Introduction of a greedy Traveling Salesman Problem algorithm,

producing better shortest path estimate than the "closest next neighbor"
heuristics. The new greedy algorithm utilizes KD tree for closest
end point search, and builds a graph to detect loops.

PerimeterGenerator newly uses the optimized TSP algorithm.

ExtrusionEntity has been refactored / simplified.
This commit is contained in:
bubnikv 2019-09-26 09:44:38 +02:00
parent 110d5b9d56
commit 41495a932a
8 changed files with 797 additions and 61 deletions

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@ -100,7 +100,7 @@ add_library(libslic3r STATIC
Geometry.cpp
Geometry.hpp
Int128.hpp
# KdTree.hpp
KdTreeIndirect.hpp
Layer.cpp
Layer.hpp
LayerRegion.cpp
@ -142,6 +142,8 @@ add_library(libslic3r STATIC
PrintObject.cpp
PrintRegion.cpp
Semver.cpp
ShortestPath.cpp
ShortestPath.hpp
SLAPrint.cpp
SLAPrint.hpp
SLA/SLAAutoSupports.hpp

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@ -16,7 +16,6 @@ ExtrusionEntityCollection& ExtrusionEntityCollection::operator=(const ExtrusionE
this->entities = other.entities;
for (size_t i = 0; i < this->entities.size(); ++i)
this->entities[i] = this->entities[i]->clone();
this->orig_indices = other.orig_indices;
this->no_sort = other.no_sort;
return *this;
}
@ -24,7 +23,6 @@ ExtrusionEntityCollection& ExtrusionEntityCollection::operator=(const ExtrusionE
void ExtrusionEntityCollection::swap(ExtrusionEntityCollection &c)
{
std::swap(this->entities, c.entities);
std::swap(this->orig_indices, c.orig_indices);
std::swap(this->no_sort, c.no_sort);
}
@ -82,10 +80,10 @@ ExtrusionEntityCollection ExtrusionEntityCollection::chained_path(bool no_revers
return coll;
}
void ExtrusionEntityCollection::chained_path(ExtrusionEntityCollection* retval, bool no_reverse, ExtrusionRole role, std::vector<size_t>* orig_indices) const
void ExtrusionEntityCollection::chained_path(ExtrusionEntityCollection* retval, bool no_reverse, ExtrusionRole role) const
{
if (this->entities.empty()) return;
this->chained_path_from(this->entities.front()->first_point(), retval, no_reverse, role, orig_indices);
this->chained_path_from(this->entities.front()->first_point(), retval, no_reverse, role);
}
ExtrusionEntityCollection ExtrusionEntityCollection::chained_path_from(Point start_near, bool no_reverse, ExtrusionRole role) const
@ -95,7 +93,7 @@ ExtrusionEntityCollection ExtrusionEntityCollection::chained_path_from(Point sta
return coll;
}
void ExtrusionEntityCollection::chained_path_from(Point start_near, ExtrusionEntityCollection* retval, bool no_reverse, ExtrusionRole role, std::vector<size_t>* orig_indices) const
void ExtrusionEntityCollection::chained_path_from(Point start_near, ExtrusionEntityCollection* retval, bool no_reverse, ExtrusionRole role) const
{
if (this->no_sort) {
*retval = *this;
@ -103,7 +101,6 @@ void ExtrusionEntityCollection::chained_path_from(Point start_near, ExtrusionEnt
}
retval->entities.reserve(this->entities.size());
retval->orig_indices.reserve(this->entities.size());
// if we're asked to return the original indices, build a map
std::map<ExtrusionEntity*,size_t> indices_map;
@ -122,8 +119,8 @@ void ExtrusionEntityCollection::chained_path_from(Point start_near, ExtrusionEnt
ExtrusionEntity *entity = entity_src->clone();
my_paths.push_back(entity);
if (orig_indices != nullptr)
indices_map[entity] = &entity_src - &this->entities.front();
// if (orig_indices != nullptr)
// indices_map[entity] = &entity_src - &this->entities.front();
}
Points endpoints;
@ -142,8 +139,8 @@ void ExtrusionEntityCollection::chained_path_from(Point start_near, ExtrusionEnt
if (start_index % 2 && !no_reverse && entity->can_reverse())
entity->reverse();
retval->entities.push_back(my_paths.at(path_index));
if (orig_indices != nullptr)
orig_indices->push_back(indices_map[entity]);
// if (orig_indices != nullptr)
// orig_indices->push_back(indices_map[entity]);
my_paths.erase(my_paths.begin() + path_index);
endpoints.erase(endpoints.begin() + 2*path_index, endpoints.begin() + 2*path_index + 2);
start_near = retval->entities.back()->last_point();

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@ -14,15 +14,14 @@ public:
ExtrusionEntity* clone_move() override { return new ExtrusionEntityCollection(std::move(*this)); }
ExtrusionEntitiesPtr entities; // we own these entities
std::vector<size_t> orig_indices; // handy for XS
bool no_sort;
ExtrusionEntityCollection(): no_sort(false) {};
ExtrusionEntityCollection(const ExtrusionEntityCollection &other) : orig_indices(other.orig_indices), no_sort(other.no_sort) { this->append(other.entities); }
ExtrusionEntityCollection(ExtrusionEntityCollection &&other) : entities(std::move(other.entities)), orig_indices(std::move(other.orig_indices)), no_sort(other.no_sort) {}
ExtrusionEntityCollection(const ExtrusionEntityCollection &other) : no_sort(other.no_sort) { this->append(other.entities); }
ExtrusionEntityCollection(ExtrusionEntityCollection &&other) : entities(std::move(other.entities)), no_sort(other.no_sort) {}
explicit ExtrusionEntityCollection(const ExtrusionPaths &paths);
ExtrusionEntityCollection& operator=(const ExtrusionEntityCollection &other);
