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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 {
int MedialAxis::id = 0;
void
MedialAxis::build(Polylines* polylines)
{
ThickPolylines tp;
this->build(&tp);
polylines->insert(polylines->end(), tp.begin(), tp.end());
}
void
MedialAxis::polyline_from_voronoi(const Lines& voronoi_edges, ThickPolylines* polylines)
{
this->lines = voronoi_edges;
construct_voronoi(lines.begin(), lines.end(), &this->vd);
/*
// DEBUG: dump all Voronoi edges
{
for (VD::const_edge_iterator edge = this->vd.edges().begin(); edge != this->vd.edges().end(); ++edge) {
if (edge->is_infinite()) continue;
ThickPolyline polyline;
polyline.points.push_back(Point( edge->vertex0()->x(), edge->vertex0()->y() ));
polyline.points.push_back(Point( edge->vertex1()->x(), edge->vertex1()->y() ));
polylines->push_back(polyline);
}
return;
}
*/
typedef const VD::vertex_type vert_t;
typedef const VD::edge_type edge_t;
// collect valid edges (i.e. prune those not belonging to MAT)
// note: this keeps twins, so it inserts twice the number of the valid edges
this->valid_edges.clear();
{
std::set<const VD::edge_type*> seen_edges;
for (VD::const_edge_iterator edge = this->vd.edges().begin(); edge != this->vd.edges().end(); ++edge) {
// if we only process segments representing closed loops, none if the
// infinite edges (if any) would be part of our MAT anyway
if (edge->is_secondary() || edge->is_infinite()) continue;
// don't re-validate twins
if (seen_edges.find(&*edge) != seen_edges.end()) continue; // TODO: is this needed?
seen_edges.insert(&*edge);
seen_edges.insert(edge->twin());
if (!this->validate_edge(&*edge)) continue;
this->valid_edges.insert(&*edge);
this->valid_edges.insert(edge->twin());
}
}
this->edges = this->valid_edges;
// iterate through the valid edges to build polylines
while (!this->edges.empty()) {
const edge_t* edge = *this->edges.begin();
// start a polyline
ThickPolyline polyline;
polyline.points.push_back(Point( edge->vertex0()->x(), edge->vertex0()->y() ));
polyline.points.push_back(Point( edge->vertex1()->x(), edge->vertex1()->y() ));
polyline.width.push_back(this->thickness[edge].first);
polyline.width.push_back(this->thickness[edge].second);
// remove this edge and its twin from the available edges
(void)this->edges.erase(edge);
(void)this->edges.erase(edge->twin());
// get next points
this->process_edge_neighbors(edge, &polyline);
// get previous points
{
ThickPolyline rpolyline;
this->process_edge_neighbors(edge->twin(), &rpolyline);
polyline.points.insert(polyline.points.begin(), rpolyline.points.rbegin(), rpolyline.points.rend());
polyline.width.insert(polyline.width.begin(), rpolyline.width.rbegin(), rpolyline.width.rend());
polyline.endpoints.first = rpolyline.endpoints.second;
}
assert(polyline.width.size() == polyline.points.size());
// prevent loop endpoints from being extended
if (polyline.first_point().coincides_with(polyline.last_point())) {
polyline.endpoints.first = false;
polyline.endpoints.second = false;
}
// append polyline to result
polylines->push_back(polyline);
}
#ifdef SLIC3R_DEBUG
{
static int iRun = 0;
dump_voronoi_to_svg(this->lines, this->vd, polylines, debug_out_path("MedialAxis-%d.svg", iRun ++).c_str());
printf("Thick lines: ");
for (ThickPolylines::const_iterator it = polylines->begin(); it != polylines->end(); ++ it) {
ThickLines lines = it->thicklines();
for (ThickLines::const_iterator it2 = lines.begin(); it2 != lines.end(); ++ it2) {
printf("%f,%f ", it2->a_width, it2->b_width);
}
}
printf("\n");
}
#endif /* SLIC3R_DEBUG */
}
void
MedialAxis::process_edge_neighbors(const VD::edge_type* edge, ThickPolyline* polyline)
{
while (true) {
// Since rot_next() works on the edge starting point but we want
// to find neighbors on the ending point, we just swap edge with
// its twin.
