Fix arachne wall ordering (#7959)

* Revert "SPE-1950: Optimization of computation complexity of perimeter ordering for Arachne generator."

This reverts commit 47ec9b9b06.

* Revert "SPE-1963: Improve ordering of perimeters with Arachne perimeter generator"

This reverts commit babb84c70a.
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Noisyfox 2025-01-22 09:58:34 +08:00 committed by GitHub
parent a3de7cf0bd
commit 2253ab304a
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8 changed files with 756 additions and 901 deletions

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@ -1,280 +0,0 @@
#include <stack>
#include <algorithm>
#include <cmath>
#include "PerimeterOrder.hpp"
#include "libslic3r/Arachne/utils/ExtrusionJunction.hpp"
#include "libslic3r/Point.hpp"
namespace Slic3r::Arachne::PerimeterOrder {
using namespace Arachne;
static size_t get_extrusion_lines_count(const Perimeters &perimeters) {
size_t extrusion_lines_count = 0;
for (const Perimeter &perimeter : perimeters)
extrusion_lines_count += perimeter.size();
return extrusion_lines_count;
}
static PerimeterExtrusions get_sorted_perimeter_extrusions_by_area(const Perimeters &perimeters) {
PerimeterExtrusions sorted_perimeter_extrusions;
sorted_perimeter_extrusions.reserve(get_extrusion_lines_count(perimeters));
for (const Perimeter &perimeter : perimeters) {
for (const ExtrusionLine &extrusion_line : perimeter) {
if (extrusion_line.empty())
continue; // This shouldn't ever happen.
const BoundingBox bbox = get_extents(extrusion_line);
// Be aware that Arachne produces contours with clockwise orientation and holes with counterclockwise orientation.
const double area = std::abs(extrusion_line.area());
const Polygon polygon = extrusion_line.is_closed ? to_polygon(extrusion_line) : Polygon{};
sorted_perimeter_extrusions.emplace_back(extrusion_line, area, polygon, bbox);
}
}
// Open extrusions have an area equal to zero, so sorting based on the area ensures that open extrusions will always be before closed ones.
std::sort(sorted_perimeter_extrusions.begin(), sorted_perimeter_extrusions.end(),
[](const PerimeterExtrusion &l, const PerimeterExtrusion &r) { return l.area < r.area; });
return sorted_perimeter_extrusions;
}
// Functions fill adjacent_perimeter_extrusions field for every PerimeterExtrusion by pointers to PerimeterExtrusions that contain or are inside this PerimeterExtrusion.
static void construct_perimeter_extrusions_adjacency_graph(PerimeterExtrusions &sorted_perimeter_extrusions) {
// Construct a graph (defined using adjacent_perimeter_extrusions field) where two PerimeterExtrusion are adjacent when one is inside the other.
std::vector<bool> root_candidates(sorted_perimeter_extrusions.size(), false);
for (PerimeterExtrusion &perimeter_extrusion : sorted_perimeter_extrusions) {
const size_t perimeter_extrusion_idx = &perimeter_extrusion - sorted_perimeter_extrusions.data();
if (!perimeter_extrusion.is_closed()) {
root_candidates[perimeter_extrusion_idx] = true;
continue;
}
for (PerimeterExtrusion &root_candidate : sorted_perimeter_extrusions) {
const size_t root_candidate_idx = &root_candidate - sorted_perimeter_extrusions.data();
if (!root_candidates[root_candidate_idx])
continue;
if (perimeter_extrusion.bbox.contains(root_candidate.bbox) && perimeter_extrusion.polygon.contains(root_candidate.extrusion.junctions.front().p)) {
perimeter_extrusion.adjacent_perimeter_extrusions.emplace_back(&root_candidate);
root_candidate.adjacent_perimeter_extrusions.emplace_back(&perimeter_extrusion);
root_candidates[root_candidate_idx] = false;
}
}
root_candidates[perimeter_extrusion_idx] = true;
}
}
// Perform the depth-first search to assign the nearest external perimeter for every PerimeterExtrusion.
// When some PerimeterExtrusion is achievable from more than one external perimeter, then we choose the
// one that comes from a contour.
static void assign_nearest_external_perimeter(PerimeterExtrusions &sorted_perimeter_extrusions) {
std::stack<PerimeterExtrusion *> stack;
for (PerimeterExtrusion &perimeter_extrusion : sorted_perimeter_extrusions) {
if (perimeter_extrusion.is_external_perimeter()) {
perimeter_extrusion.depth = 0;
perimeter_extrusion.nearest_external_perimeter = &perimeter_extrusion;
stack.push(&perimeter_extrusion);
}
}
while (!stack.empty()) {
PerimeterExtrusion *current_extrusion = stack.top();
stack.pop();
for (PerimeterExtrusion *adjacent_extrusion : current_extrusion->adjacent_perimeter_extrusions) {
const size_t adjacent_extrusion_depth = current_extrusion->depth + 1;
// Update depth when the new depth is smaller or when we can achieve the same depth from a contour.
// This will ensure that the internal perimeter will be extruded before the outer external perimeter