ExtrusionEntityCollection& operator=(ExtrusionEntityCollection &&other)
{ this->entities = std::move(other.entities); this->orig_indices = std::move(other.orig_indices); this->no_sort = other.no_sort; return *this; }
{ this->entities = std::move(other.entities); this->no_sort = other.no_sort; return *this; }
~ExtrusionEntityCollection() { clear(); }
explicit operator ExtrusionPaths() const;
@ -67,9 +66,9 @@ public:
void replace(size_t i, const ExtrusionEntity &entity);
void remove(size_t i);
ExtrusionEntityCollection chained_path(bool no_reverse = false, ExtrusionRole role = erMixed) const;
void chained_path(ExtrusionEntityCollection* retval, bool no_reverse = false, ExtrusionRole role = erMixed, std::vector<size_t>* orig_indices = nullptr) const;
void chained_path(ExtrusionEntityCollection* retval, bool no_reverse = false, ExtrusionRole role = erMixed) const;
ExtrusionEntityCollection chained_path_from(Point start_near, bool no_reverse = false, ExtrusionRole role = erMixed) const;
void chained_path_from(Point start_near, ExtrusionEntityCollection* retval, bool no_reverse = false, ExtrusionRole role = erMixed, std::vector<size_t>* orig_indices = nullptr) const;
void chained_path_from(Point start_near, ExtrusionEntityCollection* retval, bool no_reverse = false, ExtrusionRole role = erMixed) const;
void reverse();
Point first_point() const { return this->entities.front()->first_point(); }
Point last_point() const { return this->entities.back()->last_point(); }

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@ -0,0 +1,228 @@
// KD tree built upon external data set, referencing the external data by integer indices.
#ifndef slic3r_KDTreeIndirect_hpp_
#define slic3r_KDTreeIndirect_hpp_
#include <algorithm>
#include <limits>
#include <vector>
#include "Utils.hpp" // for next_highest_power_of_2()
namespace Slic3r {
// KD tree for N-dimensional closest point search.
template<size_t ANumDimensions, typename ACoordType, typename ACoordinateFn>
class KDTreeIndirect
{
public:
static constexpr size_t NumDimensions = ANumDimensions;
using CoordinateFn = ACoordinateFn;
using CoordType = ACoordType;
static constexpr size_t npos = size_t(-1);
KDTreeIndirect(CoordinateFn coordinate) : coordinate(coordinate) {}
KDTreeIndirect(CoordinateFn coordinate, std::vector<size_t> indices) : coordinate(coordinate) { this->build(std::move(indices)); }
KDTreeIndirect(CoordinateFn coordinate, std::vector<size_t> &&indices) : coordinate(coordinate) { this->build(std::move(indices)); }
KDTreeIndirect(CoordinateFn coordinate, size_t num_indices) : coordinate(coordinate) { this->build(num_indices); }
KDTreeIndirect(KDTreeIndirect &&rhs) : m_nodes(std::move(rhs.m_nodes)), coordinate(std::move(rhs.coordinate)) {}
KDTreeIndirect& operator=(KDTreeIndirect &&rhs) { m_nodes = std::move(rhs.m_nodes); coordinate = std::move(rhs.coordinate); return *this; }
void clear() { m_nodes.clear(); }
void build(size_t num_indices)
{
std::vector<size_t> indices;
indices.reserve(num_indices);
for (size_t i = 0; i < num_indices; ++ i)
indices.emplace_back(i);
this->build(std::move(indices));
}
void build(std::vector<size_t> &&indices)
{
if (indices.empty())
clear();
else {
// Allocate a next highest power of 2 nodes, because the incomplete binary tree will not have the leaves filled strictly from the left.
m_nodes.assign(next_highest_power_of_2(indices.size() + 1), npos);
build_recursive(indices, 0, 0, 0, (int)(indices.size() - 1));
}
indices.clear();
}
enum class VisitorReturnMask : unsigned int
{
CONTINUE_LEFT = 1,
CONTINUE_RIGHT = 2,
STOP = 4,
};
template<typename CoordType>
unsigned int descent_mask(const CoordType &point_coord, const CoordType &search_radius, size_t idx, size_t dimension) const
{
CoordType dist = point_coord - this->coordinate(idx, dimension);
return (dist * dist < search_radius + CoordType(EPSILON)) ?
((unsigned int)(VisitorReturnMask::CONTINUE_LEFT) | (unsigned int)(VisitorReturnMask::CONTINUE_RIGHT)) :
(dist < CoordType(0)) ? (unsigned int)(VisitorReturnMask::CONTINUE_RIGHT) : (unsigned int)(VisitorReturnMask::CONTINUE_LEFT);
}
// Visitor is supposed to return a bit mask of VisitorReturnMask.
template<typename Visitor>
void visit(Visitor &visitor) const
{
return m_nodes.empty() ? npos : visit_recursive(0, 0, visitor);
}
CoordinateFn coordinate;
private:
// Build a balanced tree by splitting the input sequence by an axis aligned plane at a dimension.
void build_recursive(std::vector<size_t> &input, size_t node, int dimension, int left, int right)
{
if (left > right)
return;
assert(node < m_nodes.size());
if (left == right) {
// Insert a node into the balanced tree.
m_nodes[node] = input[left];
return;
}
// Partition the input sequence to two equal halves.
int center = (left + right) >> 1;
partition_input(input, dimension, left, right, center);
// Insert a node into the tree.
m_nodes[node] = input[center];
// Partition the left and right subtrees.
size_t next_dimension = (++ dimension == NumDimensions) ? 0 : dimension;
build_recursive(input, (node << 1) + 1, next_dimension, left, center - 1);
build_recursive(input, (node << 1) + 2, next_dimension, center + 1, right);
}
// Partition the input m_nodes <left, right> at k using QuickSelect method.
