Segment Intersection Algorithm
The Segment Intersection Algorithm is a computational geometry technique used to determine if two line segments intersect or not. It involves finding the points of intersection between two line segments, which is a common problem in computer graphics, computer-aided design, geographic information systems, and other fields. The algorithm has several variations, but the most basic approach involves comparing the relative orientations of the end points of the two segments with respect to each other. If the orientations are different for both pairs of end points, then the segments intersect. Otherwise, they do not. This algorithm can be applied to both two-dimensional and three-dimensional spaces.
One popular version of the Segment Intersection Algorithm is the Bentley-Ottmann sweep line algorithm. This algorithm sorts the line segments by their x-coordinates and "sweeps" a vertical line across the plane from left to right, keeping track of the line segments that the sweep line intersects. When the sweep line encounters a new segment, it checks for intersections with the segments that are currently being intersected by the sweep line. This algorithm has a time complexity of O((n + k) log n), where n is the number of line segments and k is the number of intersections. It significantly improves the performance compared to naive methods that check all pairs of line segments, which would have a time complexity of O(n^2).
/*
Petar 'PetarV' Velickovic
Algorithm: Segment Intersection
*/
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <iostream>
#include <vector>
#include <list>
#include <string>
#include <algorithm>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <complex>
using namespace std;
typedef long long lld;
struct Point
{
double X, Y;
Point(double x, double y)
{
this->X = x;
this->Y = y;
}
};
//Algoritam koji odredjuje da li postoji presek izmedju dve 2D duzi (AB i CD)
//Slozenost: O(1)
inline double crossProduct(Point a, Point b, Point c)
{
return ((b.X - a.X) * (c.Y - a.Y) - (b.Y - a.Y) * (c.X - a.X));
}
inline bool isLeft(Point a, Point b, Point c)
{
return (crossProduct(a, b, c) > 0);
}
inline bool isCollinear(Point a, Point b, Point c)
{
return (crossProduct(a, b, c) == 0);
}
inline bool oppositeSides(Point a, Point b, Point c, Point d)
{
return (isLeft(a, b, c) != isLeft(a, b, d));
}
inline bool isBetween(Point a, Point b, Point c)
{
return (min(a.X, b.X) <= c.X && c.X <= max(a.X, b.X) && min(a.Y, b.Y) <= c.Y && c.Y <= max(a.Y,b.Y));
}
inline bool intersect(Point a, Point b, Point c, Point d)
{
if (isCollinear(a, b, c) && isBetween(a, b, c)) return true;
if (isCollinear(a, b, d) && isBetween(a, b, d)) return true;
if (isCollinear(c, d, a) && isBetween(c, d, a)) return true;
if (isCollinear(c, d, b) && isBetween(c, d, b)) return true;
return (oppositeSides(a, b, c, d) && oppositeSides(c, d, a, b));
}
int main()
{
Point A(0.0, 0.0), B(0.0, 2.0), C(-1.0, 2.0), D(1.0, 2.0);
printf(intersect(A,B,C,D) ? "YES" : "NO");
printf("\n");
return 0;
}