// when there are two external perimeters and one internal.
if (adjacent_extrusion_depth < adjacent_extrusion->depth) {
adjacent_extrusion->nearest_external_perimeter = current_extrusion->nearest_external_perimeter;
adjacent_extrusion->depth = adjacent_extrusion_depth;
stack.push(adjacent_extrusion);
} else if (adjacent_extrusion_depth == adjacent_extrusion->depth && !adjacent_extrusion->nearest_external_perimeter->is_contour() && current_extrusion->is_contour()) {
adjacent_extrusion->nearest_external_perimeter = current_extrusion->nearest_external_perimeter;
stack.push(adjacent_extrusion);
}
}
}
}
inline Point get_end_position(const ExtrusionLine &extrusion) {
if (extrusion.is_closed)
return extrusion.junctions[0].p; // We ended where we started.
else
return extrusion.junctions.back().p; // Pick the other end from where we started.
}
// Returns ordered extrusions.
static std::vector<const PerimeterExtrusion *> ordered_perimeter_extrusions_to_minimize_distances(Point current_position, std::vector<const PerimeterExtrusion *> extrusions) {
// Ensure that open extrusions will be placed before the closed one.
std::sort(extrusions.begin(), extrusions.end(),
[](const PerimeterExtrusion *l, const PerimeterExtrusion *r) -> bool { return l->is_closed() < r->is_closed(); });
std::vector<const PerimeterExtrusion *> ordered_extrusions;
std::vector<bool> already_selected(extrusions.size(), false);
while (ordered_extrusions.size() < extrusions.size()) {
double nearest_distance_sqr = std::numeric_limits<double>::max();
size_t nearest_extrusion_idx = 0;
bool is_nearest_closed = false;
for (size_t extrusion_idx = 0; extrusion_idx < extrusions.size(); ++extrusion_idx) {
if (already_selected[extrusion_idx])
continue;
const ExtrusionLine &extrusion_line = extrusions[extrusion_idx]->extrusion;
const Point &extrusion_start_position = extrusion_line.junctions.front().p;
const double distance_sqr = (current_position - extrusion_start_position).cast<double>().squaredNorm();
if (distance_sqr < nearest_distance_sqr) {
if (extrusion_line.is_closed || (!extrusion_line.is_closed && nearest_distance_sqr == std::numeric_limits<double>::max()) || (!extrusion_line.is_closed && !is_nearest_closed)) {
nearest_extrusion_idx = extrusion_idx;
nearest_distance_sqr = distance_sqr;
is_nearest_closed = extrusion_line.is_closed;
}
}
}
already_selected[nearest_extrusion_idx] = true;
const PerimeterExtrusion *nearest_extrusion = extrusions[nearest_extrusion_idx];
current_position = get_end_position(nearest_extrusion->extrusion);
ordered_extrusions.emplace_back(nearest_extrusion);
}
return ordered_extrusions;
}
struct GroupedPerimeterExtrusions
{
GroupedPerimeterExtrusions() = delete;
explicit GroupedPerimeterExtrusions(const PerimeterExtrusion *external_perimeter_extrusion)
: external_perimeter_extrusion(external_perimeter_extrusion) {}
std::vector<const PerimeterExtrusion *> extrusions;
const PerimeterExtrusion *external_perimeter_extrusion = nullptr;
};
// Returns vector of indexes that represent the order of grouped extrusions in grouped_extrusions.
static std::vector<size_t> order_of_grouped_perimeter_extrusions_to_minimize_distances(Point current_position, std::vector<GroupedPerimeterExtrusions> grouped_extrusions) {
// Ensure that holes will be placed before contour and open extrusions before the closed one.
std::sort(grouped_extrusions.begin(), grouped_extrusions.end(), [](const GroupedPerimeterExtrusions &l, const GroupedPerimeterExtrusions &r) -> bool {
return (l.external_perimeter_extrusion->is_contour() < r.external_perimeter_extrusion->is_contour()) ||
(l.external_perimeter_extrusion->is_contour() == r.external_perimeter_extrusion->is_contour() && l.external_perimeter_extrusion->is_closed() < r.external_perimeter_extrusion->is_closed());
});
const size_t holes_cnt = std::count_if(grouped_extrusions.begin(), grouped_extrusions.end(), [](const GroupedPerimeterExtrusions &grouped_extrusions) {
return !grouped_extrusions.external_perimeter_extrusion->is_contour();
});
std::vector<size_t> grouped_extrusions_order;
std::vector<bool> already_selected(grouped_extrusions.size(), false);
while (grouped_extrusions_order.size() < grouped_extrusions.size()) {
double nearest_distance_sqr = std::numeric_limits<double>::max();
size_t nearest_grouped_extrusions_idx = 0;
bool is_nearest_closed = false;
// First we order all holes and then we start ordering contours.
const size_t grouped_extrusion_end = grouped_extrusions_order.size() < holes_cnt ? holes_cnt: grouped_extrusions.size();
for (size_t grouped_extrusion_idx = 0; grouped_extrusion_idx < grouped_extrusion_end; ++grouped_extrusion_idx) {
if (already_selected[grouped_extrusion_idx])