// https://en.wikipedia.org/wiki/Quickselect
void partition_input(std::vector<size_t> &input, int dimension, int left, int right, int k) const
{
while (left < right) {
// Guess the k'th element.
// Pick the pivot as a median of first, center and last value.
// Sort first, center and last values.
int center = (left + right) >> 1;
auto left_value = this->coordinate(input[left], dimension);
auto center_value = this->coordinate(input[center], dimension);
auto right_value = this->coordinate(input[right], dimension);
if (center_value < left_value) {
std::swap(input[left], input[center]);
std::swap(left_value, center_value);
}
if (right_value < left_value) {
std::swap(input[left], input[right]);
std::swap(left_value, right_value);
}
if (right_value < center_value) {
std::swap(input[center], input[right]);
// No need to do that, result is not used.
// std::swap(center_value, right_value);
}
// Only two or three values are left and those are sorted already.
if (left + 3 > right)
break;
// left and right items are already at their correct positions.
// input[left].point[dimension] <= input[center].point[dimension] <= input[right].point[dimension]
// Move the pivot to the (right - 1) position.
std::swap(input[center], input[right - 1]);
// Pivot value.
double pivot = this->coordinate(input[right - 1], dimension);
// Partition the set based on the pivot.
int i = left;
int j = right - 1;
for (;;) {
// Skip left points that are already at correct positions.
// Search will certainly stop at position (right - 1), which stores the pivot.
while (this->coordinate(input[++ i], dimension) < pivot) ;
// Skip right points that are already at correct positions.
while (this->coordinate(input[-- j], dimension) > pivot && i < j) ;
if (i >= j)
break;
std::swap(input[i], input[j]);
}
// Restore pivot to the center of the sequence.
std::swap(input[i], input[right]);
// Which side the kth element is in?
if (k < i)
right = i - 1;
else if (k == i)
// Sequence is partitioned, kth element is at its place.
break;
else
left = i + 1;
}
}
template<typename Visitor>
void visit_recursive(size_t node, size_t dimension, Visitor &visitor) const
{
assert(! m_nodes.empty());
if (node >= m_nodes.size() || m_nodes[node] == npos)
return;
// Left / right child node index.
size_t left = (node << 1) + 1;
size_t right = left + 1;
unsigned int mask = visitor(m_nodes[node], dimension);
if ((mask & (unsigned int)VisitorReturnMask::STOP) == 0) {
size_t next_dimension = (++ dimension == NumDimensions) ? 0 : dimension;
if (mask & (unsigned int)VisitorReturnMask::CONTINUE_LEFT)
visit_recursive(left, next_dimension, visitor);
if (mask & (unsigned int)VisitorReturnMask::CONTINUE_RIGHT)
visit_recursive(right, next_dimension, visitor);
}
}
std::vector<size_t> m_nodes;
};
// Find a closest point using Euclidian metrics.
// Returns npos if not found.
template<typename KDTreeIndirectType, typename PointType, typename FilterFn>
size_t find_closest_point(const KDTreeIndirectType &kdtree, const PointType &point, FilterFn filter)
{
struct Visitor {
using CoordType = typename KDTreeIndirectType::CoordType;
const KDTreeIndirectType &kdtree;
const PointType &point;
const FilterFn filter;
size_t min_idx = KDTreeIndirectType::npos;
CoordType min_dist = std::numeric_limits<CoordType>::max();
Visitor(const KDTreeIndirectType &kdtree, const PointType &point, FilterFn filter) : kdtree(kdtree), point(point), filter(filter) {}
unsigned int operator()(size_t idx, size_t dimension) {
if (this->filter(idx)) {
auto dist = CoordType(0);
for (size_t i = 0; i < KDTreeIndirectType::NumDimensions; ++ i) {
CoordType d = point[i] - kdtree.coordinate(idx, i);
dist += d * d;
}
if (dist < min_dist) {
min_dist = dist;
min_idx = idx;
}
}
return kdtree.descent_mask(point[dimension], min_dist, idx, dimension);
}
} visitor(kdtree, point, filter);
kdtree.visit(visitor);
return visitor.min_idx;
}
template<typename KDTreeIndirectType, typename PointType>
size_t find_closest_point(const KDTreeIndirectType& kdtree, const PointType& point)
{
return find_closest_point(kdtree, point, [](size_t) { return true; });
}
} // namespace Slic3r
#endif /* slic3r_KDTreeIndirect_hpp_ */

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@ -13,21 +13,28 @@ public:
{}
~MutablePriorityQueue() { clear(); }
inline void clear() { m_heap.clear(); }
inline void reserve(size_t cnt) { m_heap.reserve(cnt); }
inline void push(const T &item);
inline void push(T &&item);
inline void pop();
inline T& top() { return m_heap.front(); }
inline void remove(size_t idx);
inline void update(size_t idx) { T item = m_heap[idx]; remove(idx); push(item); }
void clear() { m_heap.clear(); }
void reserve(size_t cnt) { m_heap.reserve(cnt); }
void push(const T &item);
void push(T &&item);
void pop();
T& top() { return m_heap.front(); }
void remove(size_t idx);
void update(size_t idx) { T item = m_heap[idx]; remove(idx); push(item); }
inline size_t size() const { return m_heap.size(); }
inline bool empty() const { return m_heap.empty(); }
size_t size() const { return m_heap.size(); }
bool empty() const { return m_heap.empty(); }
using iterator = typename std::vector<T>::iterator;
using const_iterator = typename std::vector<T>::const_iterator;
iterator begin() { return m_heap.begin(); }
