poj1266Cover an Arc（三角形外接圆）

链接

求出三角形的外接圆，通过圆心和半径可以知道这个圆的上下左右最远点，分别判断这个四个点跟弧的两端点A,B的关系，假如判断P点，弧内给出点为C，判断PC是否与AB相交即可判断出P是否在弧上。

精度问题 ceil-eps floor+eps

 #include <iostream>
 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 #include<stdlib.h>
 #include<vector>
 #include<cmath>
 #include<queue>
 #include<set>
 using namespace std;
 #define N 100000
 #define LL long long
 #define INF 0xfffffff
 const double eps = 1e-;
 const double pi = acos(-1.0);
 const double inf = ~0u>>;
 struct Point
 {
     double x,y;
     Point(double x=,double y=):x(x),y(y) {}
 }p[];
 typedef Point pointt;
 pointt operator + (Point a,Point b)
 {
      return Point(a.x+b.x,a.y+b.y);
 }
 pointt operator - (Point a,Point b)
 {
         return Point(a.x-b.x,a.y-b.y);
 }
 int dcmp(double x)
 {
     if(fabs(x)<eps) return ;
     else return x<?-:;
 }
 struct Circle
 {
     Point center;
     double r;
 };
 double cross(Point a,Point b)
 {
     return a.x*b.y-a.y*b.x;
 }
 double mul(Point p0,Point p1,Point p2)
 {
     return cross(p1-p0,p2-p0);
 }
 double dis(Point a)
 {
     return a.x*a.x+a.y*a.y;
 }
 double area()
 {
     return fabs(cross(p[]-p[],p[]-p[]))/;
 }
 bool seginter(pointt a1,pointt a2,pointt b1,pointt b2)
 {
      double c1 = cross(a2-a1,b1-a1),c2 = cross(a2-a1,b2-a1),
             c3 = cross(b2-b1,a1-b1),c4 = cross(b2-b1,a2-b1);
      return dcmp(c1)*dcmp(c2)<&&dcmp(c3)*dcmp(c4)<;
 }
 struct Circle Circumcircle()
 {
     Circle tmp;
     double a,b,c,c1,c2;
     double xa,ya,xb,yb,xc,yc;
     a = sqrt(dis(p[]-p[]));
     b = sqrt(dis(p[]-p[]));
     c = sqrt(dis(p[]-p[]));
     //根据s = a*b*c/R/4，求半径
     tmp.r = (a*b*c)/(area()*4.0);
     xa = p[].x;
     ya = p[].y;
     xb = p[].x;
     yb = p[].y;
     xc = p[].x;
     yc = p[].y;
     c1 = (dis(p[])-dis(p[]))/;
     c2 = (dis(p[])-dis(p[]))/;
     tmp.center.x = (c1*(ya-yc)-c2*(ya-yb))/((xa-xb)*(ya-yc)-(xa-xc)*(ya-yb));
     tmp.center.y = (c1*(xa-xc)-c2*(xa-xb))/((ya-yb)*(xa-xc)-(ya-yc)*(xa-xb));
     return tmp;
 }
 int main()
 {
     int i;
     double r;
     int w0,w1,h0,h1;
     for(i = ; i <=  ; i++)
     scanf("%lf%lf",&p[i].x,&p[i].y);
     Circle cc = Circumcircle();
     r = cc.r;

     Point q[];
     for(i =  ;i <  ;i++)
     q[i] = cc.center;
     q[].x-=r,q[].x+=r,q[].y-=r,q[].y+=r;

     if(!seginter(q[],p[],p[],p[])) w0 = floor(q[].x+eps);
     else w0 = floor(min(p[].x,p[].x)+eps);

     if(!seginter(q[],p[],p[],p[]))  w1 = ceil(q[].x-eps);
     else w1 = ceil(max(p[].x,p[].x)-eps);

     if(!seginter(q[],p[],p[],p[])) h0 = floor(q[].y+eps);
     else h0 = floor(min(p[].y,p[].y)+eps);

     if(!seginter(q[],p[],p[],p[])) h1 = ceil(q[].y-eps);
     else h1 = ceil(max(p[].y,p[].y)-eps);

     printf("%d\n",(h1-h0)*(w1-w0));
     return ;
 }