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|
#include "BoundingBox.hpp"
#include "ExPolygon.hpp"
#include "Geometry.hpp"
#include "Polygon.hpp"
#include "Line.hpp"
#include "ClipperUtils.hpp"
#include "SVG.hpp"
#include "polypartition.h"
#include "poly2tri/poly2tri.h"
#include <algorithm>
#include <cassert>
#include <list>
namespace Slic3r {
ExPolygon::operator Points() const
{
Points points;
Polygons pp = *this;
for (Polygons::const_iterator poly = pp.begin(); poly != pp.end(); ++poly) {
for (Points::const_iterator point = poly->points.begin(); point != poly->points.end(); ++point)
points.push_back(*point);
}
return points;
}
ExPolygon::operator Polygons() const
{
return to_polygons(*this);
}
ExPolygon::operator Polylines() const
{
return to_polylines(*this);
}
void
ExPolygon::scale(double factor)
{
contour.scale(factor);
for (Polygons::iterator it = holes.begin(); it != holes.end(); ++it) {
(*it).scale(factor);
}
}
void
ExPolygon::translate(double x, double y)
{
contour.translate(x, y);
for (Polygons::iterator it = holes.begin(); it != holes.end(); ++it) {
(*it).translate(x, y);
}
}
void
ExPolygon::rotate(double angle)
{
contour.rotate(angle);
for (Polygons::iterator it = holes.begin(); it != holes.end(); ++it) {
(*it).rotate(angle);
}
}
void
ExPolygon::rotate(double angle, const Point ¢er)
{
contour.rotate(angle, center);
for (Polygons::iterator it = holes.begin(); it != holes.end(); ++it) {
(*it).rotate(angle, center);
}
}
double
ExPolygon::area() const
{
double a = this->contour.area();
for (Polygons::const_iterator it = this->holes.begin(); it != this->holes.end(); ++it) {
a -= -(*it).area(); // holes have negative area
}
return a;
}
bool
ExPolygon::is_valid() const
{
if (!this->contour.is_valid() || !this->contour.is_counter_clockwise()) return false;
for (Polygons::const_iterator it = this->holes.begin(); it != this->holes.end(); ++it) {
if (!(*it).is_valid() || (*it).is_counter_clockwise()) return false;
}
return true;
}
bool
ExPolygon::contains(const Line &line) const
{
return this->contains((Polyline)line);
}
bool
ExPolygon::contains(const Polyline &polyline) const
{
return diff_pl((Polylines)polyline, *this).empty();
}
bool
ExPolygon::contains(const Polylines &polylines) const
{
#if 0
BoundingBox bbox = get_extents(polylines);
bbox.merge(get_extents(*this));
SVG svg(debug_out_path("ExPolygon_contains.svg"), bbox);
svg.draw(*this);
svg.draw_outline(*this);
svg.draw(polylines, "blue");
#endif
Polylines pl_out = diff_pl(polylines, *this);
#if 0
svg.draw(pl_out, "red");
#endif
return pl_out.empty();
}
bool
ExPolygon::contains(const Point &point) const
{
if (!this->contour.contains(point)) return false;
for (Polygons::const_iterator it = this->holes.begin(); it != this->holes.end(); ++it) {
if (it->contains(point)) return false;
}
return true;
}
// inclusive version of contains() that also checks whether point is on boundaries
bool
ExPolygon::contains_b(const Point &point) const
{
return this->contains(point) || this->has_boundary_point(point);
}
bool
ExPolygon::has_boundary_point(const Point &point) const
{
if (this->contour.has_boundary_point(point)) return true;
for (Polygons::const_iterator h = this->holes.begin(); h != this->holes.end(); ++h) {
if (h->has_boundary_point(point)) return true;
}
return false;
}
bool
ExPolygon::overlaps(const ExPolygon &other) const
{
#if 0
BoundingBox bbox = get_extents(other);
bbox.merge(get_extents(*this));
static int iRun = 0;
SVG svg(debug_out_path("ExPolygon_overlaps-%d.svg", iRun ++), bbox);
svg.draw(*this);
svg.draw_outline(*this);
svg.draw_outline(other, "blue");
#endif
Polylines pl_out = intersection_pl((Polylines)other, *this);
#if 0
svg.draw(pl_out, "red");
#endif
if (! pl_out.empty())
return true;
return ! other.contour.points.empty() && this->contains_b(other.contour.points.front());
}
void ExPolygon::simplify_p(double tolerance, Polygons* polygons) const
{
Polygons pp = this->simplify_p(tolerance);
polygons->insert(polygons->end(), pp.begin(), pp.end());
}
Polygons ExPolygon::simplify_p(double tolerance) const
{
Polygons pp;
pp.reserve(this->holes.size() + 1);
// contour
{
Polygon p = this->contour;
p.points.push_back(p.points.front());
p.points = MultiPoint::_douglas_peucker(p.points, tolerance);
p.points.pop_back();
pp.emplace_back(std::move(p));
}
// holes
for (Polygon p : this->holes) {
p.points.push_back(p.points.front());
p.points = MultiPoint::_douglas_peucker(p.points, tolerance);
p.points.pop_back();
pp.emplace_back(std::move(p));
}
return simplify_polygons(pp);
}
ExPolygons ExPolygon::simplify(double tolerance) const
{
return union_ex(this->simplify_p(tolerance));
}
void ExPolygon::simplify(double tolerance, ExPolygons* expolygons) const
{
append(*expolygons, this->simplify(tolerance));
}
/// remove point that are at SCALED_EPSILON * 2 distance.