const VD::edge_type* twin = edge->twin();
// count neighbors for this edge
std::vector<const VD::edge_type*> neighbors;
for (const VD::edge_type* neighbor = twin->rot_next(); neighbor != twin;
neighbor = neighbor->rot_next()) {
if (this->valid_edges.count(neighbor) > 0) neighbors.push_back(neighbor);
}
// if we have a single neighbor then we can continue recursively
if (neighbors.size() == 1) {
const VD::edge_type* neighbor = neighbors.front();
// break if this is a closed loop
if (this->edges.count(neighbor) == 0) return;
Point new_point(neighbor->vertex1()->x(), neighbor->vertex1()->y());
polyline->points.push_back(new_point);
polyline->width.push_back(this->thickness[neighbor].second);
(void)this->edges.erase(neighbor);
(void)this->edges.erase(neighbor->twin());
edge = neighbor;
} else if (neighbors.size() == 0) {
polyline->endpoints.second = true;
return;
} else {
// T-shaped or star-shaped joint
return;
}
}
}
bool
MedialAxis::validate_edge(const VD::edge_type* edge)
{
// prevent overflows and detect almost-infinite edges
if (std::abs(edge->vertex0()->x()) > double(CLIPPER_MAX_COORD_UNSCALED) ||
std::abs(edge->vertex0()->y()) > double(CLIPPER_MAX_COORD_UNSCALED) ||
std::abs(edge->vertex1()->x()) > double(CLIPPER_MAX_COORD_UNSCALED) ||
std::abs(edge->vertex1()->y()) > double(CLIPPER_MAX_COORD_UNSCALED))
return false;
// construct the line representing this edge of the Voronoi diagram
const Line line(
Point( edge->vertex0()->x(), edge->vertex0()->y() ),
Point( edge->vertex1()->x(), edge->vertex1()->y() )
);
// discard edge if it lies outside the supplied shape
// this could maybe be optimized (checking inclusion of the endpoints
// might give false positives as they might belong to the contour itself)
if (line.a.coincides_with(line.b)) {
// in this case, contains(line) returns a false positive
if (!this->expolygon.contains(line.a)) return false;
} else {
if (!this->expolygon.contains(line)) return false;
}
// retrieve the original line segments which generated the edge we're checking
const VD::cell_type* cell_l = edge->cell();
const VD::cell_type* cell_r = edge->twin()->cell();
const Line &segment_l = this->retrieve_segment(cell_l);
const Line &segment_r = this->retrieve_segment(cell_r);
//SVG svg("edge.svg");
//svg.draw(this->expolygon.expolygon);
//svg.draw(line);
//svg.draw(segment_l, "red");
//svg.draw(segment_r, "blue");
//svg.Close();
//
/* Calculate thickness of the cross-section at both the endpoints of this edge.
Our Voronoi edge is part of a CCW sequence going around its Voronoi cell
located on the left side. (segment_l).
This edge's twin goes around segment_r. Thus, segment_r is
oriented in the same direction as our main edge, and segment_l is oriented
in the same direction as our twin edge.
We used to only consider the (half-)distances to segment_r, and that works
whenever segment_l and segment_r are almost specular and facing. However,
at curves they are staggered and they only face for a very little length
(our very short edge represents such visibility).
Both w0 and w1 can be calculated either towards cell_l or cell_r with equal
results by Voronoi definition.
When cell_l or cell_r don't refer to the segment but only to an endpoint, we
calculate the distance to that endpoint instead. */
coordf_t w0 = cell_r->contains_segment()
? line.a.distance_to(segment_r)*2
: line.a.distance_to(this->retrieve_endpoint(cell_r))*2;
coordf_t w1 = cell_l->contains_segment()
? line.b.distance_to(segment_l)*2
: line.b.distance_to(this->retrieve_endpoint(cell_l))*2;
//don't remove the line that goes to the intersection of the contour
// we use them to create nicer thin wall lines
//if (cell_l->contains_segment() && cell_r->contains_segment()) {
// // calculate the relative angle between the two boundary segments
// double angle = fabs(segment_r.orientation() - segment_l.orientation());
// if (angle > PI) angle = 2*PI - angle;
// assert(angle >= 0 && angle <= PI);
//
// // fabs(angle) ranges from 0 (collinear, same direction) to PI (collinear, opposite direction)
// // we're interested only in segments close to the second case (facing segments)
// // so we allow some tolerance.
// // this filter ensures that we're dealing with a narrow/oriented area (longer than thick)
// // we don't run it on edges not generated by two segments (thus generated by one segment
// // and the endpoint of another segment), since their orientation would not be meaningful
// if (PI - angle > PI/8) {
// // angle is not narrow enough
//
// // only apply this filter to segments that are not too short otherwise their
// // angle could possibly be not meaningful
// if (w0 < SCALED_EPSILON || w1 < SCALED_EPSILON || line.length() >= this->min_width)
// return false;
// }
//} else {
// if (w0 < SCALED_EPSILON || w1 < SCALED_EPSILON)
// return false;
//}
// don't do that before we try to fusion them
//if (w0 < this->min_width && w1 < this->min_width)
// return false;
//
//shouldn't occur if perimeter_generator is well made
if (w0 > this->max_width && w1 > this->max_width)
return false;
this->thickness[edge] = std::make_pair(w0, w1);
this->thickness[edge->twin()] = std::make_pair(w1, w0);
return true;
}
const Line&
MedialAxis::retrieve_segment(const VD::cell_type* cell) const
{
return lines[cell->source_index()];
}
const Point&
MedialAxis::retrieve_endpoint(const VD::cell_type* cell) const
{
const Line& line = this->retrieve_segment(cell);
if (cell->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) {
return line.a;
} else {
return line.b;
}
}
/// remove point that are at SCALED_EPSILON * 2 distance.
void
remove_point_too_near(ThickPolyline* to_reduce)
{
const coord_t smallest = SCALED_EPSILON * 2;
size_t id = 1;
while (id < to_reduce->points.size() - 1) {
size_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);
newdist = to_reduce->points[id].distance_to(to_reduce->points[id - 1]);
//if you removed a point, it check if the next one isn't too near from the previous one.
