686 lines
22 KiB
C++
686 lines
22 KiB
C++
#include "BoundingBox.hpp"
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#include "ClipperUtils.hpp"
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#include "Exception.hpp"
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#include "Polygon.hpp"
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#include "Polyline.hpp"
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namespace Slic3r {
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double Polygon::length() const
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{
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double l = 0;
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if (this->points.size() > 1) {
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l = (this->points.back() - this->points.front()).cast<double>().norm();
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for (size_t i = 1; i < this->points.size(); ++ i)
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l += (this->points[i] - this->points[i - 1]).cast<double>().norm();
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}
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return l;
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}
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Lines Polygon::lines() const
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{
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return to_lines(*this);
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}
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Polyline Polygon::split_at_vertex(const Point &point) const
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{
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// find index of point
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for (const Point &pt : this->points)
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if (pt == point)
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return this->split_at_index(int(&pt - &this->points.front()));
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throw Slic3r::InvalidArgument("Point not found");
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return Polyline();
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}
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// Split a closed polygon into an open polyline, with the split point duplicated at both ends.
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Polyline Polygon::split_at_index(int index) const
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{
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Polyline polyline;
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polyline.points.reserve(this->points.size() + 1);
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for (Points::const_iterator it = this->points.begin() + index; it != this->points.end(); ++it)
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polyline.points.push_back(*it);
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for (Points::const_iterator it = this->points.begin(); it != this->points.begin() + index + 1; ++it)
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polyline.points.push_back(*it);
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return polyline;
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}
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double Polygon::area(const Points &points)
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{
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double a = 0.;
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if (points.size() >= 3) {
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Vec2d p1 = points.back().cast<double>();
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for (const Point &p : points) {
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Vec2d p2 = p.cast<double>();
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a += cross2(p1, p2);
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p1 = p2;
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}
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}
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return 0.5 * a;
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}
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double Polygon::area() const
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{
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return Polygon::area(points);
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}
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bool Polygon::is_counter_clockwise() const
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{
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return ClipperLib::Orientation(this->points);
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}
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bool Polygon::is_clockwise() const
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{
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return !this->is_counter_clockwise();
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}
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bool Polygon::make_counter_clockwise()
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{
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if (!this->is_counter_clockwise()) {
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this->reverse();
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return true;
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}
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return false;
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}
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bool Polygon::make_clockwise()
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{
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if (this->is_counter_clockwise()) {
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this->reverse();
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return true;
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}
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return false;
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}
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void Polygon::douglas_peucker(double tolerance)
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{
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this->points.push_back(this->points.front());
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Points p = MultiPoint::_douglas_peucker(this->points, tolerance);
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p.pop_back();
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this->points = std::move(p);
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}
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Polygons Polygon::simplify(double tolerance) const
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{
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// Works on CCW polygons only, CW contour will be reoriented to CCW by Clipper's simplify_polygons()!
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assert(this->is_counter_clockwise());
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// repeat first point at the end in order to apply Douglas-Peucker
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// on the whole polygon
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Points points = this->points;
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points.push_back(points.front());
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Polygon p(MultiPoint::_douglas_peucker(points, tolerance));
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p.points.pop_back();
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Polygons pp;
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pp.push_back(p);
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return simplify_polygons(pp);
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}
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// Only call this on convex polygons or it will return invalid results
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void Polygon::triangulate_convex(Polygons* polygons) const
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{
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for (Points::const_iterator it = this->points.begin() + 2; it != this->points.end(); ++it) {
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Polygon p;
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p.points.reserve(3);
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p.points.push_back(this->points.front());
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p.points.push_back(*(it-1));
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p.points.push_back(*it);
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// this should be replaced with a more efficient call to a merge_collinear_segments() method
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if (p.area() > 0) polygons->push_back(p);
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}
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}
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// center of mass
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// source: https://en.wikipedia.org/wiki/Centroid
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Point Polygon::centroid() const
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{
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double area_sum = 0.;
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Vec2d c(0., 0.);
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if (points.size() >= 3) {
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Vec2d p1 = points.back().cast<double>();
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for (const Point &p : points) {
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Vec2d p2 = p.cast<double>();
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double a = cross2(p1, p2);