void remove_point_too_near(ThickPolyline* to_reduce) {
const int32_t smallest = SCALED_EPSILON * 2;
uint32_t id = 1;
while (id < to_reduce->points.size() - 2) {
uint32_t newdist = min(to_reduce->points[id].distance_to(to_reduce->points[id - 1])
, to_reduce->points[id].distance_to(to_reduce->points[id + 1]));
if (newdist < smallest) {
to_reduce->points.erase(to_reduce->points.begin() + id);
to_reduce->width.erase(to_reduce->width.begin() + id);
} else {
++id;
}
}
}
/// add points from pattern to to_modify at the same % of the length
/// so not add if an other point is present at the correct position
void add_point_same_percent(ThickPolyline* pattern, ThickPolyline* to_modify) {
const double to_modify_length = to_modify->length();
const double percent_epsilon = SCALED_EPSILON / to_modify_length;
const double pattern_length = pattern->length();
double percent_length = 0;
for (uint32_t idx_point = 1; idx_point < pattern->points.size() - 1; ++idx_point) {
percent_length += pattern->points[idx_point-1].distance_to(pattern->points[idx_point]) / pattern_length;
//find position
uint32_t idx_other = 1;
double percent_length_other_before = 0;
double percent_length_other = 0;
while (idx_other < to_modify->points.size()) {
percent_length_other_before = percent_length_other;
percent_length_other += to_modify->points[idx_other-1].distance_to(to_modify->points[idx_other])
/ to_modify_length;
if (percent_length_other > percent_length - percent_epsilon) {
//if higher (we have gone over it)
break;
}
++idx_other;
}
if (percent_length_other > percent_length + percent_epsilon) {
//insert a new point before the position
double percent_dist = (percent_length - percent_length_other_before) / (percent_length_other - percent_length_other_before);
coordf_t new_width = to_modify->width[idx_other - 1] * (1 - percent_dist);
new_width += to_modify->width[idx_other] * (percent_dist);
Point new_point;
new_point.x = (coord_t)((double)(to_modify->points[idx_other - 1].x) * (1 - percent_dist));
new_point.x += (coord_t)((double)(to_modify->points[idx_other].x) * (percent_dist));
new_point.y = (coord_t)((double)(to_modify->points[idx_other - 1].y) * (1 - percent_dist));
new_point.y += (coord_t)((double)(to_modify->points[idx_other].y) * (percent_dist));
to_modify->width.insert(to_modify->width.begin() + idx_other, new_width);
to_modify->points.insert(to_modify->points.begin() + idx_other, new_point);
}
}
}
/// find the nearest angle in the contour (or 2 nearest if it's difficult to choose)
/// return 1 for an angle of 90° and 0 for an angle of 0° or 180°
double get_coeff_from_angle_countour(Point &point, const ExPolygon &contour) {
double nearestDist = point.distance_to(contour.contour.points.front());
Point nearest = contour.contour.points.front();
uint32_t id_nearest = 0;
double nearDist = nearestDist;
Point near = nearest;
uint32_t id_near=0;
for (uint32_t id_point = 1; id_point < contour.contour.points.size(); ++id_point) {
if (nearestDist > point.distance_to(contour.contour.points[id_point])) {
nearestDist = point.distance_to(contour.contour.points[id_point]);
near = nearest;
nearest = contour.contour.points[id_point];
id_near = id_nearest;
id_nearest = id_point;
}
}
double angle = 0;
Point point_before = id_nearest == 0 ? contour.contour.points.back() : contour.contour.points[id_nearest - 1];
Point point_after = id_nearest == contour.contour.points.size()-1 ? contour.contour.points.front() : contour.contour.points[id_nearest + 1];
//compute angle
angle = min(nearest.ccw_angle(point_before, point_after), nearest.ccw_angle(point_after, point_before));
//compute the diff from 90°
angle = abs(angle - PI / 2);
if (near != nearest && max(nearestDist, nearDist) + SCALED_EPSILON < nearest.distance_to(near)) {
//not only nearest
Point point_before = id_near == 0 ? contour.contour.points.back() : contour.contour.points[id_near - 1];
Point point_after = id_near == contour.contour.points.size() - 1 ? contour.contour.points.front() : contour.contour.points[id_near + 1];
double angle2 = min(nearest.ccw_angle(point_before, point_after), nearest.ccw_angle(point_after, point_before));
angle2 = abs(angle - PI / 2);
angle = (angle + angle2) / 2;
}
return 1-(angle/(PI/2));
}
void
ExPolygon::medial_axis(const ExPolygon &bounds, double max_width, double min_width, ThickPolylines* polylines, double height) const
{
// init helper object
Slic3r::Geometry::MedialAxis ma(max_width, min_width, this);
ma.lines = this->lines();
// compute the Voronoi diagram and extract medial axis polylines
ThickPolylines pp;
ma.build(&pp);
//{
// stringstream stri;
// stri << "medial_axis" << id << ".svg";
// SVG svg(stri.str());
// svg.draw(bounds);
// svg.draw(*this);
// svg.draw(pp);
// svg.Close();
//}
/* Find the maximum width returned; we're going to use this for validating and
filtering the output segments. */
double max_w = 0;
for (ThickPolylines::const_iterator it = pp.begin(); it != pp.end(); ++it)
max_w = fmaxf(max_w, *std::max_element(it->width.begin(), it->width.end()));
concatThickPolylines(pp);
//reoder pp by length (ascending) It's really important to do that to avoid building the line from the width insteand of the length
std::sort(pp.begin(), pp.end(), [](const ThickPolyline & a, const ThickPolyline & b) { return a.length() < b.length(); });
// Aligned fusion: Fusion the bits at the end of lines by "increasing thickness"
// For that, we have to find other lines,
// and with a next point no more distant than the max width.
