#include "BoundingBox.hpp" #include "ExPolygon.hpp" #include "Exception.hpp" #include "Geometry.hpp" #include "Polygon.hpp" #include "Line.hpp" #include "ClipperUtils.hpp" #include "SVG.hpp" #include "polypartition.h" #include "poly2tri/poly2tri.h" #include #include #include 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 (Polygon &hole : holes) hole.scale(factor); } void ExPolygon::translate(const Point &p) { contour.translate(p); for (Polygon &hole : holes) hole.translate(p); } void ExPolygon::rotate(double angle) { contour.rotate(angle); for (Polygon &hole : holes) hole.rotate(angle); } void ExPolygon::rotate(double angle, const Point ¢er) { contour.rotate(angle, center); for (Polygon &hole : holes) hole.rotate(angle, center); } double ExPolygon::area() const { double a = this->contour.area(); for (const Polygon &hole : holes) a -= - hole.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.a, line.b)); } 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)); } void ExPolygon::medial_axis(double max_width, double min_width, ThickPolylines* polylines) 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); /* SVG svg("medial_axis.svg"); 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())); /* Loop through all returned polylines in order to extend their endpoints to the expolygon boundaries */ bool removed = false; 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 && !this->has_boundary_point(new_front)) { Vec2d p1 = polyline.points.front().cast(); Vec2d p2 = polyline.points[1].cast(); // prevent the line from touching on the other side, otherwise intersection() might return that solution if (polyline.points.size() == 2) p2 = (p1 + p2) * 0.5; // Extend the start of the segment. p1 -= (p2 - p1).normalized() * max_width; this->contour.intersection(Line(p1.cast(), p2.cast()), &new_front); } if (polyline.endpoints.second && !this->has_boundary_point(new_back)) { Vec2d p1 = (polyline.points.end() - 2)->cast(); Vec2d p2 = polyline.points.back().cast(); // prevent the line from touching on the other side, otherwise intersection() might return that solution if (polyline.points.size() == 2) p1 = (p1 + p2) * 0.5; // Extend the start of the segment. p2 += (p2 - p1).normalized() * max_width; this->contour.intersection(Line(p1.cast(), p2.cast()), &new_back); } polyline.points.front() = new_front; polyline.points.back() = new_back; /* remove too short polylines (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_w*2) { pp.erase(pp.begin() + i); --i; removed = true; continue; } } /* 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. */ if (removed) { for (size_t i = 0; i < pp.size(); ++i) { ThickPolyline& polyline = pp[i]; if (polyline.endpoints.first && polyline.endpoints.second) continue; // optimization // find another polyline starting here for (size_t j = i+1; j < pp.size(); ++j) { ThickPolyline& other = pp[j]; if (polyline.last_point() == other.last_point()) { other.reverse(); } else if (polyline.first_point() == other.last_point()) { polyline.reverse(); other.reverse(); } else if (polyline.first_point() == other.first_point()) { polyline.reverse(); } else if (polyline.last_point() != other.first_point()) { continue; } polyline.points.insert(polyline.points.end(), other.points.begin() + 1, other.points.end()); polyline.width.insert(polyline.width.end(), other.width.begin(), other.width.end()); polyline.endpoints.second = other.endpoints.second; assert(polyline.width.size() == polyline.points.size()*2 - 2); pp.erase(pp.begin() + j); j = i; // restart search from i+1 } } } 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(max_width, min_width, &tp); 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 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::const_iterator x = xx.begin(); x != xx.end()-1; ++x) { coord_t next_x = *(x + 1); if (*x != next_x) // intersect with rectangle // append results to return value polygons_append(*polygons, intersection({ { { *x, bb.min.y() }, { next_x, bb.min.y() }, { next_x, bb.max.y() }, { *x, bb.max.y() } } }, 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)); } // 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 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("%zu\n0\n", ex->contour.points.size()); for (const Point &point : ex->contour.points) { size_t i = &point - &ex->contour.points.front(); p[i].x = point(0); p[i].y = point(1); //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("%zu\n1\n", hole->points.size()); for (const Point &point : hole->points) { size_t i = &point - &hole->points.front(); p[i].x = point(0); p[i].y = point(1); //printf("%ld %ld\n", point->x(), point->y()); } p.SetHole(true); input.push_back(p); } } // perform