// if not, it bypass it.
if (newdist > smallest) {
++id;
}
}
//go to next one
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 (size_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
size_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°
/// 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, coord_t min_dist_between_point) {
double nearest_dist = point.distance_to(contour.contour.points.front());
Point point_nearest = contour.contour.points.front();
size_t id_nearest = 0;
double near_dist = nearest_dist;
Point point_near = point_nearest;
size_t id_near = 0;
for (size_t id_point = 1; id_point < contour.contour.points.size(); ++id_point) {
if (nearest_dist > point.distance_to(contour.contour.points[id_point])) {
//update point_near
id_near = id_nearest;
point_near = point_nearest;
near_dist = nearest_dist;
//update nearest
nearest_dist = point.distance_to(contour.contour.points[id_point]);
point_nearest = contour.contour.points[id_point];
id_nearest = id_point;
}
}
double angle = 0;
size_t id_before = id_nearest == 0 ? contour.contour.points.size() - 1 : id_nearest - 1;
Point point_before = id_nearest == 0 ? contour.contour.points.back() : contour.contour.points[id_nearest - 1];
//Search one point far enough to be relevant
while (point_nearest.distance_to(point_before) < min_dist_between_point) {
point_before = id_before == 0 ? contour.contour.points.back() : contour.contour.points[id_before - 1];
id_before = id_before == 0 ? contour.contour.points.size() - 1 : id_before - 1;
//don't loop
if (id_before == id_nearest) {
id_before = id_nearest == 0 ? contour.contour.points.size() - 1 : id_nearest - 1;
point_before = id_nearest == 0 ? contour.contour.points.back() : contour.contour.points[id_nearest - 1];
break;
}
}
size_t id_after = id_nearest == contour.contour.points.size() - 1 ? 0 : id_nearest + 1;
Point point_after = id_nearest == contour.contour.points.size() - 1 ? contour.contour.points.front() : contour.contour.points[id_nearest + 1];
//Search one point far enough to be relevant
while (point_nearest.distance_to(point_after) < min_dist_between_point) {
point_after = id_after == contour.contour.points.size() - 1 ? contour.contour.points.front() : contour.contour.points[id_after + 1];
id_after = id_after == contour.contour.points.size() - 1 ? 0 : id_after + 1;
//don't loop
if (id_after == id_nearest) {
id_after = id_nearest == contour.contour.points.size() - 1 ? 0 : id_nearest + 1;
point_after = id_nearest == contour.contour.points.size() - 1 ? contour.contour.points.front() : contour.contour.points[id_nearest + 1];
break;
}
}
//compute angle
angle = point_nearest.ccw_angle(point_before, point_after);
if (angle >= PI) angle = 2 * PI - angle; // smaller angle
//compute the diff from 90°
angle = abs(angle - PI / 2);
if (point_near.coincides_with(point_nearest) && max(nearest_dist, near_dist) + SCALED_EPSILON < point_nearest.distance_to(point_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(point_nearest.ccw_angle(point_before, point_after), point_nearest.ccw_angle(point_after, point_before));
angle2 = abs(angle - PI / 2);
angle = (angle + angle2) / 2;
}
return 1 - (angle / (PI / 2));
}
double
dot(Line l1, Line l2)
{
Vectorf v_1 = normalize(Vectorf(l1.b.x - l1.a.x, l1.b.y - l1.a.y));
Vectorf v_2 = normalize(Vectorf(l2.b.x - l2.a.x, l2.b.y - l2.a.y));
return v_1.x*v_2.x + v_1.y*v_2.y;
}
void
MedialAxis::fusion_curve(ThickPolylines &pp)
{
//fusion Y with only 1 '0' value => the "0" branch "pull" the cross-point
bool changes = false;
for (size_t i = 0; i < pp.size(); ++i) {
ThickPolyline& polyline = pp[i];
// only consider 2-point polyline with endpoint
if (polyline.points.size() != 2) continue;
if (polyline.endpoints.first) polyline.reverse();
else if (!polyline.endpoints.second) continue;
if (polyline.width.back() > EPSILON) continue;
//check my length is small
coord_t length = (coord_t)polyline.length();
if (length > max_width) continue;
size_t closest_point_idx = this->expolygon.contour.closest_point_index(polyline.points.back());
//check the 0-wodth point is on the contour.
if (closest_point_idx == (size_t)-1) continue;
size_t prev_idx = closest_point_idx == 0 ? this->expolygon.contour.points.size() - 1 : closest_point_idx - 1;
size_t next_idx = closest_point_idx == this->expolygon.contour.points.size() - 1 ? 0 : closest_point_idx + 1;
double mindot = 1;
mindot = min(mindot, abs(dot(Line(polyline.points[polyline.points.size() - 1], polyline.points[polyline.points.size() - 2]),
(Line(this->expolygon.contour.points[closest_point_idx], this->expolygon.contour.points[prev_idx])))));
mindot = min(mindot, abs(dot(Line(polyline.points[polyline.points.size() - 1], polyline.points[polyline.points.size() - 2]),
(Line(this->expolygon.contour.points[closest_point_idx], this->expolygon.contour.points[next_idx])))));
//compute angle
double coeff_contour_angle = this->expolygon.contour.points[closest_point_idx].ccw_angle(this->expolygon.contour.points[prev_idx], this->expolygon.contour.points[next_idx]);
if (coeff_contour_angle >= PI) coeff_contour_angle = 2 * PI - coeff_contour_angle; // smaller angle
//compute the diff from 90°
coeff_contour_angle = abs(coeff_contour_angle - PI / 2);
// look if other end is a cross point with almost 90° angle
double sum_dot = 0;
double min_dot = 0;
// look if other end is a cross point with multiple other branch
vector<size_t> crosspoint;
for (size_t j = 0; j < pp.size(); ++j) {
if (j == i) continue;
ThickPolyline& other = pp[j];
if (polyline.first_point().coincides_with(other.last_point())) {
other.reverse();
crosspoint.push_back(j);
double dot_temp = dot(Line(polyline.points[0], polyline.points[1]), (Line(other.points[0], other.points[1])));
min_dot = min(min_dot, abs(dot_temp));
sum_dot += dot_temp;
} else if (polyline.first_point().coincides_with(other.first_point())) {
crosspoint.push_back(j);
double dot_temp = dot(Line(polyline.points[0], polyline.points[1]), (Line(other.points[0], other.points[1])));
min_dot = min(min_dot, abs(dot_temp));
sum_dot += dot_temp;
}
}
//only consider very shallow angle for contour
if (mindot > 0.15 &&
(1 - (coeff_contour_angle / (PI / 2))) > 0.2) continue;
//check if it's a line that we can pull
if (crosspoint.size() != 2) continue;
if (sum_dot > 0.2) continue;
if (min_dot > 0.5) continue;
//don't pull, it distords the line if there are too many points.
