{"id":25963,"date":"2017-10-25T22:00:46","date_gmt":"2017-10-25T16:30:46","guid":{"rendered":"https:\/\/www.wikitechy.com\/technology\/?p=25963"},"modified":"2017-10-25T22:00:46","modified_gmt":"2017-10-25T16:30:46","slug":"check-given-four-points-form-square","status":"publish","type":"post","link":"https:\/\/www.wikitechy.com\/technology\/check-given-four-points-form-square\/","title":{"rendered":"How to check if given four points form a square"},"content":{"rendered":"

Given coordinates of four points in a plane, find if the four points form a square or not.<\/span>
\nTo check for square, we need to check for following.
\na) All fours sides formed by points are same.
\nb) The angle between any two sides is 90 degree. (This condition is required as Quadrilateral <\/a>also has same sides.<\/p>\n

\"How<\/p>\n

The idea is to pick any point and calculate its distance from rest of the points. Let the picked picked point be \u2018p\u2019. To form a square, distance of two points must be same from \u2018p\u2019, let this distance be d. The distance from one point must be different from that d and must be equal to \u221a2 times d. Let this point with different distance be \u2018q\u2019.
\nThe above condition is not good enough as the the point with different distance can be on the other side. We also need to check that q is at same distance from 2 other points and this distance is same as d.<\/p>\n[ad type=”banner”]\n

Below is C++ implementation of above idea.<\/p>\n

\n
\n\n\n\n
\n
\n
\/\/ A C++ program to check if four given points form a square or not.<\/code><\/div>\n
<\/div>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
<\/div> 
#include<iostream>using namespace std; \/\/ Structure of a point in 2D spacestruct Point{    int x, y;}; \/\/ A utility function to find square of distance\/\/ from point 'p' to poitn 'q'int distSq(Point p, Point q){    return (p.x - q.x)*(p.x - q.x) +           (p.y - q.y)*(p.y - q.y);} \/\/ This function returns true if (p1, p2, p3, p4) form a\/\/ square, otherwise falsebool isSquare(Point p1, Point p2, Point p3, Point p4){    int d2 = distSq(p1, p2);  \/\/ from p1 to p2    int d3 = distSq(p1, p3);  \/\/ from p1 to p3    int d4 = distSq(p1, p4);  \/\/ from p1 to p4     \/\/ If lengths if (p1, p2) and (p1, p3) are same, then    \/\/ following conditions must met to form a square.    \/\/ 1) Square of length of (p1, p4) is same as twice    \/\/    the square of (p1, p2)    \/\/ 2) p4 is at same distance from p2 and p3    if (d2 == d3 && 2*d2 == d4)    {        int d = distSq(p2, p4);        return (d == distSq(p3, p4) && d == d2);    }     \/\/ The below two cases are similar to above case    if (d3 == d4 && 2*d3 == d2)    {        int d = distSq(p2, p3);        return (d == distSq(p2, p4) && d == d3);    }    if (d2 == d4 && 2*d2 == d3)    {        int d = distSq(p2, p3);        return (d == distSq(p3, p4) && d == d2);    }     return false;} \/\/ Driver program to test above functionint main(){    Point p1 = {20, 10}, p2 = {10, 20},          p3 = {20, 20}, p4 = {10, 10};    isSquare(p1, p2, p3, p4)? cout << "Yes": cout << "No";    return 0;}<\/code><\/pre> <\/div>\n<\/div>\n<\/div>\n
Output:<\/p>\n
Yes<\/pre>\n[ad type=”banner”]\n","protected":false},"excerpt":{"rendered":"
How to check if given four points form a square-Geometric Algorithm Given coordinates of four points in a plane, find if the four points form square or not.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[69969,73905],"tags":[76353,76358,76356,76354,76359,76357,76355,76360],"class_list":["post-25963","post","type-post","status-publish","format-standard","hentry","category-algorithm","category-geometric-algorithms","tag-check-if-four-points-form-a-rectangle","tag-check-if-four-points-form-a-square-java","tag-check-if-given-four-points-form-a-square-geeksforgeeks","tag-check-if-given-four-points-form-a-square-java","tag-check-if-given-four-points-form-a-square-maths","tag-how-to-check-if-given-four-points-form-a-square-c","tag-identify-whether-four-sides-can-form-a-square-a-rectangle-or-neither","tag-show-that-the-4-points-form-a-square"],"_links":{"self":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/posts\/25963","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=25963"}],"version-history":[{"count":0,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/posts\/25963\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/media?parent=25963"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/categories?post=25963"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/tags?post=25963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}