483 lines
16 KiB
C++
483 lines
16 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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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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/*
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int64_t Polygon::area2x() const
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{
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size_t n = poly.size();
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if (n < 3)
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return 0;
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int64_t a = 0;
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for (size_t i = 0, j = n - 1; i < n; ++i)
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a += int64_t(poly[j](0) + poly[i](0)) * int64_t(poly[j](1) - poly[i](1));
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j = i;
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}
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return -a * 0.5;
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}
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*/
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double Polygon::area(const Points &points)
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{
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size_t n = points.size();
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if (n < 3)
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return 0.;
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double a = 0.;
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for (size_t i = 0, j = n - 1; i < n; ++i) {
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a += ((double)points[j](0) + (double)points[i](0)) * ((double)points[i](1) - (double)points[j](1));
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j = i;
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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(Slic3rMultiPoint_to_ClipperPath(*this));
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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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// Does an unoriented polygon contain a point?
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// Tested by counting intersections along a horizontal line.
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bool Polygon::contains(const Point &point) const
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{
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// http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html
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bool result = false;
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Points::const_iterator i = this->points.begin();
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Points::const_iterator j = this->points.end() - 1;
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for (; i != this->points.end(); j = i++) {
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//FIXME this test is not numerically robust. Particularly, it does not handle horizontal segments at y == point(1) well.
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// Does the ray with y == point(1) intersect this line segment?
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#if 1
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if ( (((*i)(1) > point(1)) != ((*j)(1) > point(1)))
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&& ((double)point(0) < (double)((*j)(0) - (*i)(0)) * (double)(point(1) - (*i)(1)) / (double)((*j)(1) - (*i)(1)) + (double)(*i)(0)) )
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result = !result;
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#else
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if (((*i)(1) > point(1)) != ((*j)(1) > point(1))) {
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// Orientation predicated relative to i-th point.
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double orient = (double)(point(0) - (*i)(0)) * (double)((*j)(1) - (*i)(1)) - (double)(point(1) - (*i)(1)) * (double)((*j)(0) - (*i)(0));
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if (((*i)(1) > (*j)(1)) ? (orient > 0.) : (orient < 0.))
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result = !result;
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}
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#endif
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}
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return result;
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}
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// this only works on CCW polygons as CW will be ripped out by Clipper's simplify_polygons()
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Polygons Polygon::simplify(double tolerance) const
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{
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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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void Polygon::simplify(double tolerance, Polygons &polygons) const
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{
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Polygons pp = this->simplify(tolerance);
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polygons.reserve(polygons.size() + pp.size());
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polygons.insert(polygons.end(), pp.begin(), pp.end());
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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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Point Polygon::centroid() const
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{
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double area_temp = this->area();
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double x_temp = 0;
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double y_temp = 0;
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Polyline polyline = this->split_at_first_point();
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for (Points::const_iterator point = polyline.points.begin(); point != polyline.points.end() - 1; ++point) {
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x_temp += (double)( point->x() + (point+1)->x() ) * ( (double)point->x()*(point+1)->y() - (double)(point+1)->x()*point->y() );
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y_temp += (double)( point->y() + (point+1)->y() ) * ( (double)point->x()*(point+1)->y() - (double)(point+1)->x()*point->y() );
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}
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return Point(x_temp/(6*area_temp), y_temp/(6*area_temp));
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}
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// find all concave vertices (i.e. having an internal angle greater than the supplied angle)
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// (external = right side, thus we consider ccw orientation)
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Points Polygon::concave_points(double angle) const
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{
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Points points;
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angle = 2. * PI - angle + EPSILON;
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// check whether first point forms a concave angle
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if (this->points.front().ccw_angle(this->points.back(), *(this->points.begin()+1)) <= angle)
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points.push_back(this->points.front());
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// check whether points 1..(n-1) form concave angles
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for (Points::const_iterator p = this->points.begin()+1; p != this->points.end()-1; ++ p)
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if (p->ccw_angle(*(p-1), *(p+1)) <= angle)
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points.push_back(*p);
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// check whether last point forms a concave angle
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if (this->points.back().ccw_angle(*(this->points.end()-2), this->points.front()) <= angle)
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points.push_back(this->points.back());
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return points;
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}
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// find all convex vertices (i.e. having an internal angle smaller than the supplied angle)
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// (external = right side, thus we consider ccw orientation)
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Points Polygon::convex_points(double angle) const
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{
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Points points;
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angle = 2*PI - angle - EPSILON;
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// check whether first point forms a convex angle
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if (this->points.front().ccw_angle(this->points.back(), *(this->points.begin()+1)) >= angle)
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points.push_back(this->points.front());
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// check whether points 1..(n-1) form convex angles
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for (Points::const_iterator p = this->points.begin()+1; p != this->points.end()-1; ++p) {
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if (p->ccw_angle(*(p-1), *(p+1)) >= angle) points.push_back(*p);
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}
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// check whether last point forms a convex angle
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if (this->points.back().ccw_angle(*(this->points.end()-2), this->points.front()) >= angle)
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points.push_back(this->points.back());
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return points;
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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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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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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])) {
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// Keep the point.