iterator end() { return m_heap.end(); }
const_iterator cbegin() const { return m_heap.cbegin(); }
const_iterator cend() const { return m_heap.cend(); }
protected:
inline void update_heap_up(size_t top, size_t bottom);
inline void update_heap_down(size_t top, size_t bottom);
void update_heap_up(size_t top, size_t bottom);
void update_heap_down(size_t top, size_t bottom);
private:
std::vector<T> m_heap;

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@ -1,6 +1,8 @@
#include "PerimeterGenerator.hpp"
#include "ClipperUtils.hpp"
#include "ExtrusionEntityCollection.hpp"
#include "ShortestPath.hpp"
#include <cmath>
#include <cassert>
@ -86,24 +88,24 @@ static ExtrusionPaths thick_polyline_to_extrusion_paths(const ThickPolyline &thi
return paths;
}
static ExtrusionEntityCollection variable_width(const ThickPolylines& polylines, ExtrusionRole role, Flow flow)
static void variable_width(const ThickPolylines& polylines, ExtrusionRole role, Flow flow, std::vector<ExtrusionEntity*> &out)
{
// This value determines granularity of adaptive width, as G-code does not allow
// variable extrusion within a single move; this value shall only affect the amount
// of segments, and any pruning shall be performed before we apply this tolerance.
ExtrusionEntityCollection coll;
const float tolerance = float(scale_(0.05));
for (const ThickPolyline &p : polylines) {
ExtrusionPaths paths = thick_polyline_to_extrusion_paths(p, role, flow, tolerance);
// Append paths to collection.
if (! paths.empty()) {
if (paths.front().first_point() == paths.back().last_point())
coll.append(ExtrusionLoop(std::move(paths)));
else
coll.append(std::move(paths));
out.emplace_back(new ExtrusionLoop(std::move(paths)));
else {
for (ExtrusionPath &path : paths)
out.emplace_back(new ExtrusionPath(std::move(path)));
}
}
}
return coll;
}
// Hierarchy of perimeters.
@ -186,43 +188,47 @@ static ExtrusionEntityCollection traverse_loops(const PerimeterGenerator &perime
paths.push_back(path);
}
coll.append(ExtrusionLoop(paths, loop_role));
coll.append(ExtrusionLoop(std::move(paths), loop_role));
}
// Append thin walls to the nearest-neighbor search (only for first iteration)
if (! thin_walls.empty()) {
ExtrusionEntityCollection tw = variable_width(thin_walls, erExternalPerimeter, perimeter_generator.ext_perimeter_flow);
coll.append(tw.entities);
variable_width(thin_walls, erExternalPerimeter, perimeter_generator.ext_perimeter_flow, coll.entities);
thin_walls.clear();
}
// Sort entities into a new collection using a nearest-neighbor search,
// preserving the original indices which are useful for detecting thin walls.
ExtrusionEntityCollection sorted_coll;
coll.chained_path(&sorted_coll, false, erMixed, &sorted_coll.orig_indices);
// traverse children and build the final collection
ExtrusionEntityCollection entities;
for (const size_t &idx : sorted_coll.orig_indices) {
if (idx >= loops.size()) {
// This is a thin wall. Let's get it from the sorted collection as it might have been reversed.
entities.append(std::move(*sorted_coll.entities[&idx - &sorted_coll.orig_indices.front()]));
// Traverse children and build the final collection.
Point zero_point(0, 0);
std::vector<std::pair<size_t, bool>> chain = chain_extrusion_entities(coll.entities, &zero_point);
ExtrusionEntityCollection out;
for (const std::pair<size_t, bool> &idx : chain) {
assert(coll.entities[idx.first] != nullptr);
if (idx.first >= loops.size()) {
// This is a thin wall.
out.entities.reserve(out.entities.size() + 1);
out.entities.emplace_back(coll.entities[idx.first]);
coll.entities[idx.first] = nullptr;
if (idx.second)
out.entities.back()->reverse();
} else {
const PerimeterGeneratorLoop &loop = loops[idx];
ExtrusionLoop eloop = *dynamic_cast<ExtrusionLoop*>(coll.entities[idx]);
const PerimeterGeneratorLoop &loop = loops[idx.first];
assert(thin_walls.empty());
ExtrusionEntityCollection children = traverse_loops(perimeter_generator, loop.children, thin_walls);
out.entities.reserve(out.entities.size() + children.entities.size() + 1);
ExtrusionLoop *eloop = static_cast<ExtrusionLoop*>(coll.entities[idx.first]);
coll.entities[idx.first] = nullptr;
if (loop.is_contour) {
eloop.make_counter_clockwise();
entities.append(std::move(children.entities));
entities.append(std::move(eloop));
eloop->make_counter_clockwise();
out.append(std::move(children.entities));
out.entities.emplace_back(eloop);
} else {
eloop.make_clockwise();
entities.append(std::move(eloop));
entities.append(std::move(children.entities));
eloop->make_clockwise();
out.entities.emplace_back(eloop);
out.append(std::move(children.entities));
}
}
}
return entities;
return out;
}
void PerimeterGenerator::process()
@ -445,8 +451,8 @@ void PerimeterGenerator::process()
for (const ExPolygon &ex : gaps_ex)
ex.medial_axis(max, min, &polylines);
if (! polylines.empty()) {
ExtrusionEntityCollection gap_fill = variable_width(polylines, erGapFill, this->solid_infill_flow);
this->gap_fill->append(gap_fill.entities);
ExtrusionEntityCollection gap_fill;
variable_width(polylines, erGapFill, this->solid_infill_flow, gap_fill.entities);
/* Make sure we don't infill narrow parts that are already gap-filled
(we only consider this surface's gaps to reduce the diff() complexity).