continue;
const ExtrusionLine &external_perimeter_extrusion_line = grouped_extrusions[grouped_extrusion_idx].external_perimeter_extrusion->extrusion;
const Point &extrusion_start_position = external_perimeter_extrusion_line.junctions.front().p;
const double distance_sqr = (current_position - extrusion_start_position).cast<double>().squaredNorm();
if (distance_sqr < nearest_distance_sqr) {
if (external_perimeter_extrusion_line.is_closed || (!external_perimeter_extrusion_line.is_closed && nearest_distance_sqr == std::numeric_limits<double>::max()) || (!external_perimeter_extrusion_line.is_closed && !is_nearest_closed)) {
nearest_grouped_extrusions_idx = grouped_extrusion_idx;
nearest_distance_sqr = distance_sqr;
is_nearest_closed = external_perimeter_extrusion_line.is_closed;
}
}
}
grouped_extrusions_order.emplace_back(nearest_grouped_extrusions_idx);
already_selected[nearest_grouped_extrusions_idx] = true;
const GroupedPerimeterExtrusions &nearest_grouped_extrusions = grouped_extrusions[nearest_grouped_extrusions_idx];
const ExtrusionLine &last_extrusion_line = nearest_grouped_extrusions.extrusions.back()->extrusion;
current_position = get_end_position(last_extrusion_line);
}
return grouped_extrusions_order;
}
static PerimeterExtrusions extract_ordered_perimeter_extrusions(const PerimeterExtrusions &sorted_perimeter_extrusions, const bool external_perimeters_first) {
// Extrusions are ordered inside each group.
std::vector<GroupedPerimeterExtrusions> grouped_extrusions;
std::stack<const PerimeterExtrusion *> stack;
std::vector<bool> visited(sorted_perimeter_extrusions.size(), false);
for (const PerimeterExtrusion &perimeter_extrusion : sorted_perimeter_extrusions) {
if (!perimeter_extrusion.is_external_perimeter())
continue;
stack.push(&perimeter_extrusion);
visited.assign(sorted_perimeter_extrusions.size(), false);
grouped_extrusions.emplace_back(&perimeter_extrusion);
while (!stack.empty()) {
const PerimeterExtrusion *current_extrusion = stack.top();
const size_t current_extrusion_idx = current_extrusion - sorted_perimeter_extrusions.data();
stack.pop();
visited[current_extrusion_idx] = true;
if (current_extrusion->nearest_external_perimeter == &perimeter_extrusion) {
grouped_extrusions.back().extrusions.emplace_back(current_extrusion);
}
std::vector<const PerimeterExtrusion *> available_candidates;
for (const PerimeterExtrusion *adjacent_extrusion : current_extrusion->adjacent_perimeter_extrusions) {
const size_t adjacent_extrusion_idx = adjacent_extrusion - sorted_perimeter_extrusions.data();
if (!visited[adjacent_extrusion_idx] && !adjacent_extrusion->is_external_perimeter() && adjacent_extrusion->nearest_external_perimeter == &perimeter_extrusion) {
available_candidates.emplace_back(adjacent_extrusion);
}
}
if (available_candidates.size() == 1) {
stack.push(available_candidates.front());
} else if (available_candidates.size() > 1) {
// When there is more than one available candidate, then order candidates to minimize distances between
// candidates and also to minimize the distance from the current_position.
std::vector<const PerimeterExtrusion *> adjacent_extrusions = ordered_perimeter_extrusions_to_minimize_distances(Point::Zero(), available_candidates);
for (auto extrusion_it = adjacent_extrusions.rbegin(); extrusion_it != adjacent_extrusions.rend(); ++extrusion_it) {
stack.push(*extrusion_it);
}
}
}
if (!external_perimeters_first)
std::reverse(grouped_extrusions.back().extrusions.begin(), grouped_extrusions.back().extrusions.end());
}
const std::vector<size_t> grouped_extrusion_order = order_of_grouped_perimeter_extrusions_to_minimize_distances(Point::Zero(), grouped_extrusions);
PerimeterExtrusions ordered_extrusions;
for (size_t order_idx : grouped_extrusion_order) {
for (const PerimeterExtrusion *perimeter_extrusion : grouped_extrusions[order_idx].extrusions)
ordered_extrusions.emplace_back(*perimeter_extrusion);
}
return ordered_extrusions;
}
// FIXME: From the point of better patch planning, it should be better to do ordering when we have generated all extrusions (for now, when G-Code is exported).
// FIXME: It would be better to extract the adjacency graph of extrusions from the SkeletalTrapezoidation graph.
PerimeterExtrusions ordered_perimeter_extrusions(const Perimeters &perimeters, const bool external_perimeters_first) {
PerimeterExtrusions sorted_perimeter_extrusions = get_sorted_perimeter_extrusions_by_area(perimeters);
construct_perimeter_extrusions_adjacency_graph(sorted_perimeter_extrusions);
assign_nearest_external_perimeter(sorted_perimeter_extrusions);
return extract_ordered_perimeter_extrusions(sorted_perimeter_extrusions, external_perimeters_first);
}
} // namespace Slic3r::Arachne::PerimeterOrder

