(), graph, and sin().

Referenced by generateToolpaths().

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Friends And Related Symbol Documentation

◆ detect_voronoi_edge_intersecting_input_segment

bool detect_voronoi_edge_intersecting_input_segment	(	const Geometry::VoronoiDiagram &	voronoi_diagram,
		const std::vector< VoronoiUtils::Segment > &	segments
	)

friend

{
    for (VoronoiUtils::vd_t::cell_type cell : voronoi_diagram.cells()) {
        if (!cell.incident_edge())
            continue; // Degenerated cell, there is no spoon
 
        if (!cell.contains_segment())
            continue; // Skip cells that don't contain segments.
 
        const VoronoiUtils::Segment &source_segment      = VoronoiUtils::getSourceSegment(cell, segments);
        const Vec2d                  source_segment_from = source_segment.from().cast<double>();
        const Vec2d                  source_segment_vec  = source_segment.to().cast<double>() - source_segment_from;
 
        Point                          start_source_point, end_source_point;
        VoronoiUtils::vd_t::edge_type *begin_voronoi_edge = nullptr, *end_voronoi_edge = nullptr;
        SkeletalTrapezoidation::computeSegmentCellRange(cell, start_source_point, end_source_point, begin_voronoi_edge, end_voronoi_edge, segments);
        // All Voronoi vertices must be on left side of the source segment, otherwise Voronoi diagram is invalid.
        // FIXME Lukas H.: Be aware that begin_voronoi_edge and end_voronoi_edge could be nullptr in some specific cases.
        //                 It mostly happens when there is some missing Voronoi, for example, in GH issue #8846 (IssuesWithMysteriousPerimeters.3mf).
        if (begin_voronoi_edge != nullptr && end_voronoi_edge != nullptr)
            for (VoronoiUtils::vd_t::edge_type *edge = begin_voronoi_edge; edge != end_voronoi_edge; edge = edge->next())
                if (const Vec2d edge_v1(edge->vertex1()->x(), edge->vertex1()->y()); Slic3r::cross2(source_segment_vec, edge_v1 - source_segment_from) < 0)
                    return true;
    }
 
    return false;
}

Member Data Documentation

◆ allowed_filter_deviation

coord_t Slic3r::Arachne::SkeletalTrapezoidation::allowed_filter_deviation

private

The allowed line width deviation induced by filtering.

Referenced by dissolveNearbyTransitions().

◆ beading_propagation_transition_dist

coord_t Slic3r::Arachne::SkeletalTrapezoidation::beading_propagation_transition_dist

private

When there are different beadings propagated from below and from above, use this transitioning distance.

◆ beading_strategy

const BeadingStrategy& Slic3r::Arachne::SkeletalTrapezoidation::beading_strategy

private

The strategy to use to fill a certain shape with lines.

Various BeadingStrategies are available that differ in which lines get to print at their optimal width, where the play is being compensated, and how the joints are handled where we transition to different numbers of lines.

Referenced by dissolveNearbyTransitions(), filterNoncentralRegions(), filterTransitionMids(), generateExtraRibs(), generateTransitionEnds(), generateTransitionMids(), updateBeadCount(), and updateIsCentral().

◆ central_filter_dist

constexpr coord_t Slic3r::Arachne::SkeletalTrapezoidation::central_filter_dist = scaled<coord_t>(0.02)

staticconstexprprivate

Filter areas marked as 'central' smaller than this.

Referenced by generateToolpaths().

◆ discretization_step_size

coord_t Slic3r::Arachne::SkeletalTrapezoidation::discretization_step_size

private

approximate size of segments when parabolic VD edges get discretized (and vertex-vertex edges)

Referenced by discretize(), and generateExtraRibs().

◆ graph

graph_t Slic3r::Arachne::SkeletalTrapezoidation::graph

A skeletal graph through the polygons that we need to fill with beads.

The skeletal graph represents the medial axes through each part of the polygons, and the lines from these medial axes towards each vertex of the polygons. The graph can be used to see what the width is of a polygon in each place and where the width transitions.

Referenced by applyTransitions(), constructFromPolygons(), filterCentral(), filterNoncentralRegions(), filterOuterCentral(), filterTransitionMids(), generateAllTransitionEnds(), generateExtraRibs(), generateSegments(), generateTransitioningRibs(), generateTransitionMids(), makeNode(), separatePointyQuadEndNodes(), transferEdge(), updateBeadCount(), and updateIsCentral().