// Then, we can merge the bit from the first point to the second by following the mean.
//
int id_f = 0;
bool changes = true;
while (changes) {
changes = false;
for (size_t i = 0; i < pp.size(); ++i) {
ThickPolyline& polyline = pp[i];
//simple check to see if i can be fusionned
if (!polyline.endpoints.first && !polyline.endpoints.second) continue;
ThickPolyline* best_candidate = nullptr;
float best_dot = -1;
int best_idx = 0;
double dot_poly_branch = 0;
double dot_candidate_branch = 0;
// find another polyline starting here
for (size_t j = i + 1; j < pp.size(); ++j) {
ThickPolyline& other = pp[j];
if (polyline.last_point().coincides_with(other.last_point())) {
polyline.reverse();
other.reverse();
} else if (polyline.first_point().coincides_with(other.last_point())) {
other.reverse();
} else if (polyline.first_point().coincides_with(other.first_point())) {
} else if (polyline.last_point().coincides_with(other.first_point())) {
polyline.reverse();
} else {
continue;
}
//std::cout << " try : " << i << ":" << j << " : " <<
// (polyline.points.size() < 2 && other.points.size() < 2) <<
// (!polyline.endpoints.second || !other.endpoints.second) <<
// ((polyline.points.back().distance_to(other.points.back())
// + (polyline.width.back() + other.width.back()) / 4)
// > max_width*1.05) <<
// (abs(polyline.length() - other.length()) > max_width / 2) << "\n";
//// mergeable tests
if (polyline.points.size() < 2 && other.points.size() < 2) continue;
if (!polyline.endpoints.second || !other.endpoints.second) continue;
// test if the new width will not be too big if a fusion occur
//note that this isn't the real calcul. It's just to avoid merging lines too far apart.
if (
((polyline.points.back().distance_to(other.points.back())
+ (polyline.width.back() + other.width.back()) / 4)
> max_width*1.05))
continue;
// test if the lines are not too different in length.
if (abs(polyline.length() - other.length()) > max_width / 2) continue;
//test if we don't merge with something too different and without any relevance.
double coeffSizePolyI = 1;
if (polyline.width.back() == 0) {
coeffSizePolyI = 0.1 + 0.9*get_coeff_from_angle_countour(polyline.points.back(), *this);
}
double coeffSizeOtherJ = 1;
if (other.width.back() == 0) {
coeffSizeOtherJ = 0.1+0.9*get_coeff_from_angle_countour(other.points.back(), *this);
}
if (abs(polyline.length()*coeffSizePolyI - other.length()*coeffSizeOtherJ) > max_width / 2) continue;
//compute angle to see if it's better than previous ones (straighter = better).
Pointf v_poly(polyline.lines().front().vector().x, polyline.lines().front().vector().y);
v_poly.scale(1 / std::sqrt(v_poly.x*v_poly.x + v_poly.y*v_poly.y));
Pointf v_other(other.lines().front().vector().x, other.lines().front().vector().y);
v_other.scale(1 / std::sqrt(v_other.x*v_other.x + v_other.y*v_other.y));
float other_dot = v_poly.x*v_other.x + v_poly.y*v_other.y;
// Get the branch/line in wich we may merge, if possible
// with that, we can decide what is important, and how we can merge that.
// angle_poly - angle_candi =90° => one is useless
// both angle are equal => both are useful with same strength
// ex: Y => | both are useful to crete a nice line
// ex2: TTTTT => ----- these 90° useless lines should be discarded
bool find_main_branch = false;
int biggest_main_branch_id = 0;
int biggest_main_branch_length = 0;
for (size_t k = 0; k < pp.size(); ++k) {
//std::cout << "try to find main : " << k << " ? " << i << " " << j << " ";
if (k == i | k == j) continue;
ThickPolyline& main = pp[k];
if (polyline.first_point().coincides_with(main.last_point())) {
main.reverse();
if (!main.endpoints.second)
find_main_branch = true;
else if (biggest_main_branch_length < main.length()) {
biggest_main_branch_id = k;
biggest_main_branch_length = main.length();
}
} else if (polyline.first_point().coincides_with(main.first_point())) {
if (!main.endpoints.second)
find_main_branch = true;
else if (biggest_main_branch_length < main.length()) {
biggest_main_branch_id = k;
biggest_main_branch_length = main.length();
}
}
if (find_main_branch) {
//use this variable to store the good index and break to compute it
biggest_main_branch_id = k;
break;
}
}
if (!find_main_branch && biggest_main_branch_length == 0) {
// nothing -> it's impossible!
dot_poly_branch = 0.707;
dot_candidate_branch = 0.707;
//std::cout << "no main branch... impossible!!\n";
} else if (!find_main_branch &&
(pp[biggest_main_branch_id].length() < polyline.length() || pp[biggest_main_branch_id].length() < other.length()) ){
//the main branch should have no endpoint or be bigger!