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@ -1,51 +0,0 @@
#ifndef slic3r_GCode_PerimeterOrder_hpp_
#define slic3r_GCode_PerimeterOrder_hpp_
#include <stddef.h>
#include <limits>
#include <vector>
#include <cstddef>
#include "libslic3r/Arachne/utils/ExtrusionLine.hpp"
#include "libslic3r/BoundingBox.hpp"
#include "libslic3r/Polygon.hpp"
namespace Slic3r::Arachne::PerimeterOrder {
// Data structure stores ExtrusionLine (closed and open) together with additional data.
struct PerimeterExtrusion
{
explicit PerimeterExtrusion(const Arachne::ExtrusionLine &extrusion, const double area, const Polygon &polygon, const BoundingBox &bbox)
: extrusion(extrusion), area(area), polygon(polygon), bbox(bbox) {}
Arachne::ExtrusionLine extrusion;
// Absolute value of the area of the polygon. The value is always non-negative, even for holes.
double area = 0;
// Polygon is non-empty only for closed extrusions.
Polygon polygon;
BoundingBox bbox;
std::vector<PerimeterExtrusion *> adjacent_perimeter_extrusions;
// How far is this perimeter from the nearest external perimeter. Contour is always preferred over holes.
size_t depth = std::numeric_limits<size_t>::max();
PerimeterExtrusion *nearest_external_perimeter = nullptr;
// Returns if ExtrusionLine is a contour or a hole.
bool is_contour() const { return extrusion.is_contour(); }
// Returns if ExtrusionLine is closed or opened.
bool is_closed() const { return extrusion.is_closed; }
// Returns if ExtrusionLine is an external or an internal perimeter.
bool is_external_perimeter() const { return extrusion.is_external_perimeter(); }
};
using PerimeterExtrusions = std::vector<PerimeterExtrusion>;
PerimeterExtrusions ordered_perimeter_extrusions(const Perimeters &perimeters, bool external_perimeters_first);
} // namespace Slic3r::Arachne::PerimeterOrder
#endif // slic3r_GCode_Travels_hpp_