//// pull it a bit, depends on my size, the dot?, and the coeff at my 0-end (~14% for a square, almost 0 for a gentle curve)
//coord_t length_pull = polyline.length();
//length_pull *= 0.144 * get_coeff_from_angle_countour(polyline.points.back(), this->expolygon, min(min_width, polyline.length() / 2));
////compute dir
//Vectorf pull_direction(polyline.points[1].x - polyline.points[0].x, polyline.points[1].y - polyline.points[0].y);
//pull_direction = normalize(pull_direction);
//pull_direction.x *= length_pull;
//pull_direction.y *= length_pull;
////pull the points
//Point &p1 = pp[crosspoint[0]].points[0];
//p1.x = p1.x + (coord_t)pull_direction.x;
//p1.y = p1.y + (coord_t)pull_direction.y;
//Point &p2 = pp[crosspoint[1]].points[0];
//p2.x = p2.x + (coord_t)pull_direction.x;
//p2.y = p2.y + (coord_t)pull_direction.y;
//delete the now unused polyline
pp.erase(pp.begin() + i);
--i;
changes = true;
}
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(); });
}
}
void
MedialAxis::fusion_corners(ThickPolylines &pp)
{
//fusion Y with only 1 '0' value => the "0" branch "pull" the cross-point
bool changes = false;
for (size_t i = 0; i < pp.size(); ++i) {
ThickPolyline& polyline = pp[i];
// only consider polyline with 0-end
if (polyline.points.size() != 2) continue;
if (polyline.endpoints.first) polyline.reverse();
else if (!polyline.endpoints.second) continue;
if (polyline.width.back() > 0) continue;
//check my length is small
coord_t length = polyline.length();
if (length > max_width) continue;
// look if other end is a cross point with multiple other branch
vector<size_t> crosspoint;
for (size_t j = 0; j < pp.size(); ++j) {
if (j == i) continue;
ThickPolyline& other = pp[j];
if (polyline.first_point().coincides_with(other.last_point())) {
other.reverse();
crosspoint.push_back(j);
} else if (polyline.first_point().coincides_with(other.first_point())) {
crosspoint.push_back(j);
}
}
//check if it's a line that we can pull
if (crosspoint.size() != 2) continue;
// check if i am at the external side of a curve
double angle1 = polyline.points[0].ccw_angle(polyline.points[1], pp[crosspoint[0]].points[1]);
if (angle1 >= PI) angle1 = 2 * PI - angle1; // smaller angle
double angle2 = polyline.points[0].ccw_angle(polyline.points[1], pp[crosspoint[1]].points[1]);
if (angle2 >= PI) angle2 = 2 * PI - angle2; // smaller angle
if (angle1 + angle2 < PI) continue;
//check if is smaller or the other ones are not endpoits
if (pp[crosspoint[0]].endpoints.second && length > pp[crosspoint[0]].length()) continue;
if (pp[crosspoint[1]].endpoints.second && length > pp[crosspoint[1]].length()) continue;
//FIXME: also pull (a bit less) points that are near to this one.
// if true, pull it a bit, depends on my size, the dot?, and the coeff at my 0-end (~14% for a square, almost 0 for a gentle curve)
coord_t length_pull = polyline.length();
length_pull *= 0.144 * get_coeff_from_angle_countour(polyline.points.back(), this->expolygon, min(min_width, polyline.length() / 2));
//compute dir
Vectorf pull_direction(polyline.points[1].x - polyline.points[0].x, polyline.points[1].y - polyline.points[0].y);
pull_direction = normalize(pull_direction);
pull_direction.x *= length_pull;
pull_direction.y *= length_pull;
//pull the points
Point &p1 = pp[crosspoint[0]].points[0];
p1.x = p1.x + pull_direction.x;
p1.y = p1.y + pull_direction.y;
Point &p2 = pp[crosspoint[1]].points[0];
p2.x = p2.x + pull_direction.x;
p2.y = p2.y + pull_direction.y;
//delete the now unused polyline
pp.erase(pp.begin() + i);
--i;
changes = true;
}
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(); });
}
}
void
MedialAxis::extends_line_both_side(ThickPolylines& pp) {
const ExPolygons anchors = offset2_ex(diff_ex(this->bounds, this->expolygon), -SCALED_RESOLUTION, SCALED_RESOLUTION);
for (size_t i = 0; i < pp.size(); ++i) {
ThickPolyline& polyline = pp[i];
this->extends_line(polyline, anchors, this->min_width);
polyline.reverse();
this->extends_line(polyline, anchors, this->min_width);
}
}
void
MedialAxis::extends_line(ThickPolyline& polyline, const ExPolygons& anchors, const coord_t join_width)
{
// 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
if (polyline.endpoints.second && !bounds.has_boundary_point(polyline.points.back())) {
size_t first_idx = polyline.points.size() - 2;
Line line(*(polyline.points.begin() + first_idx), polyline.points.back());
while (line.length() < SCALED_RESOLUTION && first_idx>0) {
first_idx--;
line.a = *(polyline.points.begin() + first_idx);
}
// prevent the line from touching on the other side, otherwise intersection() might return that solution
if (polyline.points.size() == 2 && this->expolygon.contains(line.midpoint())) line.a = line.midpoint();
line.extend_end(max_width);
Point new_back;
if (this->expolygon.contour.has_boundary_point(polyline.points.back())) {
new_back = polyline.points.back();
} else {
bool finded = this->expolygon.contour.first_intersection(line, &new_back);
//verify also for holes.