Growing actual extrusions ensures that gaps not filled by medial axis
@ -456,7 +462,8 @@ void PerimeterGenerator::process()
//FIXME Vojtech: This grows by a rounded extrusion width, not by line spacing,
// therefore it may cover the area, but no the volume.
last = diff_ex(to_polygons(last), gap_fill.polygons_covered_by_width(10.f));
}
this->gap_fill->append(std::move(gap_fill.entities));
}
}
// create one more offset to be used as boundary for fill

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@ -0,0 +1,479 @@
#include "ShortestPath.hpp"
#include "KDTreeIndirect.hpp"
#include "MutablePriorityQueue.hpp"
#if 0
#undef NDEBUG
#undef assert
#endif
#include <cmath>
#include <cassert>
namespace Slic3r {
// Chain perimeters (always closed) and thin fills (closed or open) using a greedy algorithm.
// Solving a Traveling Salesman Problem (TSP) with the modification, that the sites are not always points, but points and segments.
// Solving using a greedy algorithm, where a shortest edge is added to the solution if it does not produce a bifurcation or a cycle.
// Return index and "reversed" flag.
// https://en.wikipedia.org/wiki/Multi-fragment_algorithm
// The algorithm builds a tour for the traveling salesman one edge at a time and thus maintains multiple tour fragments, each of which
// is a simple path in the complete graph of cities. At each stage, the algorithm selects the edge of minimal cost that either creates
// a new fragment, extends one of the existing paths or creates a cycle of length equal to the number of cities.
std::vector<std::pair<size_t, bool>> chain_extrusion_entities(std::vector<ExtrusionEntity*> &entities, const Point *start_near)
{
std::vector<std::pair<size_t, bool>> out;
if (entities.empty()) {
// Nothing to do.
}
else if (entities.size() == 1)
{
// Just sort the end points so that the first point visited is closest to start_near.
ExtrusionEntity *extrusion_entity = entities.front();
out.emplace_back(0, extrusion_entity->can_reverse() && start_near != nullptr &&
(extrusion_entity->last_point() - *start_near).cast<double>().squaredNorm() < (extrusion_entity->first_point() - *start_near).cast<double>().squaredNorm());
}
else
{
// End points of entities for the KD tree closest point search.
// A single end point is inserted into the search structure for loops, two end points are entered for open paths.
struct EndPoint {
EndPoint(const Vec2d &pos) : pos(pos) {}
Vec2d pos;
// Identifier of the chain, to which this end point belongs. Zero means unassigned.
size_t chain_id = 0;
// Link to the closest currently valid end point.
EndPoint *edge_out = nullptr;
// Reverse of edge_out. As there may be multiple end points with the same edge_out,
// these other edge_in points are chained using the on_circle_prev / on_circle_next cyclic loop.
EndPoint *edge_in = nullptr;
EndPoint* on_circle_prev = nullptr;
EndPoint* on_circle_next = nullptr;
void on_circle_merge(EndPoint *other)
{
EndPoint *a = this;
EndPoint *b = other;
assert(a->validate());
assert(b->validate());
if (a->on_circle_next == nullptr)
std::swap(a, b);
if (a->on_circle_next == nullptr) {
a->on_circle_next = a->on_circle_prev = b;
b->on_circle_next = b->on_circle_prev = a;
} else if (b->on_circle_next == nullptr) {
b->on_circle_next = a;
b->on_circle_prev = a->on_circle_prev;
a->on_circle_prev = b;
b->on_circle_prev->on_circle_next = b;
} else {
EndPoint *next = a->on_circle_next;
EndPoint *prev = b->on_circle_prev;
a->on_circle_next = b;
b->on_circle_prev = a;
prev->on_circle_next = next;
next->on_circle_prev = prev;
}
assert(this->validate());
}
void on_circle_detach()
{
if (this->on_circle_next) {
EndPoint *next = this->on_circle_next;
EndPoint *prev = this->on_circle_prev;
if (prev == next) {
next->on_circle_next = nullptr;
next->on_circle_prev = nullptr;
} else {
prev->on_circle_next = next;
next->on_circle_prev = prev;
}
assert(prev->validate());
assert(next->validate());
this->on_circle_next = this->on_circle_prev = nullptr;
}
assert(this->validate());
}
bool on_circle_empty() const
{
assert((this->on_circle_prev == nullptr) == (this->on_circle_next == nullptr));
assert(this->on_circle_prev == nullptr || (this->on_circle_prev != this && this->on_circle_next != this));
return this->on_circle_next == nullptr;
}
#ifndef NDEBUG
bool validate()
{
assert((this->on_circle_prev == nullptr) == (this->on_circle_next == nullptr));
assert(this->on_circle_prev == nullptr || (this->on_circle_prev != this && this->on_circle_next != this));
assert(this->edge_out == nullptr || edge_out->edge_in != nullptr);
assert(this->distance_out >= 0.);
assert(this->edge_in == nullptr || this->edge_in->edge_out == this);
// Point which is a member of path (chain_id > 0) must not be in circle of some edge_in.
