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Check if two line segments intersect
Let two line-segments are given. The points p1, p2 from the first line segment and q1, q2 from the second line segment. We have to check whether both line segments are intersecting or not.
We can say that both line segments are intersecting when these cases are satisfied:
- When (p1, p2, q1) and (p1, p2, q2) have a different orientation and
- (q1, q2, p1) and (q1, q2, p2) have a different orientation.
There is another condition is when (p1, p2, q1), (p1, p2, q2), (q1, q2, p1), (q1, q2, p2) are collinear.
Input and Output
Input: Points of two line-segments Line-segment 1: (0, 0) to (5, 5) Line-segment 2: (2, -10) to (3, 10) Output: Lines are intersecting
Algorithm
direction(a, b, c)
Input: Three points.
Output: Check whether they are collinear or anti-clockwise or clockwise direction.
Begin val := (b.y-a.y)*(c.x-b.x)-(b.x-a.x)*(c.y-b.y) if val = 0, then return collinear else if val < 0, then return anti-clockwise return clockwise End
isIntersect(l1, l2)
Input: Two line segments, each line has two points p1 and p2.
Output: True, when they are intersecting.
Begin dir1 = direction(l1.p1, l1.p2, l2.p1); dir2 = direction(l1.p1, l1.p2, l2.p2); dir3 = direction(l2.p1, l2.p2, l1.p1); dir4 = direction(l2.p1, l2.p2, l1.p2); if dir1 ≠ dir2 and dir3 ≠ dir4, then return true if dir1 =0 and l2.p1 on the line l1, then return true if dir2 = 0 and l2.p2 on the line l1, then return true if dir3 = 0 and l1.p1 on the line l2, then return true if dir4 = 0 and l1.p2 on the line l2, then return true return false End
Example
#include<iostream>
using namespace std;
struct Point {
int x, y;
};
struct line {
Point p1, p2;
};
bool onLine(line l1, Point p) { //check whether p is on the line or not
if(p.x <= max(l1.p1.x, l1.p2.x) && p.x <= min(l1.p1.x, l1.p2.x) &&
(p.y <= max(l1.p1.y, l1.p2.y) && p.y <= min(l1.p1.y, l1.p2.y)))
return true;
return false;
}
int direction(Point a, Point b, Point c) {
int val = (b.y-a.y)*(c.x-b.x)-(b.x-a.x)*(c.y-b.y);
if (val == 0)
return 0; //colinear
else if(val < 0)
return 2; //anti-clockwise direction
return 1; //clockwise direction
}
bool isIntersect(line l1, line l2) {
//four direction for two lines and points of other line
int dir1 = direction(l1.p1, l1.p2, l2.p1);
int dir2 = direction(l1.p1, l1.p2, l2.p2);
int dir3 = direction(l2.p1, l2.p2, l1.p1);
int dir4 = direction(l2.p1, l2.p2, l1.p2);
if(dir1 != dir2 && dir3 != dir4)
return true; //they are intersecting
if(dir1==0 && onLine(l1, l2.p1)) //when p2 of line2 are on the line1
return true;
if(dir2==0 && onLine(l1, l2.p2)) //when p1 of line2 are on the line1
return true;
if(dir3==0 && onLine(l2, l1.p1)) //when p2 of line1 are on the line2
return true;
if(dir4==0 && onLine(l2, l1.p2)) //when p1 of line1 are on the line2
return true;
return false;
}
int main() {
line l1 = {{0,0}, {5, 5}};
line l2 = {{2,-10}, {3, 10}};
if(isIntersect(l1, l2))
cout << "Lines are intersecting";
else
cout << "Lines are not intersecting";
}Output
Lines are intersecting
Updated on: 17-Jun-2020
4K+ Views
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