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if (j < i)
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poly.points[j] = poly.points[i];
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++ j;
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}
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}
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if (++ j < poly.points.size()) {
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poly.points[j-1] = poly.points.back();
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poly.points.erase(poly.points.begin() + j, poly.points.end());
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modified = true;
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}
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while (poly.points.size() >= 3 && is_stick(poly.points[poly.points.size()-2], poly.points.back(), poly.points.front())) {
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poly.points.pop_back();
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modified = true;
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}
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while (poly.points.size() >= 3 && is_stick(poly.points.back(), poly.points.front(), poly.points[1]))
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poly.points.erase(poly.points.begin());
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return modified;
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}
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bool remove_sticks(Polygons &polys)
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{
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bool modified = false;
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size_t j = 0;
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for (size_t i = 0; i < polys.size(); ++ i) {
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modified |= remove_sticks(polys[i]);
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if (polys[i].points.size() >= 3) {
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if (j < i)
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std::swap(polys[i].points, polys[j].points);
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++ j;
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}
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}
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if (j < polys.size())
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polys.erase(polys.begin() + j, polys.end());
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return modified;
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}
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bool remove_degenerate(Polygons &polys)
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{
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bool modified = false;
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size_t j = 0;
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for (size_t i = 0; i < polys.size(); ++ i) {
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if (polys[i].points.size() >= 3) {
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if (j < i)
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std::swap(polys[i].points, polys[j].points);
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++ j;
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} else
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modified = true;
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}
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if (j < polys.size())
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polys.erase(polys.begin() + j, polys.end());
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return modified;
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}
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bool remove_small(Polygons &polys, double min_area)
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{
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bool modified = false;
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size_t j = 0;
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for (size_t i = 0; i < polys.size(); ++ i) {
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if (std::abs(polys[i].area()) >= min_area) {
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if (j < i)
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std::swap(polys[i].points, polys[j].points);
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++ j;
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} else
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modified = true;
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}
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if (j < polys.size())
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polys.erase(polys.begin() + j, polys.end());
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return modified;
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}
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void remove_collinear(Polygon &poly)
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{
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if (poly.points.size() > 2) {
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// copy points and append both 1 and last point in place to cover the boundaries
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Points pp;
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pp.reserve(poly.points.size()+2);
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pp.push_back(poly.points.back());
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pp.insert(pp.begin()+1, poly.points.begin(), poly.points.end());
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pp.push_back(poly.points.front());
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// delete old points vector. Will be re-filled in the loop
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poly.points.clear();
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size_t i = 0;
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size_t k = 0;
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while (i < pp.size()-2) {
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k = i+1;
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const Point &p1 = pp[i];
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while (k < pp.size()-1) {
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const Point &p2 = pp[k];
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const Point &p3 = pp[k+1];
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Line l(p1, p3);
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if(l.distance_to(p2) < SCALED_EPSILON) {
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k++;
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} else {
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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);
|
|
}
|
|
|
|
}
|