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-8;
const double pi = acos(-1.0);
const double inf = ~0u>>2;
struct Point
{
double x,y;
Point(double x=0,double y=0):x(x),y(y) {}
}p[4];
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 0;
else return x<0?-1:1;
}
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[1]-p[3],p[2]-p[3]))/2;
}
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)<0&&dcmp(c3)*dcmp(c4)<0;
}
struct Circle Circumcircle()
{
Circle tmp;
double a,b,c,c1,c2;
double xa,ya,xb,yb,xc,yc;
a = sqrt(dis(p[3]-p[1]));
b = sqrt(dis(p[1]-p[2]));
c = sqrt(dis(p[2]-p[3]));
//根据s = a*b*c/R/4，求半径
tmp.r = (a*b*c)/(area()*4.0);
xa = p[3].x;
ya = p[3].y;
xb = p[1].x;
yb = p[1].y;
xc = p[2].x;
yc = p[2].y;
c1 = (dis(p[3])-dis(p[1]))/2;
c2 = (dis(p[3])-dis(p[2]))/2;
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 = 1; i <= 3 ; i++)
scanf("%lf%lf",&p[i].x,&p[i].y);
Circle cc = Circumcircle();
r = cc.r;

Point q[5];
for(i = 1 ;i < 5 ;i++)
q[i] = cc.center;
q[1].x-=r,q[2].x+=r,q[3].y-=r,q[4].y+=r;

if(!seginter(q[1],p[3],p[1],p[2])) w0 = floor(q[1].x+eps);
else w0 = floor(min(p[1].x,p[2].x)+eps);

if(!seginter(q[2],p[3],p[1],p[2]))  w1 = ceil(q[2].x-eps);
else w1 = ceil(max(p[1].x,p[2].x)-eps);

if(!seginter(q[3],p[3],p[1],p[2])) h0 = floor(q[3].y+eps);
else h0 = floor(min(p[1].y,p[2].y)+eps);

if(!seginter(q[4],p[3],p[1],p[2])) h1 = ceil(q[4].y-eps);
else h1 = ceil(max(p[1].y,p[2].y)-eps);

printf("%d\n",(h1-h0)*(w1-w0));
return 0;
}

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