Point new_back_temp;
for (Polygon hole : this->expolygon.holes) {
if (hole.first_intersection(line, &new_back_temp)) {
if (!finded || line.a.distance_to(new_back_temp) < line.a.distance_to(new_back)) {
finded = true;
new_back = new_back_temp;
}
}
}
// safety check if no intersection
if (!finded) {
if (!this->expolygon.contains(line.b)) {
//it's outside!!!
if (!this->expolygon.contains(line.a)) {
std::cout << "Error, a line is formed that start outside a polygon, end outside of it and don't cross it!\n";
} else {
std::cout << "Error, a line is formed that start in a polygon, end outside of it and don't cross it!\n";
}
}
new_back = line.b;
}
polyline.points.push_back(new_back);
polyline.width.push_back(polyline.width.back());
}
Point new_bound;
bool finded = bounds.contour.first_intersection(line, &new_bound);
//verify also for holes.
Point new_bound_temp;
for (Polygon hole : bounds.holes) {
if (hole.first_intersection(line, &new_bound_temp)) {
if (!finded || line.a.distance_to(new_bound_temp) < line.a.distance_to(new_bound)) {
finded = true;
new_bound = new_bound_temp;
}
}
}
// safety check if no intersection
if (!finded) {
if (line.b.coincides_with_epsilon(polyline.points.back())) {
return;
}
//check if we don't over-shoot inside us
bool is_in_anchor = false;
for (const ExPolygon& a : anchors) {
if (a.contains(line.b)) {
is_in_anchor = true;
break;
}
}
if (!is_in_anchor) std::cout << "not in anchor:\n";
if (!is_in_anchor) return;
new_bound = line.b;
}
/* if (new_bound.coincides_with_epsilon(new_back)) {
return;
}*/
// find anchor
Point best_anchor;
double shortest_dist = max_width;
for (const ExPolygon& a : anchors) {
Point p_maybe_inside = a.contour.centroid();
double test_dist = new_bound.distance_to(p_maybe_inside) + new_back.distance_to(p_maybe_inside);
//if (test_dist < max_width / 2 && (test_dist < shortest_dist || shortest_dist < 0)) {
double angle_test = new_back.ccw_angle(p_maybe_inside, line.a);
if (angle_test > PI) angle_test = 2 * PI - angle_test;
if (test_dist < max_width && test_dist<shortest_dist && abs(angle_test) > PI / 2) {
shortest_dist = test_dist;
best_anchor = p_maybe_inside;
}
}
if (best_anchor.x != 0 && best_anchor.y != 0) {
Point p_obj = best_anchor + new_bound;
p_obj.x /= 2;
p_obj.y /= 2;
Line l2 = Line(new_back, p_obj);
l2.extend_end(max_width);
(void)bounds.contour.first_intersection(l2, &new_bound);
}
if (new_bound.coincides_with_epsilon(new_back)) {
return;
}
polyline.points.push_back(new_bound);
//polyline.width.push_back(join_width);
//it thickens the line a bit too early, imo
polyline.width.push_back(polyline.width.back());
}
}
void
MedialAxis::main_fusion(ThickPolylines& pp)
{
//int idf = 0;
bool changes = true;
map<Point, double> coeff_angle_cache;
while (changes) {
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) {
bool ahas0 = a.width.front() == 0 || a.width.back() == 0;
bool bhas0 = b.width.front() == 0 || b.width.back() == 0;
if (ahas0 && !bhas0) return true;
if (!ahas0 && bhas0) return false;
return a.length() < b.length();
});
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;
size_t 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) << "\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) 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->expolygon, min(min_width, polyline.length() / 2));
}
double coeffSizeOtherJ = 1;
if (other.width.back() == 0) {
coeffSizeOtherJ = 0.1 + 0.9*get_coeff_from_angle_countour(other.points.back(), this->expolygon, min(min_width, polyline.length() / 2));
}
//std::cout << " try2 : " << i << ":" << j << " : "
// << (abs(polyline.length()*coeffSizePolyI - other.length()*coeffSizeOtherJ) > max_width / 2)
// << (abs(polyline.length()*coeffSizePolyI - other.length()*coeffSizeOtherJ) > max_width)
// << "\n";
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).