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area_sum += a;
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c += (p1 + p2) * a;
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p1 = p2;
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}
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}
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return Point(Vec2d(c / (3. * area_sum)));
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}
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bool Polygon::intersection(const Line &line, Point *intersection) const
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{
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if (this->points.size() < 2)
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return false;
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if (Line(this->points.front(), this->points.back()).intersection(line, intersection))
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return true;
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for (size_t i = 1; i < this->points.size(); ++ i)
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if (Line(this->points[i - 1], this->points[i]).intersection(line, intersection))
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return true;
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return false;
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}
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bool Polygon::first_intersection(const Line& line, Point* intersection) const
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{
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if (this->points.size() < 2)
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return false;
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bool found = false;
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double dmin = 0.;
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Line l(this->points.back(), this->points.front());
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for (size_t i = 0; i < this->points.size(); ++ i) {
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l.b = this->points[i];
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Point ip;
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if (l.intersection(line, &ip)) {
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if (! found) {
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found = true;
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dmin = (line.a - ip).cast<double>().squaredNorm();
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*intersection = ip;
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} else {
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double d = (line.a - ip).cast<double>().squaredNorm();
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if (d < dmin) {
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dmin = d;
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*intersection = ip;
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}
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}
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}
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l.a = l.b;
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}
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return found;
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}
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bool Polygon::intersections(const Line &line, Points *intersections) const
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{
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if (this->points.size() < 2)
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return false;
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size_t intersections_size = intersections->size();
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Line l(this->points.back(), this->points.front());
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for (size_t i = 0; i < this->points.size(); ++ i) {
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l.b = this->points[i];
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Point intersection;
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if (l.intersection(line, &intersection))
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intersections->emplace_back(std::move(intersection));
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l.a = l.b;
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}
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return intersections->size() > intersections_size;
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}
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bool Polygon::overlaps(const Polygons& other) const
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{
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if (this->empty() || other.empty())
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return false;
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Polylines pl_out = intersection_pl(to_polylines(other), *this);
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// See unit test SCENARIO("Clipper diff with polyline", "[Clipper]")
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// for in which case the intersection_pl produces any intersection.
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return !pl_out.empty() ||
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// If *this is completely inside other, then pl_out is empty, but the expolygons overlap. Test for that situation.
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std::any_of(other.begin(), other.end(), [this](auto& poly) {return poly.contains(this->points.front()); });
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}
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// Filter points from poly to the output with the help of FilterFn.
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// filter function receives two vectors:
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// v1: this_point - previous_point
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// v2: next_point - this_point
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// and returns true if the point is to be copied to the output.
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template<typename FilterFn>
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Points filter_points_by_vectors(const Points &poly, FilterFn filter)
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{
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// Last point is the first point visited.
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Point p1 = poly.back();
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// Previous vector to p1.
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Vec2d v1 = (p1 - *(poly.end() - 2)).cast<double>();
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Points out;
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for (Point p2 : poly) {
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// p2 is next point to the currently visited point p1.
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Vec2d v2 = (p2 - p1).cast<double>();
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if (filter(v1, v2))
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out.emplace_back(p2);
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v1 = v2;
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p1 = p2;
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}
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return out;
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}
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template<typename ConvexConcaveFilterFn>
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Points filter_convex_concave_points_by_angle_threshold(const Points &poly, double angle_threshold, ConvexConcaveFilterFn convex_concave_filter)
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{
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assert(angle_threshold >= 0.);
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if (angle_threshold < EPSILON) {
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double cos_angle = cos(angle_threshold);
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return filter_points_by_vectors(poly, [convex_concave_filter, cos_angle](const Vec2d &v1, const Vec2d &v2){
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return convex_concave_filter(v1, v2) && v1.normalized().dot(v2.normalized()) < cos_angle;
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});
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} else {
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return filter_points_by_vectors(poly, [convex_concave_filter](const Vec2d &v1, const Vec2d &v2){
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return convex_concave_filter(v1, v2);
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});
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}
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}
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Points Polygon::convex_points(double angle_threshold) const
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{
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return filter_convex_concave_points_by_angle_threshold(this->points, angle_threshold, [](const Vec2d &v1, const Vec2d &v2){ return cross2(v1, v2) > 0.; });
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}
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Points Polygon::concave_points(double angle_threshold) const
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{
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return filter_convex_concave_points_by_angle_threshold(this->points, angle_threshold, [](const Vec2d &v1, const Vec2d &v2){ return cross2(v1, v2) < 0.; });
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}
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// Projection of a point onto the polygon.