assert(this->chain_id == 0 || this->on_circle_empty());
if (! this->on_circle_empty()) {
// Iterate over the cycle and validate the loop.
std::set<const EndPoint*> visited;
const EndPoint *ep = this;
bool edge_in_found = false;
do {
// This end point is visited for the first time.
assert(visited.insert(ep).second);
assert(ep->on_circle_next != ep);
assert(ep->on_circle_prev != ep);
assert(ep->on_circle_next->on_circle_prev == ep);
assert(ep->on_circle_prev->on_circle_next == ep);
assert(ep->edge_out != nullptr && ep->edge_out == this->edge_out);
if (ep->edge_out->edge_in == ep)
edge_in_found = true;
ep = ep->on_circle_next;
} while (ep != this);
assert(edge_in_found);
}
return true;
}
#endif /* NDEBUG */
// Distance to the next end point following the link.
// Zero value -> start of the final path.
double distance_out = std::numeric_limits<double>::max();
size_t heap_idx = std::numeric_limits<size_t>::max();
};
std::vector<EndPoint> end_points;
end_points.reserve(entities.size() * 2);
for (const ExtrusionEntity* const &entity : entities) {
end_points.emplace_back(entity->first_point().cast<double>());
end_points.emplace_back(entity->last_point().cast<double>());
}
// Construct the closest point KD tree over end points of extrusion entities.
auto coordinate_fn = [&end_points](size_t idx, size_t dimension) -> double { return end_points[idx].pos[dimension]; };
KDTreeIndirect<2, double, decltype(coordinate_fn)> kdtree(coordinate_fn, end_points.size());
// Helper to detect loops in already connected paths.
// Unique chain IDs are assigned to paths. If paths are connected, end points will not have their chain IDs updated, but the chain IDs
// will remember an "equivalent" chain ID, which is the lowest ID of all the IDs in the path, and the lowest ID is equivalent to itself.
class EquivalentChains {
public:
// Zero'th chain ID is invalid.
EquivalentChains(size_t reserve) { m_equivalent_with.reserve(reserve); m_equivalent_with.emplace_back(0); }
// Generate next equivalence class.
size_t next() {
m_equivalent_with.emplace_back(++ m_last_chain_id);
return m_last_chain_id;
}
// Get equivalence class for chain ID.
size_t operator()(size_t chain_id) {
if (chain_id != 0) {
for (size_t last = chain_id;;) {
size_t lower = m_equivalent_with[last];
if (lower == last) {
m_equivalent_with[chain_id] = lower;
chain_id = lower;
break;
}
last = lower;
}
}
return chain_id;
}
size_t merge(size_t chain_id1, size_t chain_id2) {
size_t chain_id = std::min((*this)(chain_id1), (*this)(chain_id2));
m_equivalent_with[chain_id1] = chain_id;
m_equivalent_with[chain_id2] = chain_id;
return chain_id;
}
#ifndef NDEBUG
bool validate()
{
assert(m_last_chain_id > 0);
assert(m_last_chain_id + 1 == m_equivalent_with.size());
for (size_t i = 0; i < m_equivalent_with.size(); ++ i) {
for (size_t last = i;;) {
size_t lower = m_equivalent_with[last];
assert(lower <= last);
if (lower == last)
break;
last = lower;
}
}
return true;
}
#endif /* NDEBUG */
private:
// Unique chain ID assigned to chains of end points of entities.
size_t m_last_chain_id = 0;
std::vector<size_t> m_equivalent_with;
} equivalent_chain(entities.size());
// Find the first end point closest to start_near.
EndPoint *first_point = nullptr;
size_t first_point_idx = std::numeric_limits<size_t>::max();
if (start_near != nullptr) {
size_t idx = find_closest_point(kdtree, start_near->cast<double>());
assert(idx != kdtree.npos);
assert(idx < end_points.size());
first_point = &end_points[idx];
first_point->distance_out = 0.;
first_point->chain_id = equivalent_chain.next();
first_point_idx = idx;
}
#ifndef NDEBUG
auto validate_graph = [&end_points, &equivalent_chain]() -> bool {
for (EndPoint& ep : end_points)
ep.validate();
assert(equivalent_chain.validate());
return true;
};
#endif /* NDEBUG */
// Assign the closest point and distance to the end points.
assert(validate_graph());
for (EndPoint &end_point : end_points) {
assert(end_point.edge_out == nullptr);
if (&end_point != first_point) {
size_t this_idx = &end_point - &end_points.front();
// Find the closest point to this end_point, which lies on a different extrusion path (filtered by the lambda).