//here, it have an endpoint, and is not the biggest -> bad!
continue;
} else {
//compute the dot (biggest_main_branch_id)
Pointf v_poly(polyline.lines().front().vector().x, polyline.lines().front().vector().y);
v_poly.scale(1 / std::sqrt(v_poly.x*v_poly.x + v_poly.y*v_poly.y));
Pointf v_candid(other.lines().front().vector().x, other.lines().front().vector().y);
v_candid.scale(1 / std::sqrt(v_candid.x*v_candid.x + v_candid.y*v_candid.y));
Pointf v_branch(-pp[biggest_main_branch_id].lines().front().vector().x, -pp[biggest_main_branch_id].lines().front().vector().y);
v_branch.scale(1 / std::sqrt(v_branch.x*v_branch.x + v_branch.y*v_branch.y));
dot_poly_branch = v_poly.x*v_branch.x + v_poly.y*v_branch.y;
dot_candidate_branch = v_candid.x*v_branch.x + v_candid.y*v_branch.y;
if (dot_poly_branch < 0) dot_poly_branch = 0;
if (dot_candidate_branch < 0) dot_candidate_branch = 0;
}
//test if it's useful to merge or not
//ie, don't merge 'T' but ok for 'Y', merge only lines of not disproportionate different length (ratio max: 4)
if (dot_poly_branch < 0.1 || dot_candidate_branch < 0.1 ||
(polyline.length()>other.length() ? polyline.length() / other.length() : other.length() / polyline.length()) > 4) {
continue;
}
if (other_dot > best_dot) {
best_candidate = &other;
best_idx = j;
best_dot = other_dot;
}
}
if (best_candidate != nullptr) {
// delete very near points
remove_point_too_near(&polyline);
remove_point_too_near(best_candidate);
// add point at the same pos than the other line to have a nicer fusion
add_point_same_percent(&polyline, best_candidate);
add_point_same_percent(best_candidate, &polyline);
//get the angle of the nearest points of the contour to see : _| (good) \_ (average) __(bad)
//sqrt because the result are nicer this way: don't over-penalize /_ angles
//TODO: try if we can achieve a better result if we use a different algo if the angle is <90°
const double coeff_angle_poly = (get_coeff_from_angle_countour(polyline.points.back(), *this));
const double coeff_angle_candi = (get_coeff_from_angle_countour(best_candidate->points.back(), *this));
//this will encourage to follow the curve, a little, because it's shorter near the center
//without that, it tends to go to the outter rim.
double weight_poly = 2 - polyline.length() / max(polyline.length(), best_candidate->length());
double weight_candi = 2 - best_candidate->length() / max(polyline.length(), best_candidate->length());
weight_poly *= coeff_angle_poly;
weight_candi *= coeff_angle_candi;
const double coeff_poly = (dot_poly_branch * weight_poly) / (dot_poly_branch * weight_poly + dot_candidate_branch * weight_candi);
const double coeff_candi = 1.0 - coeff_poly;
//iterate the points
// as voronoi should create symetric thing, we can iterate synchonously
unsigned int idx_point = 1;
while (idx_point < min(polyline.points.size(), best_candidate->points.size())) {
//fusion
polyline.points[idx_point].x = polyline.points[idx_point].x * coeff_poly + best_candidate->points[idx_point].x * coeff_candi;
polyline.points[idx_point].y = polyline.points[idx_point].y * coeff_poly + best_candidate->points[idx_point].y * coeff_candi;
// The width decrease with distance from the centerline.
// This formula is what works the best, even if it's not perfect (created empirically). 0->3% error on a gap fill on some tests.
//If someone find an other formula based on the properties of the voronoi algorithm used here, and it works better, please use it.
//or maybe just use the distance to nearest edge in bounds...
double value_from_current_width = 0.5*polyline.width[idx_point] * dot_poly_branch / max(dot_poly_branch, dot_candidate_branch);
value_from_current_width += 0.5*best_candidate->width[idx_point] * dot_candidate_branch / max(dot_poly_branch, dot_candidate_branch);
double value_from_dist = 2 * polyline.points[idx_point].distance_to(best_candidate->points[idx_point]);
value_from_dist *= sqrt(min(dot_poly_branch, dot_candidate_branch) / max(dot_poly_branch, dot_candidate_branch));
polyline.width[idx_point] = value_from_current_width + value_from_dist;
//failsafe
if (polyline.width[idx_point] > max_width) polyline.width[idx_point] = max_width;
++idx_point;
}
if (idx_point < best_candidate->points.size()) {
if (idx_point + 1 < best_candidate->points.size()) {
//create a new polyline
pp.emplace_back();
pp.back().endpoints.first = true;
pp.back().endpoints.second = best_candidate->endpoints.second;
for (int idx_point_new_line = idx_point; idx_point_new_line < best_candidate->points.size(); ++idx_point_new_line) {
pp.back().points.push_back(best_candidate->points[idx_point_new_line]);
pp.back().width.push_back(best_candidate->width[idx_point_new_line]);
}
} else {
//Add last point
polyline.points.push_back(best_candidate->points[idx_point]);
polyline.width.push_back(best_candidate->width[idx_point]);
//select if an end opccur
polyline.endpoints.second &= best_candidate->endpoints.second;
}
} else {
//select if an end opccur
polyline.endpoints.second &= best_candidate->endpoints.second;
}
//remove points that are the same or too close each other, ie simplify
for (unsigned int idx_point = 1; idx_point < polyline.points.size(); ++idx_point) {
if (polyline.points[idx_point - 1].distance_to(polyline.points[idx_point]) < SCALED_EPSILON) {
if (idx_point < polyline.points.size() -1) {
polyline.points.erase(polyline.points.begin() + idx_point);
polyline.width.erase(polyline.width.begin() + idx_point);
} else {