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Point Polygon::point_projection(const Point &point) const
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{
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Point proj = point;
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double dmin = std::numeric_limits<double>::max();
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if (! this->points.empty()) {
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for (size_t i = 0; i < this->points.size(); ++ i) {
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const Point &pt0 = this->points[i];
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const Point &pt1 = this->points[(i + 1 == this->points.size()) ? 0 : i + 1];
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double d = (point - pt0).cast<double>().norm();
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if (d < dmin) {
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dmin = d;
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proj = pt0;
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}
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d = (point - pt1).cast<double>().norm();
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if (d < dmin) {
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dmin = d;
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proj = pt1;
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}
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Vec2d v1(coordf_t(pt1(0) - pt0(0)), coordf_t(pt1(1) - pt0(1)));
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coordf_t div = v1.squaredNorm();
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if (div > 0.) {
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Vec2d v2(coordf_t(point(0) - pt0(0)), coordf_t(point(1) - pt0(1)));
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coordf_t t = v1.dot(v2) / div;
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if (t > 0. && t < 1.) {
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Point foot(coord_t(floor(coordf_t(pt0(0)) + t * v1(0) + 0.5)), coord_t(floor(coordf_t(pt0(1)) + t * v1(1) + 0.5)));
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d = (point - foot).cast<double>().norm();
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if (d < dmin) {
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dmin = d;
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proj = foot;
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}
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}
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}
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}
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}
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return proj;
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}
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std::vector<float> Polygon::parameter_by_length() const
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{
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// Parametrize the polygon by its length.
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std::vector<float> lengths(points.size()+1, 0.);
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for (size_t i = 1; i < points.size(); ++ i)
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lengths[i] = lengths[i-1] + (points[i] - points[i-1]).cast<float>().norm();
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lengths.back() = lengths[lengths.size()-2] + (points.front() - points.back()).cast<float>().norm();
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return lengths;
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}
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void Polygon::densify(float min_length, std::vector<float>* lengths_ptr)
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{
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std::vector<float> lengths_local;
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std::vector<float>& lengths = lengths_ptr ? *lengths_ptr : lengths_local;
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if (! lengths_ptr) {
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// Length parametrization has not been provided. Calculate our own.
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lengths = this->parameter_by_length();
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}
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assert(points.size() == lengths.size() - 1);
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for (size_t j=1; j<=points.size(); ++j) {
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bool last = j == points.size();
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int i = last ? 0 : j;
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if (lengths[j] - lengths[j-1] > min_length) {
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Point diff = points[i] - points[j-1];
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float diff_len = lengths[j] - lengths[j-1];
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float r = (min_length/diff_len);
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Point new_pt = points[j-1] + Point(r*diff[0], r*diff[1]);
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points.insert(points.begin() + j, new_pt);
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lengths.insert(lengths.begin() + j, lengths[j-1] + min_length);
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}
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}
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assert(points.size() == lengths.size() - 1);
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}
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Polygon Polygon::transform(const Transform3d& trafo) const
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{
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unsigned int vertices_count = (unsigned int)points.size();
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Polygon dstpoly;
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dstpoly.points.resize(vertices_count);
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if (vertices_count == 0)
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return dstpoly;
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unsigned int data_size = 3 * vertices_count * sizeof(float);
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Eigen::MatrixXd src(3, vertices_count);
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for (size_t i = 0; i < vertices_count; i++)
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{
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src.col(i) = Vec3d{ double(points[i].x()), double(points[i].y()),0. };
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}
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Eigen::MatrixXd dst(3, vertices_count);
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dst = trafo * src.colwise().homogeneous();
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for (size_t i = 0; i < vertices_count; i++)
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{
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dstpoly.points[i] = { dst(0,i),dst(1,i) };
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}
