POJ 1329 Circle Through Three Points(三角形外接圆)

本是古典何须时尚 2023-06-01 11:14 7阅读 0赞

题目链接：[http://poj.org/problem?id=1329][http_poj.org_problem_id_1329]

1 #include<cstdio>
      2 #include<cmath>
      3 #include<algorithm>
      4 #include<iostream>
      5 #include<cstring>
      6 using namespace std;
      7 typedef long long ll;
      8 const double eps = 1e-8;
      9 int sgn(double x)
     10 {
     11     if(fabs(x) < eps) return 0;
     12     else return x < 0 ? -1 : 1;
     13 }
     14 struct Point{
     15     double x, y;
     16     Point(){}
     17     Point(double _x, double _y){
     18         x = _x, y = _y;
     19     }
     20     bool operator == (Point b) const{
     21         return sgn(x - b.x) == 0 && sgn(y - b.y) == 0;
     22     }
     23     bool operator < (Point b)const{
     24         return sgn(x - b.x) == 0 ? sgn(y - b.y < 0) : x < b.x;
     25     }
     26     Point operator - (const Point &b)const{
     27         return Point(x - b.x, y - b.y);
     28     }
     29     //叉积
     30     double operator ^(const Point &b){
     31         return x * b.y - y * b.x;
     32     }
     33     //点积
     34     double operator *(const Point &b){
     35         return x * b.x + y * b.y;
     36     }
     37     double len(){
     38         return hypot(x, y);
     39     }
     40     double len2(){
     41     return x * x + y * y;
     42     }
     43     double distant(Point p){
     44         return hypot(x - p.x, y - p.y);
     45     }
     46     Point operator + (const Point &b)const{
     47         return Point (x + b.x, y + b.y);
     48     }
     49     Point operator * (const double &k)const{
     50         return Point(x * k, y * k);
     51     }
     52     Point operator / (const double &k)const{
     53         return Point(x / k, y / k);
     54     }
     55     //逆时针旋转90度
     56     Point rotleft(){
     57         return Point(- y, x);
     58     }
     59     //顺时针旋转90度
     60     Point rotright(){
     61         return Point(y, -x);
     62     }
     63 };
     64 struct Line{
     65     Point s, e;
     66     Line(){}
     67     Line(Point _s, Point _e){s = _s, e = _e;}
     68     Point crosspoint(Line v){
     69         double a1 = (v.e - v.s)^(s - v.s);
     70         double a2 = (v.e - v.s)^(e - v.s);
     71         return Point((s.x*a2 - e.x*a1)/(a2 - a1),(s.y*a2 - e.y*a1)/(a2 - a1));
     72     }
     73 };
     74 struct circle{
     75     Point p;
     76     double r;
     77     circle(){}
     78     circle(Point _p, double _r){
     79         p = _p, r = _r;
     80     }
     81     circle(double x, double y, double _r){
     82         p = Point(x, y);
     83         r = _r;
     84     }
     85     //三角形外接圆
     86     circle(Point a, Point b, Point c){
     87         Line u = Line( (a + b) / 2,((a + b) / 2) + ((b - a).rotleft()) );
     88         Line v = Line( (b + c) / 2,((b + c) / 2) + ((c - b).rotleft()) );
     89         p = u.crosspoint(v);
     90         r = p.distant(a);
     91     }
     92 };
     93 void print(double num) {
     94     if (sgn(num) < 0) {
     95             printf("- "); num = -num;
     96     }
     97     else printf("+ ");
     98     printf("%.3f", num);
     99 }
    100 int main()
    101 {
    102     double x1, x2, x3, y1, y2, y3;
    103     while(~scanf("%lf%lf%lf%lf%lf%lf",&x1, &y1, &x2, &y2, &x3, &y3))
    104     {
    105         circle a = circle(Point(x1, y1), Point(x2, y2), Point(x3, y3));
    106         double c = a.r * a.r - (a.p.x * a.p.x + a.p.y * a.p.y);
    107         if (sgn(a.p.x) == 0)printf("x^2");
    108         else { printf("(x "); print(-a.p.x); printf(")^2"); }
    109         printf(" + ");
    110         if (sgn(a.p.y) == 0)printf("y^2");
    111         else { printf("(y "); print(-a.p.y); printf(")^2"); }
    112         printf(" = %.3f^2\n", a.r);
    113         printf("x^2 + y^2 ");
    114         print(-a.p.x * 2.0);
    115         printf("x ");
    116         print(-a.p.y * 2.0);
    117         printf("y ");
    118         print(-c);
    119         printf(" = 0\n");
    120         printf("\n");
    121     }
    122     return 0;
    123 }

转载于:https://www.cnblogs.com/Carered/p/11406704.html

[http_poj.org_problem_id_1329]: http://poj.org/problem?id=1329