polyline.points.erase(polyline.points.begin() + idx_point - 1);
polyline.width.erase(polyline.width.begin() + idx_point - 1);
}
--idx_point;
}
}
//remove points that are outside of the geometry
for (unsigned int idx_point = 0; idx_point < polyline.points.size(); ++idx_point) {
if (!bounds.contains_b(polyline.points[idx_point])) {
polyline.points.erase(polyline.points.begin() + idx_point);
polyline.width.erase(polyline.width.begin() + idx_point);
--idx_point;
}
}
if (polyline.points.size() < 2) {
//remove self
pp.erase(pp.begin() + i);
--i;
--best_idx;
}
pp.erase(pp.begin() + best_idx);
changes = true;
break;
}
}
if (changes) {
concatThickPolylines(pp);
///reorder, in case of change
std::sort(pp.begin(), pp.end(), [](const ThickPolyline & a, const ThickPolyline & b) { return a.length() < b.length(); });
}
}
// remove too small extrusion at start & end of polylines
changes = false;
for (size_t i = 0; i < pp.size(); ++i) {
ThickPolyline& polyline = pp[i];
// remove bits with too small extrusion
while (polyline.points.size() > 1 && polyline.width.front() < min_width && polyline.endpoints.first) {
//try to split if possible
if (polyline.width[1] > min_width) {
double percent_can_keep = (min_width - polyline.width[0]) / (polyline.width[1] - polyline.width[0]);
if (polyline.points.front().distance_to(polyline.points[1]) * percent_can_keep > max_width / 2
&& polyline.points.front().distance_to(polyline.points[1])* (1 - percent_can_keep) > max_width / 2) {
//Can split => move the first point and assign a new weight.
//the update of endpoints wil be performed in concatThickPolylines
polyline.points.front().x = polyline.points.front().x +
(coord_t)((polyline.points[1].x - polyline.points.front().x) * percent_can_keep);
polyline.points.front().y = polyline.points.front().y +
(coord_t)((polyline.points[1].y - polyline.points.front().y) * percent_can_keep);
polyline.width.front() = min_width;
changes = true;
break;
}
}
polyline.points.erase(polyline.points.begin());
polyline.width.erase(polyline.width.begin());
changes = true;
}
while (polyline.points.size() > 1 && polyline.width.back() < min_width && polyline.endpoints.second) {
//try to split if possible
if (polyline.width[polyline.points.size()-2] > min_width) {
double percent_can_keep = (min_width - polyline.width.back()) / (polyline.width[polyline.points.size() - 2] - polyline.width.back());
if (polyline.points.back().distance_to(polyline.points[polyline.points.size() - 2]) * percent_can_keep > max_width / 2
&& polyline.points.back().distance_to(polyline.points[polyline.points.size() - 2]) * (1-percent_can_keep) > max_width / 2) {
//Can split => move the first point and assign a new weight.
//the update of endpoints wil be performed in concatThickPolylines
polyline.points.back().x = polyline.points.back().x +
(coord_t)((polyline.points[polyline.points.size() - 2].x - polyline.points.back().x) * percent_can_keep);
polyline.points.back().y = polyline.points.back().y +
(coord_t)((polyline.points[polyline.points.size() - 2].y - polyline.points.back().y) * percent_can_keep);
polyline.width.back() = min_width;
changes = true;
break;
}
}
polyline.points.erase(polyline.points.end()-1);
polyline.width.erase(polyline.width.end() - 1);
changes = true;
}
if (polyline.points.size() < 2) {
//remove self if too small
pp.erase(pp.begin() + i);
--i;
}
}
if (changes) concatThickPolylines(pp);
// Loop through all returned polylines in order to extend their endpoints to the
// expolygon boundaries
for (size_t i = 0; i < pp.size(); ++i) {
ThickPolyline& polyline = pp[i];
// extend initial and final segments of each polyline if they're actual endpoints
// We assign new endpoints to temporary variables because in case of a single-line
// polyline, after we extend the start point it will be caught by the intersection()
// call, so we keep the inner point until we perform the second intersection() as well
Point new_front = polyline.points.front();
Point new_back = polyline.points.back();
if (polyline.endpoints.first && !bounds.has_boundary_point(new_front)) {
Line line(polyline.points[1], polyline.points.front());
// prevent the line from touching on the other side, otherwise intersection() might return that solution
if (polyline.points.size() == 2) line.a = line.midpoint();
line.extend_end(max_width);
(void)bounds.contour.first_intersection(line, &new_front);
}
if (polyline.endpoints.second && !bounds.has_boundary_point(new_back)) {
Line line(
*(polyline.points.end() - 2),
polyline.points.back()
);
// prevent the line from touching on the other side, otherwise intersection() might return that solution
if (polyline.points.size() == 2) line.a = line.midpoint();
line.extend_end(max_width);
(void)bounds.contour.first_intersection(line, &new_back);
}
polyline.points.front() = new_front;
polyline.points.back() = new_back;
}
// concatenate, but even where multiple thickpolyline join, to create nice long strait polylines
/* If we removed any short polylines we now try to connect consecutive polylines
in order to allow loop detection. Note that this algorithm is greedier than
MedialAxis::process_edge_neighbors() as it will connect random pairs of
polylines even when more than two start from the same point. This has no
drawbacks since we optimize later using nearest-neighbor which would do the
same, but should we use a more sophisticated optimization algorithm we should
not connect polylines when more than two meet.