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return dstpoly;
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}
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BoundingBox get_extents(const Polygon &poly)
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{
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return poly.bounding_box();
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}
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BoundingBox get_extents(const Polygons &polygons)
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{
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BoundingBox bb;
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if (! polygons.empty()) {
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bb = get_extents(polygons.front());
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for (size_t i = 1; i < polygons.size(); ++ i)
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bb.merge(get_extents(polygons[i]));
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}
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return bb;
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}
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BoundingBox get_extents_rotated(const Polygon &poly, double angle)
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{
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return get_extents_rotated(poly.points, angle);
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}
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BoundingBox get_extents_rotated(const Polygons &polygons, double angle)
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{
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BoundingBox bb;
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if (! polygons.empty()) {
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bb = get_extents_rotated(polygons.front().points, angle);
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for (size_t i = 1; i < polygons.size(); ++ i)
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bb.merge(get_extents_rotated(polygons[i].points, angle));
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}
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return bb;
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}
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extern std::vector<BoundingBox> get_extents_vector(const Polygons &polygons)
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{
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std::vector<BoundingBox> out;
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out.reserve(polygons.size());
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for (Polygons::const_iterator it = polygons.begin(); it != polygons.end(); ++ it)
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out.push_back(get_extents(*it));
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return out;
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}
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// Polygon must be valid (at least three points), collinear points and duplicate points removed.
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bool polygon_is_convex(const Points &poly)
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{
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if (poly.size() < 3)
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return false;
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Point p0 = poly[poly.size() - 2];
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Point p1 = poly[poly.size() - 1];
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for (size_t i = 0; i < poly.size(); ++ i) {
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Point p2 = poly[i];
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auto det = cross2((p1 - p0).cast<int64_t>(), (p2 - p1).cast<int64_t>());
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if (det < 0)
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return false;
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p0 = p1;
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p1 = p2;
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}
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return true;
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}
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bool has_duplicate_points(const Polygons &polys)
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{
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#if 1
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// Check globally.
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size_t cnt = 0;
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for (const Polygon &poly : polys)
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cnt += poly.points.size();
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std::vector<Point> allpts;
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allpts.reserve(cnt);
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for (const Polygon &poly : polys)
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allpts.insert(allpts.end(), poly.points.begin(), poly.points.end());
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return has_duplicate_points(std::move(allpts));
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#else
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// Check per contour.
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for (const Polygon &poly : polys)
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if (has_duplicate_points(poly))
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return true;
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return false;
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#endif
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}
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static inline bool is_stick(const Point &p1, const Point &p2, const Point &p3)
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{
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Point v1 = p2 - p1;
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Point v2 = p3 - p2;
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int64_t dir = int64_t(v1(0)) * int64_t(v2(0)) + int64_t(v1(1)) * int64_t(v2(1));
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if (dir > 0)
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// p3 does not turn back to p1. Do not remove p2.
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return false;
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double l2_1 = double(v1(0)) * double(v1(0)) + double(v1(1)) * double(v1(1));
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double l2_2 = double(v2(0)) * double(v2(0)) + double(v2(1)) * double(v2(1));
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if (dir == 0)
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// p1, p2, p3 may make a perpendicular corner, or there is a zero edge length.
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// Remove p2 if it is coincident with p1 or p2.
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return l2_1 == 0 || l2_2 == 0;
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// p3 turns back to p1 after p2. Are p1, p2, p3 collinear?