◆ p_generated_toolpaths

std::vector<VariableWidthLines>* Slic3r::Arachne::SkeletalTrapezoidation::p_generated_toolpaths

protected

(Eventual) returned 'polylines per index' result (from generateToolpaths):

Referenced by generateToolpaths().

◆ snap_dist

constexpr coord_t Slic3r::Arachne::SkeletalTrapezoidation::snap_dist = scaled<coord_t>(0.02)

staticconstexprprivate

Generic arithmatic inaccuracy. Only used to determine whether a transition really needs to insert an extra edge.

Referenced by applyTransitions(), and generateExtraRibs().

◆ transition_filter_dist

coord_t Slic3r::Arachne::SkeletalTrapezoidation::transition_filter_dist

private

Filter transition mids (i.e. anchors) closer together than this.

Referenced by filterTransitionMids().

◆ transitioning_angle

double Slic3r::Arachne::SkeletalTrapezoidation::transitioning_angle

private

How pointy a region should be before we apply the method. Equals 180* - limit_bisector_angle.

Referenced by discretize().

◆ vd_edge_to_he_edge

ankerl::unordered_dense::map<vd_t::edge_type*, edge_t*> Slic3r::Arachne::SkeletalTrapezoidation::vd_edge_to_he_edge

protected

mapping each voronoi VD edge to the corresponding halfedge HE edge In case the result segment is discretized, we map the VD edge to the last HE edge

Referenced by constructFromPolygons(), and transferEdge().

◆ vd_node_to_he_node

ankerl::unordered_dense::map<vd_t::vertex_type*, node_t*> Slic3r::Arachne::SkeletalTrapezoidation::vd_node_to_he_node

protected

Referenced by constructFromPolygons(), makeNode(), and transferEdge().

The documentation for this class was generated from the following files:

src/libslic3r/Arachne/SkeletalTrapezoidation.hpp
src/libslic3r/Arachne/SkeletalTrapezoidation.cpp

Classes

Public Types

Public Member Functions

Public Attributes

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Private Types

Private Attributes

Static Private Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ Beading

◆ BeadingPropagation

◆ edge_t

◆ graph_t

◆ node_t

◆ NodeSet

◆ PointMap

◆ pos_t

◆ ptr_vector_t

◆ Segment

◆ TransitionEnd

◆ TransitionMiddle

◆ vd_t

Constructor & Destructor Documentation

◆ SkeletalTrapezoidation()

Member Function Documentation

◆ addToolpathSegment()

◆ applyTransitions()

◆ computePointCellRange()

◆ computeSegmentCellRange()

◆ connectJunctions()

◆ constructFromPolygons()

◆ discretize()

◆ dissolveBeadCountRegion()

◆ dissolveNearbyTransitions()

◆ filterCentral() [1/2]

◆ filterCentral() [2/2]

◆ filterEndOfCentralTransition()

◆ filterNoncentralRegions() [1/2]

◆ filterNoncentralRegions() [2/2]

◆ filterOuterCentral()

◆ filterTransitionMids()

◆ generateAllTransitionEnds()

◆ generateExtraRibs()

◆ generateJunctions()

◆ generateLocalMaximaSingleBeads()

◆ generateSegments()

◆ generateToolpaths()

◆ generateTransitionEnd()

◆ generateTransitionEnds()

◆ generateTransitioningRibs()

◆ generateTransitionMids()

◆ getNearestBeading()

◆ getOrCreateBeading()

◆ getQuadMaxRedgeTo()

◆ interpolate() [1/2]

◆ interpolate() [2/2]

◆ isEndOfCentral()

◆ isGoingDown()

◆ makeNode()

◆ propagateBeadingsDownward() [1/2]

◆ propagateBeadingsDownward() [2/2]

◆ propagateBeadingsUpward()

◆ separatePointyQuadEndNodes()

◆ transferEdge()

◆ updateBeadCount()

◆ updateIsCentral()

Friends And Related Symbol Documentation

◆ detect_voronoi_edge_intersecting_input_segment

Member Data Documentation

◆ allowed_filter_deviation

◆ beading_propagation_transition_dist

◆ beading_strategy

◆ central_filter_dist

◆ discretization_step_size

◆ graph

◆ p_generated_toolpaths