在本教程中,我们将讨论一个寻找三角形外接点的程序。
为此,我们将提供三个非共线点。我们的任务是找到由这些点形成的三角形的外心。
#include <iostream> #include <cfloat> using namespace std; //存储X和Y值 #define pdd pair<double, double> void lineFromPoints(pdd P, pdd Q, double &a, double &b, double &c){ a = Q.second - P.second; b = P.first - Q.first; c = a*(P.first)+ b*(P.second); } void perpendicularBisectorFromLine(pdd P, pdd Q, double &a, double &b, double &c){ pdd mid_point = make_pair((P.first + Q.first)/2, (P.second + Q.second)/2); c = -b*(mid_point.first) + a*(mid_point.second); double temp = a; a = -b; b = temp; } pdd lineLineIntersection(double a1, double b1, double c1, double a2, double b2, double c2){ double determinant = a1*b2 - a2*b1; if (determinant == 0){ return make_pair(FLT_MAX, FLT_MAX); } else { double x = (b2*c1 - b1*c2)/determinant; double y = (a1*c2 - a2*c1)/determinant; return make_pair(x, y); } } void findCircumCenter(pdd P, pdd Q, pdd R){ double a, b, c; lineFromPoints(P, Q, a, b, c); double e, f, g; lineFromPoints(Q, R, e, f, g); perpendicularBisectorFromLine(P, Q, a, b, c); perpendicularBisectorFromLine(Q, R, e, f, g); pdd circumcenter = lineLineIntersection(a, b, c, e, f, g); if (circumcenter.first == FLT_MAX && circumcenter.second == FLT_MAX){ cout << "两条垂直平分线 " "找到了平行线" << endl; cout << "因此,给定的点不会形成 " "三角形且共线" << endl; } else { cout << "三角形PQR的外心为: "; cout << "(" << circumcenter.first << ", " << circumcenter.second << ")" << endl; } } int main(){ pdd P = make_pair(6, 0); pdd Q = make_pair(0, 0); pdd R = make_pair(0, 8); findCircumCenter(P, Q, R); return 0; }
输出结果
三角形PQR的外心为: (3, 4)