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// Calculate distance from p3 to a segment (p1, p2) or from p1 to a segment(p2, p3),
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// whichever segment is longer
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double cross = double(v1(0)) * double(v2(1)) - double(v2(0)) * double(v1(1));
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double dist2 = cross * cross / std::max(l2_1, l2_2);
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return dist2 < EPSILON * EPSILON;
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}
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bool remove_sticks(Polygon &poly)
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{
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bool modified = false;
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size_t j = 1;
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for (size_t i = 1; i + 1 < poly.points.size(); ++ i) {
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|
if (! is_stick(poly[j-1], poly[i], poly[i+1])) {
|
|
// Keep the point.
|
|
if (j < i)
|
|
poly.points[j] = poly.points[i];
|
|
++ j;
|
|
}
|
|
}
|
|
if (++ j < poly.points.size()) {
|
|
poly.points[j-1] = poly.points.back();
|
|
poly.points.erase(poly.points.begin() + j, poly.points.end());
|
|
modified = true;
|
|
}
|
|
while (poly.points.size() >= 3 && is_stick(poly.points[poly.points.size()-2], poly.points.back(), poly.points.front())) {
|
|
poly.points.pop_back();
|
|
modified = true;
|
|
}
|
|
while (poly.points.size() >= 3 && is_stick(poly.points.back(), poly.points.front(), poly.points[1]))
|
|
poly.points.erase(poly.points.begin());
|
|
return modified;
|
|
}
|
|
|
|
bool remove_sticks(Polygons &polys)
|
|
{
|
|
bool modified = false;
|
|
size_t j = 0;
|
|
for (size_t i = 0; i < polys.size(); ++ i) {
|
|
modified |= remove_sticks(polys[i]);
|
|
if (polys[i].points.size() >= 3) {
|
|
if (j < i)
|
|
std::swap(polys[i].points, polys[j].points);
|
|
++ j;
|
|
}
|
|
}
|
|
if (j < polys.size())
|
|
polys.erase(polys.begin() + j, polys.end());
|
|
return modified;
|
|
}
|
|
|
|
bool remove_degenerate(Polygons &polys)
|
|
{
|
|
bool modified = false;
|
|
size_t j = 0;
|
|
for (size_t i = 0; i < polys.size(); ++ i) {
|
|
if (polys[i].points.size() >= 3) {
|
|
if (j < i)
|
|
std::swap(polys[i].points, polys[j].points);
|
|
++ j;
|
|
} else
|
|
modified = true;
|
|
}
|
|
if (j < polys.size())
|
|
polys.erase(polys.begin() + j, polys.end());
|
|
return modified;
|
|
}
|
|
|
|
bool remove_small(Polygons &polys, double min_area)
|
|
{
|
|
bool modified = false;
|
|
size_t j = 0;
|
|
for (size_t i = 0; i < polys.size(); ++ i) {
|
|
if (std::abs(polys[i].area()) >= min_area) {
|
|
if (j < i)
|
|
std::swap(polys[i].points, polys[j].points);
|
|
++ j;
|
|
} else
|
|
modified = true;
|
|
}
|
|
if (j < polys.size())
|
|
polys.erase(polys.begin() + j, polys.end());
|
|
return modified;
|
|
}
|
|
|
|
void remove_collinear(Polygon &poly)
|
|
{
|
|
if (poly.points.size() > 2) {
|
|
// copy points and append both 1 and last point in place to cover the boundaries
|
|
Points pp;
|
|
pp.reserve(poly.points.size()+2);
|
|
pp.push_back(poly.points.back());
|
|
pp.insert(pp.begin()+1, poly.points.begin(), poly.points.end());
|
|
pp.push_back(poly.points.front());
|
|
// delete old points vector. Will be re-filled in the loop
|
|
poly.points.clear();
|
|
|
|
size_t i = 0;
|
|
size_t k = 0;
|
|
while (i < pp.size()-2) {
|
|
k = i+1;
|
|
const Point &p1 = pp[i];
|
|
while (k < pp.size()-1) {
|
|
const Point &p2 = pp[k];
|
|
const Point &p3 = pp[k+1];
|
|
Line l(p1, p3);
|
|
if(l.distance_to(p2) < SCALED_EPSILON) {
|
|
k++;
|
|
} else {
|
|
if(i > 0) poly.points.push_back(p1); // implicitly removes the first point we appended above
|
|
i = k;
|
|
break;
|
|
}
|
|
}
|
|
if(k > pp.size()-2) break; // all remaining points are collinear and can be skipped
|
|
}
|
|
poly.points.push_back(pp[i]);
|
|
}
|
|
}
|
|
|
|
void remove_collinear(Polygons &polys)
|
|
{
|
|
for (Polygon &poly : polys)
|
|
remove_collinear(poly);
|
|
}
|
|
|
|
Polygons polygons_simplify(const Polygons &source_polygons, double tolerance)
|
|
{
|
|
Polygons out;
|
|
out.reserve(source_polygons.size());
|
|
for (const Polygon &source_polygon : source_polygons) {
|
|
// Run Douglas / Peucker simplification algorithm on an open polyline (by repeating the first point at the end of the polyline),
|
|
Points simplified = MultiPoint::_douglas_peucker(to_polyline(source_polygon).points, tolerance);
|
|
// then remove the last (repeated) point.