Optimisation of the old algorithm : now we select the most "strait line" choice
when we merge with an other line at a point with more than two meet.
*/
changes = false;
for (size_t i = 0; i < pp.size(); ++i) {
ThickPolyline& polyline = pp[i];
if (polyline.endpoints.first && polyline.endpoints.second) continue; // optimization
ThickPolyline* best_candidate = nullptr;
float best_dot = -1;
int best_idx = 0;
// find another polyline starting here
for (size_t j = i + 1; j < pp.size(); ++j) {
ThickPolyline& other = pp[j];
if (polyline.last_point().coincides_with(other.last_point())) {
other.reverse();
} else if (polyline.first_point().coincides_with(other.last_point())) {
polyline.reverse();
other.reverse();
} else if (polyline.first_point().coincides_with(other.first_point())) {
polyline.reverse();
} else if (!polyline.last_point().coincides_with(other.first_point())) {
continue;
}
Pointf v_poly(polyline.lines().back().vector().x, polyline.lines().back().vector().y);
v_poly.scale(1 / std::sqrt(v_poly.x*v_poly.x + v_poly.y*v_poly.y));
Pointf v_other(other.lines().front().vector().x, other.lines().front().vector().y);
v_other.scale(1 / std::sqrt(v_other.x*v_other.x + v_other.y*v_other.y));
float other_dot = v_poly.x*v_other.x + v_poly.y*v_other.y;
if (other_dot > best_dot) {
best_candidate = &other;
best_idx = j;
best_dot = other_dot;
}
}
if (best_candidate != nullptr) {
polyline.points.insert(polyline.points.end(), best_candidate->points.begin() + 1, best_candidate->points.end());
polyline.width.insert(polyline.width.end(), best_candidate->width.begin() + 1, best_candidate->width.end());
polyline.endpoints.second = best_candidate->endpoints.second;
assert(polyline.width.size() == polyline.points.size());
changes = true;
pp.erase(pp.begin() + best_idx);
}
}
if (changes) concatThickPolylines(pp);
//remove too thin polylines points (inside a polyline : split it)
for (size_t i = 0; i < pp.size(); ++i) {
ThickPolyline& polyline = pp[i];
// remove bits with too small extrusion
size_t idx_point = 0;
while (idx_point<polyline.points.size()) {
if (polyline.width[idx_point] < min_width) {
if (idx_point == 0) {
//too thin at start
polyline.points.erase(polyline.points.begin());
polyline.width.erase(polyline.width.begin());
idx_point = 0;
} else if (idx_point == 1) {
//too thin at start
polyline.points.erase(polyline.points.begin());
polyline.width.erase(polyline.width.begin());
polyline.points.erase(polyline.points.begin());
polyline.width.erase(polyline.width.begin());
idx_point = 0;
} else if (idx_point == polyline.points.size() - 2) {
//too thin at (near) end
polyline.points.erase(polyline.points.end() - 1);
polyline.width.erase(polyline.width.end() - 1);
polyline.points.erase(polyline.points.end() - 1);
polyline.width.erase(polyline.width.end() - 1);
} else if (idx_point == polyline.points.size() - 1) {
//too thin at end
polyline.points.erase(polyline.points.end() - 1);
polyline.width.erase(polyline.width.end() - 1);
} else {
//too thin in middle : split
pp.emplace_back();
ThickPolyline &newone = pp.back();
newone.points.insert(newone.points.begin(), polyline.points.begin() + idx_point + 1, polyline.points.end());
newone.width.insert(newone.width.begin(), polyline.width.begin() + idx_point + 1, polyline.width.end());
polyline.points.erase(polyline.points.begin() + idx_point, polyline.points.end());
polyline.width.erase(polyline.width.begin() + idx_point, polyline.width.end());
}
} else idx_point++;
if (polyline.points.size() < 2) {
//remove self if too small
pp.erase(pp.begin() + i);
--i;
break;
}
}
}
//remove too short polyline
changes = true;
while (changes) {
changes = false;
double shortest_size = max_w * 2;
int32_t shortest_idx = -1;
for (size_t i = 0; i < pp.size(); ++i) {
ThickPolyline& polyline = pp[i];
// Remove the shortest polylines : polyline that are shorter than wider
// (we can't do this check before endpoints extension and clipping because we don't
// know how long will the endpoints be extended since it depends on polygon thickness
// which is variable - extension will be <= max_width/2 on each side)
if ((polyline.endpoints.first || polyline.endpoints.second)
&& polyline.length() < max_width / 2) {
if (shortest_size > polyline.length()) {
shortest_size = polyline.length();
shortest_idx = i;
}
}
}
if (shortest_idx >= 0 && shortest_idx < pp.size()) {
pp.erase(pp.begin() + shortest_idx);
changes = true;
}
if (changes) concatThickPolylines(pp);
}
//TODO: reduce the flow at the intersection ( + ) points ?
