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main.cpp
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main.cpp
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#include <iostream>
#include <vector>
#include <map>
#include <cmath>
struct Point
{
char letter;
double x, y;
Point & operator = (Point const & b) { letter = b.letter; x = b.x; y = b.y; return *this; }
Point(const Point & b) : letter(b.letter), x(b.x), y(b.y) {}
Point(char _letter, double _x, double _y) : letter(_letter), x(_x), y(_y) {}
bool operator <(const Point & b) const
{
if (y < b.y - 1.0e-9) return true;
else if (y > b.y + 1.0e-9) return false;
else if (x < b.x - 1.0e-9) return true;
else return false;
}
bool operator ==(const Point & b) const
{
return fabs(y - b.y) < 1.0e-9 && fabs(x - b.x) < 1.0e-9;
}
bool operator !=(const Point & b) const
{
return fabs(y - b.y) > 1.0e-9 || fabs(x - b.x) > 1.0e-9;
}
};
struct Segment
{
Point beg, end;
Segment & operator = (Segment const & b) { beg = b.beg; end = b.end; return *this; }
Segment(const Segment & b) : beg(b.beg), end(b.end) {}
Segment(const Point & _beg, const Point & _end) : beg(_beg), end(_end) {}
};
#define SEG_START 0
#define SEG_END 1
class event_less
{
public:
bool operator()(const std::pair<double, int> & a, const std::pair<double, int> & b) const
{
if (a.first < b.first - 1.0e-9)
return true;
else if (a.first > b.first + 1.0e-9)
return false;
else if (a.second < b.second)
return true;
return false;
}
};
std::pair<bool, Point> intersect(const Segment & a, const Segment & b, bool print)
{
Point ret('a', 0, 0);
double div = (a.beg.x - a.end.x)*(b.beg.y - b.end.y) - (a.beg.y - a.end.y)*(b.beg.x - b.end.x), t;
if (fabs(div) < 1.0e-13)
{
if (print) std::cout << "divisor is zero" << std::endl;
return std::make_pair(false, ret);
}
ret.x = ((a.beg.x*a.end.y - a.beg.y*a.end.x)*(b.beg.x - b.end.x) - (a.beg.x - a.end.x)*(b.beg.x*b.end.y - b.beg.y*b.end.x)) / div;
ret.y = ((a.beg.x*a.end.y - a.beg.y*a.end.x)*(b.beg.y - b.end.y) - (a.beg.y - a.end.y)*(b.beg.x*b.end.y - b.beg.y*b.end.x)) / div;
if (print) std::cout << "found (" << ret.x << "," << ret.y << ")" << std::endl;
//probably some of these tests are redundant
if (fabs(a.end.x - a.beg.x) > 1.0e-9)
{
t = (ret.x - a.beg.x) / (a.end.x - a.beg.x);
if (t < 1.0e-9 || t > 1.0 - 1.0e-9) { if (print) std::cout << "out of bound: " << t << std::endl; return std::make_pair(false, ret); }
}
if (fabs(a.end.y - a.beg.y) > 1.0e-9)
{
t = (ret.y - a.beg.y) / (a.end.y - a.beg.y);
if (t < 1.0e-9 || t > 1.0 - 1.0e-9) { if (print) std::cout << "out of bound: " << t << std::endl; return std::make_pair(false, ret); }
}
if (fabs(b.end.x - b.beg.x) > 1.0e-9)
{
t = (ret.x - b.beg.x) / (b.end.x - b.beg.x);
if (t < 1.0e-9 || t > 1.0 - 1.0e-9) { if (print) std::cout << "out of bound: " << t << std::endl; return std::make_pair(false, ret); }
}
if (fabs(b.end.y - b.beg.y) > 1.0e-9)
{
t = (ret.y - b.beg.y) / (b.end.y - b.beg.y);
if (t < 1.0e-9 || t > 1.0 - 1.0e-9) { if (print) std::cout << "out of bound: " << t << std::endl; return std::make_pair(false, ret); }
}
if (print) std::cout << "intersection accepted" << std::endl;
return std::make_pair(true, ret);
}
void intersect(int a, int b, const Point & I, std::vector<Segment> & segments, std::multimap<Point, int> & sweep, std::multimap<std::pair<double,int>, int,event_less> & events, bool print)
{
//remove event of ending of old segment
{
int rem_end_events[2];
rem_end_events[0] = a;
rem_end_events[1] = b;
for (int k = 0; k < 2; ++k)
{
std::pair< std::multimap<std::pair<double,int>, int,event_less>::iterator, std::multimap<std::pair<double,int>,int,event_less>::iterator > del = events.equal_range(std::make_pair(segments[rem_end_events[k]].end.x,SEG_END)); //get all events at position of the end
bool flag = false;
for (std::multimap<std::pair<double,int>, int,event_less>::iterator it = del.first; it != del.second; ++it) //search over all events
{
if (it->first.second == SEG_END && it->second == rem_end_events[k]) //event is end of segment and segment matches current