// Ignore the starting point as the starting point is considered to be occupied, no end point coud connect to it.
size_t next_idx = find_closest_point(kdtree, end_point.pos,
[this_idx, first_point_idx](size_t idx){ return idx != first_point_idx && (idx ^ this_idx) > 1; });
assert(next_idx != kdtree.npos);
assert(next_idx < end_points.size());
EndPoint &end_point2 = end_points[next_idx];
end_point.edge_out = &end_point2;
if (end_point2.edge_in == nullptr)
end_point2.edge_in = &end_point;
else {
assert(end_point.on_circle_empty());
assert(end_point2.edge_in->edge_out == &end_point2);
end_point.on_circle_merge(end_point2.edge_in);
}
end_point.distance_out = (end_point2.pos - end_point.pos).squaredNorm();
}
assert(validate_graph());
}
// Initialize a heap of end points sorted by the lowest distance to the next valid point of a path.
auto queue = make_mutable_priority_queue<EndPoint*>(
[](EndPoint *ep, size_t idx){ ep->heap_idx = idx; },
[](EndPoint *l, EndPoint *r){ return l->distance_out < r->distance_out; });
queue.reserve(end_points.size() * 2 - 1);
for (EndPoint &ep : end_points)
if (first_point != &ep)
queue.push(&ep);
#ifndef NDEBUG
auto validate_graph_and_queue = [&validate_graph, &end_points, &queue, first_point]() -> bool {
assert(validate_graph());
for (EndPoint &ep : end_points) {
if (ep.heap_idx < queue.size()) {
// End point is on the heap.
assert(*(queue.cbegin() + ep.heap_idx) == &ep);
assert(ep.chain_id == 0);
// Point on the heap may only points to other points on the heap.
assert(ep.edge_in == nullptr || ep.edge_in ->heap_idx < queue.size());
assert(ep.edge_out == nullptr || ep.edge_out->heap_idx < queue.size());
} else {
// End point is NOT on the heap, therefore it is part of the output path.
assert(ep.heap_idx == std::numeric_limits<size_t>::max());
assert(ep.chain_id != 0);
assert(ep.on_circle_empty());
if (&ep == first_point) {
assert(ep.edge_in == nullptr);
assert(ep.edge_out == nullptr);
} else {
assert(ep.edge_in != nullptr);
assert(ep.edge_out != nullptr);
assert(ep.edge_in != &ep);
assert(ep.edge_in == ep.edge_out);
assert(ep.edge_in->edge_out == &ep);
assert(ep.edge_out->edge_in == &ep);
assert(ep.edge_in->heap_idx == std::numeric_limits<size_t>::max());
// Detect loops.
for (EndPoint *pt = &ep; pt != nullptr;) {
// Out of queue. It is a final point.
assert(pt->heap_idx == std::numeric_limits<size_t>::max());
EndPoint *pt_other = &end_points[(pt - &end_points.front()) ^ 1];
if (pt_other->heap_idx < queue.size())
// The other side of this segment is undecided yet.
break;
pt = pt_other->edge_out;
}
}
}
}
for (EndPoint *ep : queue)
// Points in the queue are not connected yet.
assert(ep->chain_id == 0);
return true;
};
#endif /* NDEBUG */
// Chain the end points: find (entities.size() - 1) shortest links not forming bifurcations or loops.
std::vector<EndPoint*> end_points_update;
end_points_update.reserve(16);
assert(entities.size() >= 2);
for (int iter = int(entities.size()) - 2;; -- iter) {
assert(validate_graph_and_queue());
// Take the first end point, for which the link points to the currently closest valid neighbor.
EndPoint &end_point1 = *queue.top();
assert(end_point1.edge_out != nullptr);
// No point on the queue may be connected yet.
assert(end_point1.chain_id == 0);
// Take the closest end point to the first end point,
EndPoint &end_point2 = *end_point1.edge_out;
// The closest point must not be connected yet.
assert(end_point2.chain_id == 0);
// If end_point1.edge_out == end_point2, then end_point2.edge_in == &end_point1, or end_point2.edge_in points to some point on loop of end_point1.
assert(end_point2.edge_in != nullptr);
// End points of the opposite ends of the segments.
size_t end_point1_other_chain_id = equivalent_chain(end_points[(&end_point1 - &end_points.front()) ^ 1].chain_id);
size_t end_point2_other_chain_id = equivalent_chain(end_points[(&end_point2 - &end_points.front()) ^ 1].chain_id);
if (end_point1_other_chain_id == end_point2_other_chain_id && end_point1_other_chain_id != 0) {
// This edge forms a loop. Update end_point1 and try another one.
++ iter;
assert(end_point1.edge_out != nullptr);
assert(end_point1.edge_out->edge_in != nullptr);
assert(! end_point1.on_circle_empty() || end_point1.edge_out->edge_in == &end_point1);
end_point1.edge_out->edge_in = end_point1.on_circle_empty() ? nullptr : end_point1.on_circle_next;
end_point1.edge_out = nullptr;
if (! end_point1.on_circle_empty())
end_point1.on_circle_detach();
assert(validate_graph_and_queue());
end_points_update.emplace_back(&end_point1);
} else {
// Remove the first and second point from the queue.
queue.pop();
queue.remove(end_point2.heap_idx);
#ifndef NDEBUG
// Mark them as removed from the queue.
end_point1.heap_idx = std::numeric_limits<size_t>::max();
end_point2.heap_idx = std::numeric_limits<size_t>::max();
#endif /* NDEBUG */
// Collect the other end points pointing to this one, detach them from the on_circle linked list.
for (EndPoint *pt_first : { end_point1.edge_in, end_point2.edge_in })
if (pt_first != nullptr) {
EndPoint *pt = pt_first;
do {
if (pt != &end_point1 && pt != &end_point2) {
// Point is in the queue.
assert(pt->heap_idx < queue.size());
// Point is not connected yet.
assert(pt->chain_id == 0);
end_points_update.emplace_back(pt);
pt->edge_out = nullptr;
}
EndPoint *next = pt->on_circle_next;
pt->on_circle_prev = nullptr;
pt->on_circle_next = nullptr;
pt = next;
} while (pt != nullptr && pt != pt_first);
}
// If end_point1 was on a circle, the circle belonged to end_point2.edge_in, which was broken in the loop above.
assert(end_point1.on_circle_empty());
// If end_point2 pointed to end_point1, then end_point2 was on a circle that belonged to end_point1.edge_in, which was broken in the loop above.
