{"id":25834,"date":"2017-10-25T20:58:56","date_gmt":"2017-10-25T15:28:56","guid":{"rendered":"https:\/\/www.wikitechy.com\/technology\/?p=25834"},"modified":"2017-10-25T20:58:56","modified_gmt":"2017-10-25T15:28:56","slug":"how-to-check-if-two-given-line-segments-intersect","status":"publish","type":"post","link":"https:\/\/www.wikitechy.com\/technology\/how-to-check-if-two-given-line-segments-intersect\/","title":{"rendered":"How to check if two given line segments intersect?"},"content":{"rendered":"

Given two line segments (p1, q1) and (p2, q2), find if the given line segments intersect with each other.<\/span><\/p>\n

Before we discuss solution, let us define notion of orientation<\/strong><\/a>. Orientation of an ordered triplet of points in the\u00a0plane can be
\n\u2013counterclockwise
\n\u2013clockwise
\n\u2013colinear
\nThe following diagram shows different possible orientations of (a, b, c)<\/p>\n

\"How<\/p>\n

\n

[ad type=”banner”]<\/h4>\n

How is Orientation useful here?<\/strong><\/h4>\n<\/div>\n

Two segments (p1,q1) and (p2,q2) intersect if and only if\u00a0one of the following two conditions is verified<\/p>\n

1.\u00a0General Case:<\/em><\/strong>
\n\u2013 (p1, q1, p2) and (p1, q1, q2) have different\u00a0orientations and
\n\u2013 (p2, q2,\u00a0p1) and (p2, q2,\u00a0q1) have different\u00a0orientations.<\/p>\n

\"How<\/p>\n

 <\/p>\n

\"How<\/p>\n

 <\/p>\n[ad type=”banner”]\n

2. Special Case <\/em><\/strong>
\n\u2013 (p1, q1, p2), (p1, q1, q2), (p2, q2, p1), and (p2, q2, q1) are\u00a0all collinear and
\n\u2013\u00a0the x-projections of (p1, q1) and (p2, q2) intersect
\n\u2013 the y-projections of (p1, q1) and (p2, q2) intersect<\/p>\n

\"How<\/p>\n

Following is C++ implementation based on above idea.<\/p>\n

\n
\n\n\n\n
\n
\n
\n

\/\/ A C++ program to check if two given line segments intersect<\/code><\/p>\n

<\/div> 
#include <iostream>using namespace std; struct Point{    int x;    int y;}; \/\/ Given three colinear points p, q, r, the function checks if\/\/ point q lies on line segment 'pr'bool onSegment(Point p, Point q, Point r){    if (q.x <= max(p.x, r.x) && q.x >= min(p.x, r.x) &&        q.y <= max(p.y, r.y) && q.y >= min(p.y, r.y))       return true;     return false;} \/\/ To find orientation of ordered triplet (p, q, r).\/\/ The function returns following values\/\/ 0 --> p, q and r are colinear\/\/ 1 --> Clockwise\/\/ 2 --> Counterclockwiseint orientation(Point p, Point q, Point r){    \/\/ See http:\/\/www.geeksforgeeks.org\/orientation-3-ordered-points\/    \/\/ for details of below formula.    int val = (q.y - p.y) * (r.x - q.x) -              (q.x - p.x) * (r.y - q.y);     if (val == 0) return 0;  \/\/ colinear     return (val > 0)? 1: 2; \/\/ clock or counterclock wise} \/\/ The main function that returns true if line segment 'p1q1'\/\/ and 'p2q2' intersect.bool doIntersect(Point p1, Point q1, Point p2, Point q2){    \/\/ Find the four orientations needed for general and    \/\/ special cases    int o1 = orientation(p1, q1, p2);    int o2 = orientation(p1, q1, q2);    int o3 = orientation(p2, q2, p1);    int o4 = orientation(p2, q2, q1);     \/\/ General case    if (o1 != o2 && o3 != o4)        return true;     \/\/ Special Cases    \/\/ p1, q1 and p2 are colinear and p2 lies on segment p1q1    if (o1 == 0 && onSegment(p1, p2, q1)) return true;     \/\/ p1, q1 and p2 are colinear and q2 lies on segment p1q1    if (o2 == 0 && onSegment(p1, q2, q1)) return true;     \/\/ p2, q2 and p1 are colinear and p1 lies on segment p2q2    if (o3 == 0 && onSegment(p2, p1, q2)) return true;      \/\/ p2, q2 and q1 are colinear and q1 lies on segment p2q2    if (o4 == 0 && onSegment(p2, q1, q2)) return true;     return false; \/\/ Doesn't fall in any of the above cases} \/\/ Driver program to test above functionsint main(){    struct Point p1 = {1, 1}, q1 = {10, 1};    struct Point p2 = {1, 2}, q2 = {10, 2};     doIntersect(p1, q1, p2, q2)? cout << "Yes\\n": cout << "No\\n";     p1 = {10, 0}, q1 = {0, 10};    p2 = {0, 0}, q2 = {10, 10};    doIntersect(p1, q1, p2, q2)? cout << "Yes\\n": cout << "No\\n";     p1 = {-5, -5}, q1 = {0, 0};    p2 = {1, 1}, q2 = {10, 10};    doIntersect(p1, q1, p2, q2)? cout << "Yes\\n": cout << "No\\n";     return 0;}<\/code><\/pre> <\/div>\n<\/div>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
Output:<\/p>\n
No\r\nYes\r\nNo<\/pre>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
How to check if two given line segments intersect? – Geometric Algorithms – Orientation of an ordered triplet of points in the plane.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[69969,1,73905],"tags":[75746,75745,75751,75747,75748,75750,75752,75753,75749],"class_list":["post-25834","post","type-post","status-publish","format-standard","hentry","category-algorithm","category-coding","category-geometric-algorithms","tag-a-line-that-intersects-two-non-intersecting-planes","tag-a-line-that-intersects-two-or-more-lines","tag-intersecting-lines-definition","tag-intersection-of-two-lines-in-3d","tag-line-line-intersection","tag-line-segment-intersection","tag-parallel-lines-definition","tag-perpendicular-line","tag-what-is-the-intersection-of-two-planes"],"_links":{"self":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/posts\/25834","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/comments?post=25834"}],"version-history":[{"count":0,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/posts\/25834\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/media?parent=25834"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/categories?post=25834"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/tags?post=25834"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}