{
events.erase(it); //remove that segment
flag = true;
break; //do not expect any more
}
}
if (!flag) std::cout << "Cannot find proper ending event for segment" << std::endl;
}
}
//add new segment with intersection point up to end
segments.push_back(Segment(I, segments[a].end));
//add event of starting of new segment
events.insert(std::make_pair(std::make_pair(I.x,SEG_START), (int)segments.size() - 1));
//add event of ending of new segment
events.insert(std::make_pair(std::make_pair(segments.back().end.x,SEG_END),(int)segments.size() - 1));
//change ending point for current segment
segments[a].end = I;
//add event of ending of old segment
events.insert(std::make_pair(std::make_pair(I.x,SEG_END), a));
//add new segment with intersection point up to end
segments.push_back(Segment(I, segments[b].end));
//add event of starting of new segment
events.insert(std::make_pair(std::make_pair(I.x,SEG_START), (int)segments.size() - 1));
//add event of ending of new segment
events.insert(std::make_pair(std::make_pair(segments.back().end.x,SEG_END), (int)segments.size() - 1));
//change ending point for current segment
segments[b].end = I;
//add event of ending of old segment
events.insert(std::make_pair(std::make_pair(I.x,SEG_END), b));
if (print)
{
std::cout << "Number of events: " << events.size() << std::endl;
for (std::multimap<std::pair<double, int>, int,event_less>::iterator it = events.begin(); it != events.end(); ++it)
std::cout << "x: " << it->first.first << " type " << (it->first.second == SEG_START ? "start" : "end") << " segment " << it->second << std::endl;
}
}
//find all intersection points
void intersect(std::vector<Segment> & segments, std::vector<Point> & intersections, bool print)
{
std::multimap<std::pair<double,int>,int,event_less> events;
std::multimap<Point,int> sweep;
if( print )
{
std::cout << "Input segments[" << segments.size() << "]: " << std::endl;
for (std::vector<Segment>::iterator it = segments.begin(); it != segments.end(); ++it)
std::cout << "[ " << it->beg.letter << "(" << it->beg.x << "," << it->beg.y << "), " << it->end.letter << "(" << it->end.x << "," << it->end.y << ") ] " << std::endl;
std::cout << "Create events based on segments." << std::endl;
}
for (int k = 0; k < (int)segments.size(); ++k)
{
if (segments[k].beg.x > segments[k].end.x)
std::swap(segments[k].beg, segments[k].end);
events.insert(std::make_pair(std::make_pair(segments[k].beg.x,SEG_START),k));
events.insert(std::make_pair(std::make_pair(segments[k].end.x,SEG_END), k));
}
if (print)
{
std::cout << "Number of events: " << events.size() << std::endl;
for (std::multimap<std::pair<double, int>, int,event_less>::iterator it = events.begin(); it != events.end(); ++it)
std::cout << "x: " << it->first.first << " type " << (it->first.second == SEG_START ? "start" : "end") << " segment " << it->second << std::endl;
std::cout << " Start parsing events" << std::endl;
}
while (!events.empty())
{
std::multimap<std::pair<double,int>,int,event_less>::iterator first = events.begin();
int t = first->first.second;
int s = first->second;
events.erase(first);
if (t == SEG_START)
{
if( print ) std::cout << "Segment " << s << " start" << std::endl;
//check if there is a line with same position
std::multimap<Point, int>::iterator ins = sweep.insert(std::make_pair(segments[s].beg, s));
if (print)
{
std::cout << "Inserted into sweep" << std::endl;
for (std::multimap<Point, int>::iterator it = sweep.begin(); it != sweep.end(); ++it)
std::cout << it->first.letter << "(" << it->first.x << "," << it->first.y << ")" << " segment " << it->second << std::endl;
}
//check line (or lines above current)
for (int dir = 0; dir <= 1; ++dir) // look up or down
{
if( print ) std::cout << "Looking " << (dir ? "up" : "down") << std::endl;
std::multimap<Point, int>::iterator iter = ins;
while ((dir ? ++iter : iter--) != (dir ? sweep.end() : sweep.begin())) //y is greater for next
{
if (print) std::cout << "test " << s << " with " << iter->second << std::endl;