triangulation std::list output; int res = TPPLPartition().Triangulate_MONO(&input, &output); if (res != 1) throw Slic3r::RuntimeError("Triangulation failed"); // convert output polygons for (std::list::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](0) = coord_t((*poly)[i].x); p.points[i](1) = coord_t((*poly)[i].y); } polygons->push_back(p); } } */ std::list expoly_to_polypartition_input(const ExPolygon &ex) { std::list input; // contour { input.emplace_back(); TPPLPoly &p = input.back(); p.Init(int(ex.contour.points.size())); for (const Point &point : ex.contour.points) { size_t i = &point - &ex.contour.points.front(); p[i].x = point(0); p[i].y = point(1); } p.SetHole(false); } // holes for (const Polygon &hole : ex.holes) { input.emplace_back(); TPPLPoly &p = input.back(); p.Init(hole.points.size()); for (const Point &point : hole.points) { size_t i = &point - &hole.points.front(); p[i].x = point(0); p[i].y = point(1); } p.SetHole(true); } return input; } std::list expoly_to_polypartition_input(const ExPolygons &expps) { std::list input; for (const ExPolygon &ex : expps) { // contour { input.emplace_back(); TPPLPoly &p = input.back(); p.Init(int(ex.contour.points.size())); for (const Point &point : ex.contour.points) { size_t i = &point - &ex.contour.points.front(); p[i].x = point(0); p[i].y = point(1); } p.SetHole(false); } // holes for (const Polygon &hole : ex.holes) { input.emplace_back(); TPPLPoly &p = input.back(); p.Init(hole.points.size()); for (const Point &point : hole.points) { size_t i = &point - &hole.points.front(); p[i].x = point(0); p[i].y = point(1); } p.SetHole(true); } } return input; } std::vector polypartition_output_to_triangles(const std::list &output) { size_t num_triangles = 0; for (const TPPLPoly &poly : output) if (poly.GetNumPoints() >= 3) num_triangles += (size_t)poly.GetNumPoints() - 2; std::vector triangles; triangles.reserve(triangles.size() + num_triangles * 3); for (const TPPLPoly &poly : output) { long num_points = poly.GetNumPoints(); if (num_points >= 3) { const TPPLPoint *pt0 = &poly[0]; const TPPLPoint *pt1 = nullptr; const TPPLPoint *pt2 = &poly[1]; for (long i = 2; i < num_points; ++ i) { pt1 = pt2; pt2 = &poly[i]; triangles.emplace_back(coord_t(pt0->x), coord_t(pt0->y)); triangles.emplace_back(coord_t(pt1->x), coord_t(pt1->y)); triangles.emplace_back(coord_t(pt2->x), coord_t(pt2->y)); } } } return triangles; } void ExPolygon::triangulate_pp(Points *triangles) const { ExPolygons expp = union_ex(simplify_polygons(to_polygons(*this), true)); std::list input = expoly_to_polypartition_input(expp); // perform triangulation std::list output; int res = TPPLPartition().Triangulate_MONO(&input, &output); // int TPPLPartition::Triangulate_EC(TPPLPolyList *inpolys, TPPLPolyList *triangles) { if (res != 1) throw Slic3r::RuntimeError("Triangulation failed"); *triangles = polypartition_output_to_triangles(output); } // Uses the Poly2tri library maintained by Jan Niklas Hasse @jhasse // https://github.com/jhasse/poly2tri // See https://github.com/jhasse/poly2tri/blob/master/README.md for the limitations of the library! // No duplicate points are allowed, no very close points, holes must not touch outer contour etc. 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 ContourPoints; for (const Point &pt : ex->contour.points) // We should delete each p2t::Point object ContourPoints.push_back(new p2t::Point(pt(0), pt(1))); p2t::CDT cdt(ContourPoints); // holes for (Polygons::const_iterator hole = ex->holes.begin(); hole != ex->holes.end(); ++hole) { std::vector points; for (const Point &pt : hole->points) // will be destructed in SweepContext::~SweepContext points.push_back(new p2t::Point(pt(0), pt(1))); cdt.AddHole(points); } // perform triangulation try { cdt.Triangulate(); std::vector triangles = cdt.GetTriangles(); for (std::vector::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); } } catch (const Slic3r::RuntimeError & /* err */) { assert(false); // just ignore, don't triangulate } for (p2t::Point *ptr : ContourPoints) delete ptr; } } 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; } 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 get_extents_vector(const ExPolygons &polygons) { std::vector 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); } void keep_largest_contour_only(ExPolygons &polygons) { if (polygons.size() > 1) { double max_area = 0.; ExPolygon* max_area_polygon = nullptr; for (ExPolygon& p : polygons) { double a = p.contour.area(); if (a > max_area) { max_area = a; max_area_polygon = &p; } } assert(max_area_polygon != nullptr); ExPolygon p(std::move(*max_area_polygon)); polygons.clear(); polygons.emplace_back(std::move(p)); } } } // namespace Slic3r