//we need to add how strait we are from our main.
float test_dot = dot(polyline.lines().front(), other.lines().front());
// 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;
size_t biggest_main_branch_id = 0;
coord_t 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() && (polyline.width.back() != 0 || pp[biggest_main_branch_id].width.back() ==0))
|| (pp[biggest_main_branch_id].length() < other.length() && (other.width.back() != 0 || pp[biggest_main_branch_id].width.back() == 0)))) {
//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)
dot_poly_branch = -dot(Line(polyline.points[0], polyline.points[1]), Line(pp[biggest_main_branch_id].points[0], pp[biggest_main_branch_id].points[1]));
dot_candidate_branch = -dot(Line(other.points[0], other.points[1]), Line(pp[biggest_main_branch_id].points[0], pp[biggest_main_branch_id].points[1]));
if (dot_poly_branch < 0) dot_poly_branch = 0;
if (dot_candidate_branch < 0) dot_candidate_branch = 0;
if (pp[biggest_main_branch_id].width.back()>0)
test_dot += 2 * dot_poly_branch ;
}
//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) (or they are both with 0-width end)
if (dot_poly_branch < 0.1 || dot_candidate_branch < 0.1 ||
(
((polyline.length()>other.length() ? polyline.length() / other.length() : other.length() / polyline.length()) > 4)
&& !(polyline.width.back() == 0 && other.width.back()==0)
) ){
continue;
}
if (test_dot > best_dot) {
best_candidate = &other;
best_idx = j;
best_dot = test_dot;
}
}
if (best_candidate != nullptr) {
//idf++;
//std::cout << " == fusion " << id <<" : "<< idf << " ==\n";
// 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 = (coeff_angle_cache.find(polyline.points.back()) != coeff_angle_cache.end())
? coeff_angle_cache[polyline.points.back()]
: (get_coeff_from_angle_countour(polyline.points.back(), this->expolygon, min(min_width, polyline.length() / 2)));
const double coeff_angle_candi = (coeff_angle_cache.find(best_candidate->points.back()) != coeff_angle_cache.end())
? coeff_angle_cache[best_candidate->points.back()]
: (get_coeff_from_angle_countour(best_candidate->points.back(), this->expolygon, min(min_width, best_candidate->length() / 2)));
//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.
//std::cout << " max(polyline.length(), best_candidate->length())=" << max(polyline.length(), best_candidate->length())
// << ", polyline.length()=" << polyline.length()
// << ", best_candidate->length()=" << best_candidate->length()
// << ", polyline.length() / max=" << (polyline.length() / max(polyline.length(), best_candidate->length()))
// << ", best_candidate->length() / max=" << (best_candidate->length() / max(polyline.length(), best_candidate->length()))
// << "\n";
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;
//std::cout << "coeff_angle_poly=" << coeff_angle_poly
// << ", coeff_angle_candi=" << coeff_angle_candi
// << ", weight_poly=" << (2 - (polyline.length() / max(polyline.length(), best_candidate->length())))
// << ", weight_candi=" << (2 - (best_candidate->length() / max(polyline.length(), best_candidate->length())))
// << ", sumpoly=" << weight_poly
// << ", sumcandi=" << weight_candi
// << ", dot_poly_branch=" << dot_poly_branch
// << ", dot_candidate_branch=" << dot_candidate_branch
// << ", coeff_poly=" << coeff_poly
// << ", coeff_candi=" << coeff_candi
// << "\n";
//iterate the points
// as voronoi should create symetric thing, we can iterate synchonously
size_t 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;
//std::cout << "width:" << polyline.width[idx_point] << " = " << value_from_current_width << " + " << value_from_dist
// << " (<" << max_width << " && " << (bounds.contour.closest_point(polyline.points[idx_point])->distance_to(polyline.points[idx_point]) * 2.1)<<")\n";
//failsafes
if (polyline.width[idx_point] > max_width)
polyline.width[idx_point] = max_width;
const coord_t max_width_contour = bounds.contour.closest_point(polyline.points[idx_point])->distance_to(polyline.points[idx_point]) * 2.1;
if (polyline.width[idx_point] > max_width_contour)
polyline.width[idx_point] = max_width_contour;
++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 (size_t 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 occur
polyline.endpoints.second &= best_candidate->endpoints.second;
}
} else {
//select if an end occur
polyline.endpoints.second &= best_candidate->endpoints.second;
}
//remove points that are the same or too close each other, ie simplify
for (size_t 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 (size_t 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;
}
}
//update cache
coeff_angle_cache[polyline.points.back()] = coeff_angle_poly * coeff_poly + coeff_angle_candi * coeff_candi;
if (polyline.points.size() < 2) {
//remove self
pp.erase(pp.begin() + i);
--i;
--best_idx;
}
pp.erase(pp.begin() + best_idx);
//{
// stringstream stri;
// stri << "medial_axis_2.0_aft_fus_" << id << "_" << idf << ".svg";
// SVG svg(stri.str());
// svg.draw(bounds);
// svg.draw(this->expolygon);
// svg.draw(pp);
// svg.Close();
//}
changes = true;
break;
}
}
}
}
void
MedialAxis::remove_too_thin_extrusion(ThickPolylines& pp)
{
// remove too thin extrusion at start & end of polylines
bool 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() < this->min_width && polyline.endpoints.first) {
//try to split if possible
if (polyline.width[1] > min_width) {
double percent_can_keep = 1 - (min_width - polyline.width[0]) / (polyline.width[1] - polyline.width[0]);
if (polyline.points.front().distance_to(polyline.points[1]) * percent_can_keep > SCALED_RESOLUTION) {
//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) * (1 - percent_can_keep));
polyline.points.front().y = polyline.points.front().y +
(coord_t)((polyline.points[1].y - polyline.points.front().y) * (1 - percent_can_keep));
polyline.width.front() = min_width;
} else {
/// almost 0-length, Remove
polyline.points.erase(polyline.points.begin());
polyline.width.erase(polyline.width.begin());
}
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() < this->min_width && polyline.endpoints.second) {
//try to split if possible
if (polyline.width[polyline.points.size() - 2] > min_width) {
double percent_can_keep = 1 - (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 > SCALED_RESOLUTION) {
//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) * (1 - percent_can_keep));
polyline.points.back().y = polyline.points.back().y +
(coord_t)((polyline.points[polyline.points.size() - 2].y - polyline.points.back().y) * (1 - percent_can_keep));
polyline.width.back() = min_width;
} else {
/// almost 0-length, Remove
polyline.points.erase(polyline.points.end() - 1);
polyline.width.erase(polyline.width.end() - 1);
}
changes = true;
break;
}
polyline.points.erase(polyline.points.end() - 1);
polyline.width.erase(polyline.width.end() - 1);
changes = true;
}
//remove points and bits that comes from a "main line"
if (polyline.points.size() < 2 || (changes && polyline.length() < max_width && polyline.points.size() ==2)) {
//remove self if too small
pp.erase(pp.begin() + i);
--i;
}
}
if (changes) concatThickPolylines(pp);
}
void
MedialAxis::concatenate_polylines_with_crossing(ThickPolylines& pp)
{
// 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.