//assert(end_point2.on_circle_empty() == (end_point2.edge_out == &end_point1));
assert(end_point2.on_circle_empty() || end_point2.edge_out != nullptr);
end_point2.edge_out->edge_in = end_point2.on_circle_empty() ? nullptr : end_point2.on_circle_next;
// The end_point2.link may not necessarily point back to end_point1 due to numeric issues and points on circles.
// Update the link back.
end_point1.edge_out = &end_point2;
end_point1.edge_in = &end_point2;
end_point2.edge_out = &end_point1;
end_point2.edge_in = &end_point1;
end_point2.distance_out = end_point1.distance_out;
// Assign chain IDs to the newly connected end points, set equivalent_chain if two chains were merged.
size_t chain_id =
(end_point1_other_chain_id == 0) ?
((end_point2_other_chain_id == 0) ? equivalent_chain.next() : end_point2_other_chain_id) :
((end_point2_other_chain_id == 0) ? end_point1_other_chain_id :
(end_point1_other_chain_id == end_point2_other_chain_id) ?
end_point1_other_chain_id :
equivalent_chain.merge(end_point1_other_chain_id, end_point2_other_chain_id));
end_point1.chain_id = chain_id;
end_point2.chain_id = chain_id;
if (! end_point2.on_circle_empty())
end_point2.on_circle_detach();
assert(validate_graph_and_queue());
}
#ifndef NDEBUG
for (EndPoint *end_point : end_points_update) {
assert(end_point->edge_out == nullptr);
// Point is in the queue.
assert(end_point->heap_idx < queue.size());
// Point is not connected yet.
assert(end_point->chain_id == 0);
}
#endif /* NDEBUG */
if (iter == 0) {
// Last iteration. There shall be exactly one or two end points waiting to be connected.
if (first_point == nullptr) {
// Two unconnected points are the end points of the constructed path.
assert(end_points_update.size() == 2);
first_point = end_points_update.front();
} else
assert(end_points_update.size() == 1);
// Mark both points as ends of the path.
for (EndPoint *end_point : end_points_update)
end_point->edge_in = end_point->edge_out = nullptr;
break;
}
// Update links, distances and queue positions of all points that used to point to end_point1 or end_point2.
for (EndPoint *end_point : end_points_update) {
size_t this_idx = end_point - &end_points.front();
// Find the closest point to this end_point, which lies on a different extrusion path (filtered by the filter lambda).
size_t next_idx = find_closest_point(kdtree, end_point->pos, [&end_points, &equivalent_chain, this_idx](size_t idx) {
assert(end_points[this_idx].edge_out == nullptr);
assert(end_points[this_idx].chain_id == 0);
if ((idx ^ this_idx) <= 1 || end_points[idx].chain_id != 0)
// Points of the same segment shall not be connected,
// cannot connect to an already connected point (ideally those would be removed from the KD tree, but the update is difficult).
return false;
size_t chain1 = equivalent_chain(end_points[this_idx ^ 1].chain_id);
size_t chain2 = equivalent_chain(end_points[idx ^ 1].chain_id);
return chain1 != chain2 || chain1 == 0;
});
assert(next_idx != kdtree.npos);
assert(next_idx < end_points.size());
EndPoint &end_point2 = end_points[next_idx];
end_point->edge_out = &end_point2;
if (end_point2.edge_in == nullptr)
end_point2.edge_in = end_point;
else {
assert(end_point->on_circle_empty());
assert(end_point2.edge_in->edge_out == &end_point2);
end_point->on_circle_merge(end_point2.edge_in);
}
end_point->distance_out = (end_points[next_idx].pos - end_point->pos).squaredNorm();
// Update position of this end point in the queue based on the distance calculated at the line above.
queue.update(end_point->heap_idx);
//FIXME Remove the other end point from the KD tree.
// As the KD tree update is expensive, do it only after some larger number of points is removed from the queue.
assert(validate_graph_and_queue());
}
end_points_update.clear();
}
assert(queue.size() == (first_point == nullptr) ? 1 : 2);
// Now interconnect pairs of segments into a chain.
assert(first_point != nullptr);
do {
size_t first_point_id = first_point - &end_points.front();
size_t extrusion_entity_id = first_point_id >> 1;
EndPoint *second_point = &end_points[first_point_id ^ 1];
ExtrusionEntity *extrusion_entity = entities[extrusion_entity_id];
out.emplace_back(extrusion_entity_id, extrusion_entity->can_reverse() && (first_point_id & 1));
first_point = second_point->edge_out;
} while (first_point != nullptr);
}
assert(out.size() == entities.size());
return out;
}
} // namespace Slic3r

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#ifndef slic3r_ShortestPath_hpp_
#define slic3r_ShortestPath_hpp_
#include "libslic3r.h"
#include "ExtrusionEntity.hpp"
#include "Point.hpp"
#include <utility>
#include <vector>
namespace Slic3r {
std::vector<std::pair<size_t, bool>> chain_extrusion_entities(std::vector<ExtrusionEntity*> &entities, const Point *start_near = nullptr);
} // namespace Slic3r
#endif /* slic3r_ShortestPath_hpp_ */