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@ -782,4 +782,98 @@ bool WallToolPaths::removeEmptyToolPaths(std::vector<VariableWidthLines> &toolpa
return toolpaths.empty();
}
/*!
* Get the order constraints of the insets when printing walls per region / hole.
* Each returned pair consists of adjacent wall lines where the left has an inset_idx one lower than the right.
*
* Odd walls should always go after their enclosing wall polygons.
*
* \param outer_to_inner Whether the wall polygons with a lower inset_idx should go before those with a higher one.
*/
WallToolPaths::ExtrusionLineSet WallToolPaths::getRegionOrder(const std::vector<ExtrusionLine *> &input, const bool outer_to_inner)
{
ExtrusionLineSet order_requirements;
// We build a grid where we map toolpath vertex locations to toolpaths,
// so that we can easily find which two toolpaths are next to each other,
// which is the requirement for there to be an order constraint.
//
// We use a PointGrid rather than a LineGrid to save on computation time.
// In very rare cases two insets might lie next to each other without having neighboring vertices, e.g.
// \ .
// | / .
// | / .
// || .
// | \ .
// | \ .
// / .
// However, because of how Arachne works this will likely never be the case for two consecutive insets.
// On the other hand one could imagine that two consecutive insets of a very large circle
// could be simplify()ed such that the remaining vertices of the two insets don't align.
// In those cases the order requirement is not captured,
// which means that the PathOrderOptimizer *might* result in a violation of the user set path order.
// This problem is expected to be not so severe and happen very sparsely.
coord_t max_line_w = 0u;
for (const ExtrusionLine *line : input) // compute max_line_w
for (const ExtrusionJunction &junction : *line)
max_line_w = std::max(max_line_w, junction.w);
if (max_line_w == 0u)
return order_requirements;
struct LineLoc
{
ExtrusionJunction j;
const ExtrusionLine *line;
};
struct Locator
{
Point operator()(const LineLoc &elem) { return elem.j.p; }
};
// How much farther two verts may be apart due to corners.
// This distance must be smaller than 2, because otherwise
// we could create an order requirement between e.g.
// wall 2 of one region and wall 3 of another region,
// while another wall 3 of the first region would lie in between those two walls.
// However, higher values are better against the limitations of using a PointGrid rather than a LineGrid.
constexpr float diagonal_extension = 1.9f;
const auto searching_radius = coord_t(max_line_w * diagonal_extension);
using GridT = SparsePointGrid<LineLoc, Locator>;
GridT grid(searching_radius);
for (const ExtrusionLine *line : input)
for (const ExtrusionJunction &junction : *line) grid.insert(LineLoc{junction, line});
for (const std::pair<const SquareGrid::GridPoint, LineLoc> &pair : grid) {
const LineLoc &lineloc_here = pair.second;
const ExtrusionLine *here = lineloc_here.line;
Point loc_here = pair.second.j.p;
std::vector<LineLoc> nearby_verts = grid.getNearby(loc_here, searching_radius);
for (const LineLoc &lineloc_nearby : nearby_verts) {
const ExtrusionLine *nearby = lineloc_nearby.line;
if (nearby == here)
continue;
if (nearby->inset_idx == here->inset_idx)
continue;
if (nearby->inset_idx > here->inset_idx + 1)
continue; // not directly adjacent
if (here->inset_idx > nearby->inset_idx + 1)
continue; // not directly adjacent
if (!shorter_then(loc_here - lineloc_nearby.j.p, (lineloc_here.j.w + lineloc_nearby.j.w) / 2 * diagonal_extension))
continue; // points are too far away from each other
if (here->is_odd || nearby->is_odd) {
if (here->is_odd && !nearby->is_odd && nearby->inset_idx < here->inset_idx)
order_requirements.emplace(std::make_pair(nearby, here));
if (nearby->is_odd && !here->is_odd && here->inset_idx < nearby->inset_idx)
order_requirements.emplace(std::make_pair(here, nearby));
} else if ((nearby->inset_idx < here->inset_idx) == outer_to_inner) {
order_requirements.emplace(std::make_pair(nearby, here));
} else {
assert((nearby->inset_idx > here->inset_idx) == outer_to_inner);
order_requirements.emplace(std::make_pair(here, nearby));
}
}
}
return order_requirements;
}
} // namespace Slic3r::Arachne