*/
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;
size_t best_idx = 0;
// find another polyline starting here
for (size_t j = 0; j < pp.size(); ++j) {
if (j == i) continue;
ThickPolyline& other = pp[j];
if (other.endpoints.first && other.endpoints.second) continue;
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());
if (best_idx < i) i--;
pp.erase(pp.begin() + best_idx);
}
}
}
void
MedialAxis::remove_too_thin_points(ThickPolylines& 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;
}
}
}
}
void
MedialAxis::remove_too_short_polylines(ThickPolylines& pp, const coord_t min_size)
{
//remove too short polyline
bool changes = true;
while (changes) {
changes = false;
double shortest_size = min_size;
size_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 < pp.size()) {
pp.erase(pp.begin() + shortest_idx);
changes = true;
}
if (changes) concatThickPolylines(pp);
}
}
void
MedialAxis::ensure_not_overextrude(ThickPolylines& pp)
{
//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 (const Polygon &hole : bounds.holes) {
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 (coordf_t &width : polyline.width) {
width *= reduce_by;
width *= reduce_by;
}
}
}
}
ExPolygon
MedialAxis::simplify_polygon_frontier()
{
//simplify the boundary between us and the bounds.
//it will remove every point in the surface contour that aren't on the bounds contour
ExPolygon simplified_poly = this->surface;
if (&this->surface != &this->bounds) {
bool need_intersect = false;
for (size_t i = 0; i < simplified_poly.contour.points.size(); i++) {
Point &p_check = simplified_poly.contour.points[i];
//if (!find) {
if (!bounds.has_boundary_point(p_check)) {
//check if we put it at a bound point instead of delete it
size_t prev_i = i == 0 ? simplified_poly.contour.points.size() - 1 : (i - 1);
size_t next_i = i == simplified_poly.contour.points.size() - 1 ? 0 : (i + 1);
const Point* closest = bounds.contour.closest_point(p_check);
if (closest != nullptr && closest->distance_to(p_check) + SCALED_EPSILON
< min(p_check.distance_to(simplified_poly.contour.points[prev_i]), p_check.distance_to(simplified_poly.contour.points[next_i])) / 2) {
p_check.x = closest->x;
p_check.y = closest->y;
need_intersect = true;
} else {
simplified_poly.contour.points.erase(simplified_poly.contour.points.begin() + i);
i--;
}
}
}
if (need_intersect) {
ExPolygons simplified_polys = intersection_ex(simplified_poly, bounds);
if (simplified_polys.size() == 1) {
simplified_poly = simplified_polys[0];
} else {
simplified_poly = this->surface;
}
}
}
if (!simplified_poly.contour.points.empty())
simplified_poly.remove_point_too_near(SCALED_RESOLUTION);
return simplified_poly;
}
void
MedialAxis::build(ThickPolylines* polylines_out)
{
this->id++;
//std::cout << layerid << "\n";
//{
// stringstream stri;
// stri << "medial_axis_0_enter_" << id << ".svg";
// SVG svg(stri.str());
// svg.draw(this->surface);
// svg.Close();
//}
this->expolygon = simplify_polygon_frontier();
//{
// stringstream stri;
// stri << "medial_axis_0.5_simplified_" << id << ".svg";
// SVG svg(stri.str());
// svg.draw(bounds);
// svg.draw(this->expolygon);
// svg.Close();
//}
//safety check
if (this->expolygon.area() < this->min_width * this->min_width) this->expolygon = this->surface;
if (this->expolygon.area() < this->min_width * this->min_width) return;
//std::cout << "simplify_polygon_frontier\n";
// compute the Voronoi diagram and extract medial axis polylines
ThickPolylines pp;
this->polyline_from_voronoi(this->expolygon.lines(), &pp);
concatThickPolylines(pp);
//std::cout << "concatThickPolylines\n";
//{
// stringstream stri;
// stri << "medial_axis_1_voronoi_" << id << ".svg";
// SVG svg(stri.str());
// svg.draw(bounds);
// svg.draw(this->expolygon);
// 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()));
fusion_curve(pp);
//{
// stringstream stri;
// stri << "medial_axis_2_curve_" << id << ".svg";
// SVG svg(stri.str());
// svg.draw(bounds);
// svg.draw(this->expolygon);
// svg.draw(pp);
// svg.Close();
//}
// 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.