|
|
simplified.pop_back();
|
|
// Simplify the decimated contour by ClipperLib.
|
|
bool ccw = ClipperLib::Area(simplified) > 0.;
|
|
for (Points &path : ClipperLib::SimplifyPolygons(ClipperUtils::SinglePathProvider(simplified), ClipperLib::pftNonZero)) {
|
|
if (! ccw)
|
|
// ClipperLib likely reoriented negative area contours to become positive. Reverse holes back to CW.
|
|
std::reverse(path.begin(), path.end());
|
|
out.emplace_back(std::move(path));
|
|
}
|
|
}
|
|
return out;
|
|
}
|
|
|
|
// Do polygons match? If they match, they must have the same topology,
|
|
// however their contours may be rotated.
|
|
bool polygons_match(const Polygon &l, const Polygon &r)
|
|
{
|
|
if (l.size() != r.size())
|
|
return false;
|
|
auto it_l = std::find(l.points.begin(), l.points.end(), r.points.front());
|
|
if (it_l == l.points.end())
|
|
return false;
|
|
auto it_r = r.points.begin();
|
|
for (; it_l != l.points.end(); ++ it_l, ++ it_r)
|
|
if (*it_l != *it_r)
|
|
return false;
|
|
it_l = l.points.begin();
|
|
for (; it_r != r.points.end(); ++ it_l, ++ it_r)
|
|
if (*it_l != *it_r)
|
|
return false;
|
|
return true;
|
|
}
|
|
|
|
bool overlaps(const Polygons& polys1, const Polygons& polys2)
|
|
{
|
|
for (const Polygon& poly1 : polys1) {
|
|
if (poly1.overlaps(polys2))
|
|
return true;
|
|
}
|
|
return false;
|
|
}
|
|
|
|
bool contains(const Polygon &polygon, const Point &p, bool border_result)
|
|
{
|
|
if (const int poly_count_inside = ClipperLib::PointInPolygon(p, polygon.points);
|
|
poly_count_inside == -1)
|
|
return border_result;
|
|
else
|
|
return (poly_count_inside % 2) == 1;
|
|
}
|
|
|
|
bool contains(const Polygons &polygons, const Point &p, bool border_result)
|
|
{
|
|
int poly_count_inside = 0;
|
|
for (const Polygon &poly : polygons) {
|
|
const int is_inside_this_poly = ClipperLib::PointInPolygon(p, poly.points);
|
|
if (is_inside_this_poly == -1)
|
|
return border_result;
|
|
poly_count_inside += is_inside_this_poly;
|
|
}
|
|
return (poly_count_inside % 2) == 1;
|
|
}
|
|
|
|
Polygon make_circle(double radius, double error)
|
|
{
|
|
double angle = 2. * acos(1. - error / radius);
|
|
size_t num_segments = size_t(ceil(2. * M_PI / angle));
|
|
return make_circle_num_segments(radius, num_segments);
|
|
}
|
|
|
|
Polygon make_circle_num_segments(double radius, size_t num_segments)
|
|
{
|
|
Polygon out;
|
|
out.points.reserve(num_segments);
|
|
double angle_inc = 2.0 * M_PI / num_segments;
|
|
for (size_t i = 0; i < num_segments; ++ i) {
|
|
const double angle = angle_inc * i;
|
|
out.points.emplace_back(coord_t(cos(angle) * radius), coord_t(sin(angle) * radius));
|
|
}
|
|
return out;
|
|
}
|
|
} |