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@ -90,6 +90,16 @@ public:
using ExtrusionLineSet = ankerl::unordered_dense::set<std::pair<const ExtrusionLine *, const ExtrusionLine *>, boost::hash<std::pair<const ExtrusionLine *, const ExtrusionLine *>>>;
/*!
* Get the order constraints of the insets when printing walls per region / hole.
* Each returned pair consists of adjacent wall lines where the left has an inset_idx one lower than the right.
*
* Odd walls should always go after their enclosing wall polygons.
*
* \param outer_to_inner Whether the wall polygons with a lower inset_idx should go before those with a higher one.
*/
static ExtrusionLineSet getRegionOrder(const std::vector<ExtrusionLine *> &input, bool outer_to_inner);
protected:
/*!
* Stitch the polylines together and form closed polygons.

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@ -264,10 +264,9 @@ bool ExtrusionLine::is_contour() const
return poly.is_clockwise();
}
double ExtrusionLine::area() const {
if (!this->is_closed)
return 0.;
double ExtrusionLine::area() const
{
assert(this->is_closed);
double a = 0.;
if (this->junctions.size() >= 3) {
Vec2d p1 = this->junctions.back().p.cast<double>();
@ -277,25 +276,9 @@ double ExtrusionLine::area() const {
p1 = p2;
}
}
return 0.5 * a;
}
Points to_points(const ExtrusionLine &extrusion_line) {
Points points;
points.reserve(extrusion_line.junctions.size());
for (const ExtrusionJunction &junction : extrusion_line.junctions)
points.emplace_back(junction.p);
return points;
}
BoundingBox get_extents(const ExtrusionLine &extrusion_line) {
BoundingBox bbox;
for (const ExtrusionJunction &junction : extrusion_line.junctions)
bbox.merge(junction.p);
return bbox;
}
} // namespace Slic3r::Arachne
namespace Slic3r {

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@ -199,8 +199,6 @@ struct ExtrusionLine
bool is_contour() const;
double area() const;
bool is_external_perimeter() const { return this->inset_idx == 0; }
};
template<class PathType>
@ -227,7 +225,6 @@ static inline Slic3r::ThickPolyline to_thick_polyline(const PathType &path)
static inline Polygon to_polygon(const ExtrusionLine &line)
{
Polygon out;
assert(line.is_closed);
assert(line.junctions.size() >= 3);
assert(line.junctions.front().p == line.junctions.back().p);
out.points.reserve(line.junctions.size() - 1);
@ -236,11 +233,24 @@ static inline Polygon to_polygon(const ExtrusionLine &line)
return out;
}
Points to_points(const ExtrusionLine &extrusion_line);
BoundingBox get_extents(const ExtrusionLine &extrusion_line);
static Points to_points(const ExtrusionLine &extrusion_line)
{
Points points;
points.reserve(extrusion_line.junctions.size());
for (const ExtrusionJunction &junction : extrusion_line.junctions)
points.emplace_back(junction.p);
return points;
}
#if 0
static BoundingBox get_extents(const ExtrusionLine &extrusion_line)
{
BoundingBox bbox;
for (const ExtrusionJunction &junction : extrusion_line.junctions)
bbox.merge(junction.p);
return bbox;
}
static BoundingBox get_extents(const std::vector<ExtrusionLine> &extrusion_lines)
{
BoundingBox bbox;
@ -271,8 +281,6 @@ static std::vector<Points> to_points(const std::vector<const ExtrusionLine *> &e
#endif
using VariableWidthLines = std::vector<ExtrusionLine>; //<! The ExtrusionLines generated by libArachne
using Perimeter = VariableWidthLines;
using Perimeters = std::vector<Perimeter>;
} // namespace Slic3r::Arachne

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@ -433,8 +433,6 @@ set(lisbslic3r_sources
Arachne/utils/PolygonsSegmentIndex.hpp
Arachne/utils/PolylineStitcher.hpp
Arachne/utils/PolylineStitcher.cpp
Arachne/PerimeterOrder.hpp
Arachne/PerimeterOrder.cpp
Arachne/SkeletalTrapezoidation.hpp
Arachne/SkeletalTrapezoidation.cpp
Arachne/SkeletalTrapezoidationEdge.hpp

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