//
main_fusion(pp);
//{
// stringstream stri;
// stri << "medial_axis_3_fusion_" << id << ".svg";
// SVG svg(stri.str());
// svg.draw(bounds);
// svg.draw(this->expolygon);
// svg.draw(pp);
// svg.Close();
//}
//fusion right-angle corners.
fusion_corners(pp);
if (stop_at_min_width) {
extends_line_both_side(pp);
}
//reduce extrusion when it's too thin to be printable
remove_too_thin_extrusion(pp);
//{
// stringstream stri;
// stri << "medial_axis_4_thinok_" << id << ".svg";
// SVG svg(stri.str());
// svg.draw(bounds);
// svg.draw(this->expolygon);
// svg.draw(pp);
// svg.Close();
//}
remove_too_thin_points(pp);
//{
// stringstream stri;
// stri << "medial_axis_5.0_thuinner_" << id << ".svg";
// SVG svg(stri.str());
// svg.draw(bounds);
// svg.draw(this->expolygon);
// svg.draw(pp);
// svg.Close();
//}
// Loop through all returned polylines in order to extend their endpoints to the
// expolygon boundaries
if (!stop_at_min_width) {
extends_line_both_side(pp);
}
//{
// stringstream stri;
// stri << "medial_axis_5_expand_" << id << ".svg";
// SVG svg(stri.str());
// svg.draw(bounds);
// svg.draw(this->expolygon);
// svg.draw(pp);
// svg.Close();
//}
concatenate_polylines_with_crossing(pp);
//{
// stringstream stri;
// stri << "medial_axis_6_concat_" << id << ".svg";
// SVG svg(stri.str());
// svg.draw(bounds);
// svg.draw(this->expolygon);
// svg.draw(pp);
// svg.Close();
//}
remove_too_short_polylines(pp, max_w * 2);
//{
// stringstream stri;
// stri << "medial_axis_8_tooshort_" << id << ".svg";
// SVG svg(stri.str());
// svg.draw(bounds);
// svg.draw(this->expolygon);
// svg.draw(pp);
// svg.Close();
//}
//TODO: reduce the flow at the intersection ( + ) points ?
ensure_not_overextrude(pp);
//{
// stringstream stri;
// stri << "medial_axis_9_endn_" << id << ".svg";
// SVG svg(stri.str());
// svg.draw(bounds);
// svg.draw(this->expolygon);
// svg.draw(pp);
// svg.Close();
//}
polylines_out->insert(polylines_out->end(), pp.begin(), pp.end());
}
ExtrusionEntityCollection thin_variable_width(const ThickPolylines &polylines, ExtrusionRole role, Flow flow) {
// 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
const double tolerance = scale_(0.05);
int id_line = 0;
ExtrusionEntityCollection coll;
for (const ThickPolyline &p : polylines) {
id_line++;
ExtrusionPaths paths;
ExtrusionPath path(role);
ThickLines lines = p.thicklines();
for (int i = 0; i < (int)lines.size(); ++i) {
const ThickLine& line = lines[i];
const coordf_t line_len = line.length();
if (line_len < SCALED_EPSILON) continue;
double thickness_delta = fabs(line.a_width - line.b_width);
if (thickness_delta > tolerance) {
const unsigned short segments = ceil(thickness_delta / tolerance);
const coordf_t seg_len = line_len / segments;
Points pp;
std::vector<coordf_t> width;
{
pp.push_back(line.a);
width.push_back(line.a_width);
for (size_t j = 1; j < segments; ++j) {
pp.push_back(line.point_at(j*seg_len));
coordf_t w = line.a_width + (j*seg_len) * (line.b_width - line.a_width) / line_len;
width.push_back(w);
width.push_back(w);
}
pp.push_back(line.b);
width.push_back(line.b_width);
assert(pp.size() == segments + 1);
assert(width.size() == segments * 2);
}
// delete this line and insert new ones
lines.erase(lines.begin() + i);
for (size_t j = 0; j < segments; ++j) {
ThickLine new_line(pp[j], pp[j + 1]);
new_line.a_width = width[2 * j];
new_line.b_width = width[2 * j + 1];
lines.insert(lines.begin() + i + j, new_line);
}
--i;
continue;
}
const double w = fmax(line.a_width, line.b_width);
if (path.polyline.points.empty()) {
path.polyline.append(line.a);
path.polyline.append(line.b);
// Convert from spacing to extrusion width based on the extrusion model
// of a square extrusion ended with semi circles.
flow.width = unscale(w) + flow.height * (1. - 0.25 * PI);
#ifdef SLIC3R_DEBUG
printf(" filling %f gap\n", flow.width);
#endif
path.mm3_per_mm = flow.mm3_per_mm();
path.width = flow.width;
path.height = flow.height;
} else {
thickness_delta = fabs(scale_(flow.width) - w);
if (thickness_delta <= tolerance / 2) {
// the width difference between this line and the current flow width is
// within the accepted tolerance
path.polyline.append(line.b);
} else {
// we need to initialize a new line
paths.emplace_back(std::move(path));
path = ExtrusionPath(role);
--i;
}
}
}
if (path.polyline.is_valid())
paths.emplace_back(std::move(path));
// Append paths to collection.
if (!paths.empty()) {
if (paths.front().first_point().coincides_with(paths.back().last_point())) {
coll.append(ExtrusionLoop(paths));
} else {
//not a loop : avoid to "sort" it.
ExtrusionEntityCollection unsortable_coll(paths);
unsortable_coll.no_sort = true;
coll.append(unsortable_coll);
}
}
}
return coll;
}
} // namespace Slic3r
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