//ensure the volume extruded is correct for what we have been asked
// => don't over-extrude
double surface = 0;
double volume = 0;
for (ThickPolyline& polyline : pp) {
for (ThickLine l : polyline.thicklines()) {
surface += l.length() * (l.a_width + l.b_width) / 2;
double width_mean = (l.a_width + l.b_width) / 2;
volume += height * (width_mean - height * (1. - 0.25 * PI)) * l.length();
}
}
// compute bounds volume
double boundsVolume = 0;
boundsVolume += height*bounds.area();
// add external "perimeter gap"
double perimeterRoundGap = bounds.contour.length() * height * (1 - 0.25*PI) * 0.5;
// add holes "perimeter gaps"
double holesGaps = 0;
for (auto hole = bounds.holes.begin(); hole != bounds.holes.end(); ++hole) {
holesGaps += hole->length() * height * (1 - 0.25*PI) * 0.5;
}
boundsVolume += perimeterRoundGap + holesGaps;
if (boundsVolume < volume) {
//reduce width
double reduce_by = boundsVolume / volume;
for (ThickPolyline& polyline : pp) {
for (ThickLine l : polyline.thicklines()) {
l.a_width *= reduce_by;
l.b_width *= reduce_by;
}
}
}
polylines->insert(polylines->end(), pp.begin(), pp.end());
}
void
ExPolygon::medial_axis(double max_width, double min_width, Polylines* polylines) const
{
ThickPolylines tp;
this->medial_axis(*this, max_width, min_width, &tp, max_width/2.0);
polylines->insert(polylines->end(), tp.begin(), tp.end());
}
void
ExPolygon::get_trapezoids(Polygons* polygons) const
{
ExPolygons expp;
expp.push_back(*this);
boost::polygon::get_trapezoids(*polygons, expp);
}
void
ExPolygon::get_trapezoids(Polygons* polygons, double angle) const
{
ExPolygon clone = *this;
clone.rotate(PI/2 - angle, Point(0,0));
clone.get_trapezoids(polygons);
for (Polygons::iterator polygon = polygons->begin(); polygon != polygons->end(); ++polygon)
polygon->rotate(-(PI/2 - angle), Point(0,0));
}
// This algorithm may return more trapezoids than necessary
// (i.e. it may break a single trapezoid in several because
// other parts of the object have x coordinates in the middle)
void
ExPolygon::get_trapezoids2(Polygons* polygons) const
{
// get all points of this ExPolygon
Points pp = *this;
// build our bounding box
BoundingBox bb(pp);
// get all x coordinates
std::vector<coord_t> xx;
xx.reserve(pp.size());
for (Points::const_iterator p = pp.begin(); p != pp.end(); ++p)
xx.push_back(p->x);
std::sort(xx.begin(), xx.end());
// find trapezoids by looping from first to next-to-last coordinate
for (std::vector<coord_t>::const_iterator x = xx.begin(); x != xx.end()-1; ++x) {
coord_t next_x = *(x + 1);
if (*x == next_x) continue;
// build rectangle
Polygon poly;
poly.points.resize(4);
poly[0].x = *x;
poly[0].y = bb.min.y;
poly[1].x = next_x;
poly[1].y = bb.min.y;
poly[2].x = next_x;
poly[2].y = bb.max.y;
poly[3].x = *x;
poly[3].y = bb.max.y;
// intersect with this expolygon
// append results to return value
polygons_append(*polygons, intersection(poly, to_polygons(*this)));
}
}
void
ExPolygon::get_trapezoids2(Polygons* polygons, double angle) const {
ExPolygon clone = *this;
clone.rotate(PI / 2 - angle, Point(0, 0));
clone.get_trapezoids2(polygons);
for (Polygons::iterator polygon = polygons->begin(); polygon != polygons->end(); ++polygon)
polygon->rotate(-(PI / 2 - angle), Point(0, 0));
}
void
ExPolygon::get_trapezoids3_half(Polygons* polygons, float spacing) const {
// get all points of this ExPolygon
Points pp = *this;
if (pp.empty()) return;
// build our bounding box
BoundingBox bb(pp);
// get all x coordinates
int min_x = pp[0].x, max_x = pp[0].x;
std::vector<coord_t> xx;
for (Points::const_iterator p = pp.begin(); p != pp.end(); ++p) {
if (min_x > p->x) min_x = p->x;
if (max_x < p->x) max_x = p->x;
}
for (int x = min_x; x < max_x-spacing/2; x += spacing) {
xx.push_back(x);
}
xx.push_back(max_x);
//std::sort(xx.begin(), xx.end());
// find trapezoids by looping from first to next-to-last coordinate
for (std::vector<coord_t>::const_iterator x = xx.begin(); x != xx.end() - 1; ++x) {
coord_t next_x = *(x + 1);
if (*x == next_x) continue;
// build rectangle
Polygon poly;
poly.points.resize(4);
poly[0].x = *x +spacing / 4;
poly[0].y = bb.min.y;
poly[1].x = next_x -spacing / 4;
poly[1].y = bb.min.y;
poly[2].x = next_x -spacing / 4;
poly[2].y = bb.max.y;
poly[3].x = *x +spacing / 4;
poly[3].y = bb.max.y;
// intersect with this expolygon
// append results to return value
polygons_append(*polygons, intersection(poly, to_polygons(*this)));
}
}
// While this triangulates successfully, it's NOT a constrained triangulation
// as it will create more vertices on the boundaries than the ones supplied.