if (segments[s].beg != segments[iter->second].beg) //ignore same starting position
{
if (print) std::cout << "checking intersection" << std::endl;
std::pair<bool, Point> I = intersect(segments[s], segments[iter->second],print);
if (I.first)
{
I.second.letter += (char)intersections.size();
if( print ) std::cout << "Intersection of " << s << " and " << iter->second << " at " << I.second.letter << "(" << I.second.x << "," << I.second.y << ")" << std::endl;
intersections.push_back(I.second);
intersect(s, iter->second, I.second, segments, sweep, events,print);
}
}
else if (print) std::cout << "skipping segments with same starting point" << std::endl;
if ((2*dir-1)*(iter->first.y - ins->first.y) > 0) //visited line is above (below) current
break; //stop search
}
}
}
else if (t == SEG_END)
{
if( print ) std::cout << "Segment " << s << " end" << std::endl;
//remove segment from sweep
std::pair< std::multimap<Point, int>::iterator, std::multimap<Point, int>::iterator > range = sweep.equal_range(segments[s].beg);
if( print ) std::cout << "Range distance " << std::distance(range.first,range.second) << " sweep size " << sweep.size() << std::endl;
std::multimap<Point, int>::iterator above = range.second, below = range.first;
bool flag = false, test = true;
if( below-- == sweep.begin() ) test = false;
if( above == sweep.end() ) test = false;
if( test && print ) std::cout << "Test will be performed" << std::endl;
for (std::multimap<Point, int>::iterator it = range.first; it != range.second; ++it) //search over all events
{
if( it->second == s) //found necessery segment
{
if (print)
{
std::cout << "Erase segment " << s << " from sweep: " << std::endl;
for (std::multimap<Point, int>::iterator it = sweep.begin(); it != sweep.end(); ++it)
std::cout << it->first.letter << "(" << it->first.x << "," << it->first.y << ")" << " segment " << it->second << std::endl;
}
sweep.erase(it);
flag = true;
break; //do not expect any more
}
}
if (!flag) std::cout << __FILE__ << ":" << __LINE__ << " Error: cannot find segment " << s << " in sweep" << std::endl;
if (test)
{
if (print) std::cout << "test " << below->second << " with " << above->second << std::endl;
if (segments[above->second].beg != segments[below->second].beg)
{
if (print) std::cout << "checking intersection" << std::endl;
std::pair<bool, Point> I = intersect(segments[below->second], segments[above->second],print);
if (I.first)
{
I.second.letter += (char)intersections.size();
if( print ) std::cout << "Intersection of " << below->second << " and " << above->second << " at " << I.second.letter << "(" << I.second.x << "," << I.second.y << ")" << std::endl;
intersections.push_back(I.second);
intersect(below->second, above->second, I.second, segments, sweep, events,print);
}
}
else if (print) std::cout << "skipping segments with same starting point" << std::endl;
}
}
}
}
int main()
{
std::vector<Point> intersections;
std::vector<Segment> segments;
segments.push_back(Segment(Point('A',-7.41, -0.58), Point('C',-1.3,-0.79)));
segments.push_back(Segment(Point('B',-4.0, 1.27), Point('D',-4.21, -2.99)));
segments.push_back(Segment(Point('F',-4.92, 0.71), Point('G',-4.26, -1.40)));
segments.push_back(Segment(Point('I',-4.55, -1.24), Point('J',-2.54, -0.42)));
segments.push_back(Segment(Point('K',-3.70, 0.48), Point('L',-3.70, -2.41))); //vertical
intersect(segments, intersections,false);
std::cout << "Intersection points[" << intersections.size() << "]: " << std::endl;
for (std::vector<Point>::iterator it = intersections.begin(); it != intersections.end(); ++it)
std::cout << it->letter << "(" << it->x << "," << it->y << ") " << std::endl;
std::cout << "Segments[" << segments.size() << "]: " << std::endl;
for (std::vector<Segment>::iterator it = segments.begin(); it != segments.end(); ++it)
std::cout << "[ " << it->beg.letter << "(" << it->beg.x << "," << it->beg.y << "), " << it->end.letter << "(" << it->end.x << "," << it->end.y << ") ] " << std::endl;
return 0;
}