void
ExPolygon::triangulate(Polygons* polygons) const
{
// first make trapezoids
Polygons trapezoids;
this->get_trapezoids2(&trapezoids);
// then triangulate each trapezoid
for (Polygons::iterator polygon = trapezoids.begin(); polygon != trapezoids.end(); ++polygon)
polygon->triangulate_convex(polygons);
}
void
ExPolygon::triangulate_pp(Polygons* polygons) const
{
// convert polygons
std::list<TPPLPoly> input;
ExPolygons expp = union_ex(simplify_polygons(to_polygons(*this), true));
for (ExPolygons::const_iterator ex = expp.begin(); ex != expp.end(); ++ex) {
// contour
{
TPPLPoly p;
p.Init(int(ex->contour.points.size()));
//printf(PRINTF_ZU "\n0\n", ex->contour.points.size());
for (Points::const_iterator point = ex->contour.points.begin(); point != ex->contour.points.end(); ++point) {
p[ point-ex->contour.points.begin() ].x = point->x;
p[ point-ex->contour.points.begin() ].y = point->y;
//printf("%ld %ld\n", point->x, point->y);
}
p.SetHole(false);
input.push_back(p);
}
// holes
for (Polygons::const_iterator hole = ex->holes.begin(); hole != ex->holes.end(); ++hole) {
TPPLPoly p;
p.Init(hole->points.size());
//printf(PRINTF_ZU "\n1\n", hole->points.size());
for (Points::const_iterator point = hole->points.begin(); point != hole->points.end(); ++point) {
p[ point-hole->points.begin() ].x = point->x;
p[ point-hole->points.begin() ].y = point->y;
//printf("%ld %ld\n", point->x, point->y);
}
p.SetHole(true);
input.push_back(p);
}
}
// perform triangulation
std::list<TPPLPoly> output;
int res = TPPLPartition().Triangulate_MONO(&input, &output);
if (res != 1) CONFESS("Triangulation failed");
// convert output polygons
for (std::list<TPPLPoly>::iterator poly = output.begin(); poly != output.end(); ++poly) {
long num_points = poly->GetNumPoints();
Polygon p;
p.points.resize(num_points);
for (long i = 0; i < num_points; ++i) {
p.points[i].x = coord_t((*poly)[i].x);
p.points[i].y = coord_t((*poly)[i].y);
}
polygons->push_back(p);
}
}
void
ExPolygon::triangulate_p2t(Polygons* polygons) const
{
ExPolygons expp = simplify_polygons_ex(*this, true);
for (ExPolygons::const_iterator ex = expp.begin(); ex != expp.end(); ++ex) {
// TODO: prevent duplicate points
// contour
std::vector<p2t::Point*> ContourPoints;
for (Points::const_iterator point = ex->contour.points.begin(); point != ex->contour.points.end(); ++point) {
// We should delete each p2t::Point object
ContourPoints.push_back(new p2t::Point(point->x, point->y));
}
p2t::CDT cdt(ContourPoints);
// holes
for (Polygons::const_iterator hole = ex->holes.begin(); hole != ex->holes.end(); ++hole) {
std::vector<p2t::Point*> points;
for (Points::const_iterator point = hole->points.begin(); point != hole->points.end(); ++point) {
// will be destructed in SweepContext::~SweepContext
points.push_back(new p2t::Point(point->x, point->y));
}
cdt.AddHole(points);
}
// perform triangulation
cdt.Triangulate();
std::vector<p2t::Triangle*> triangles = cdt.GetTriangles();
for (std::vector<p2t::Triangle*>::const_iterator triangle = triangles.begin(); triangle != triangles.end(); ++triangle) {
Polygon p;
for (int i = 0; i <= 2; ++i) {
p2t::Point* point = (*triangle)->GetPoint(i);
p.points.push_back(Point(point->x, point->y));
}
polygons->push_back(p);
}
for(std::vector<p2t::Point*>::iterator it = ContourPoints.begin(); it != ContourPoints.end(); ++it) {
delete *it;
}
}
}
Lines
ExPolygon::lines() const
{
Lines lines = this->contour.lines();
for (Polygons::const_iterator h = this->holes.begin(); h != this->holes.end(); ++h) {
Lines hole_lines = h->lines();
lines.insert(lines.end(), hole_lines.begin(), hole_lines.end());
}
return lines;
}
std::string
ExPolygon::dump_perl() const
{
std::ostringstream ret;
ret << "[" << this->contour.dump_perl();
for (Polygons::const_iterator h = this->holes.begin(); h != this->holes.end(); ++h)
ret << "," << h->dump_perl();
ret << "]";
return ret.str();
}
BoundingBox get_extents(const ExPolygon &expolygon)
{
return get_extents(expolygon.contour);
}
BoundingBox get_extents(const ExPolygons &expolygons)
{
BoundingBox bbox;
if (! expolygons.empty()) {
for (size_t i = 0; i < expolygons.size(); ++ i)
if (! expolygons[i].contour.points.empty())
bbox.merge(get_extents(expolygons[i]));
}
return bbox;
}
BoundingBox get_extents_rotated(const ExPolygon &expolygon, double angle)
{
return get_extents_rotated(expolygon.contour, angle);
}
BoundingBox get_extents_rotated(const ExPolygons &expolygons, double angle)
{
BoundingBox bbox;
if (! expolygons.empty()) {
bbox = get_extents_rotated(expolygons.front().contour, angle);
for (size_t i = 1; i < expolygons.size(); ++ i)
bbox.merge(get_extents_rotated(expolygons[i].contour, angle));
}
return bbox;
}
extern std::vector<BoundingBox> get_extents_vector(const ExPolygons &polygons)
{
std::vector<BoundingBox> out;
out.reserve(polygons.size());
for (ExPolygons::const_iterator it = polygons.begin(); it != polygons.end(); ++ it)
out.push_back(get_extents(*it));
return out;
}
bool remove_sticks(ExPolygon &poly)
{
return remove_sticks(poly.contour) || remove_sticks(poly.holes);
}
} // namespace Slic3r
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