HDU 1221 Rectangle and Circle(判断圆与矩形是否相交)
2013-07-26 10:46
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这个题目算是比较简单的题目,但是过的人不是很多,AC率也不是很高,主要是这个问题要注意和多细节,卡精度倒也没那么严格
1、如果矩形的四个顶点到圆心的距离全部大于半径,那么显然不会相交(很多人都死在这里)
2、把圆圆心按照矩形的边滚一圈,圆所覆盖的区域,只要圆心在这个区域内部就符合相交的条件
具体判断见下面代码三种情况,离横边距离,竖边距离,和四个顶点的距离
#include <iostream>
#include <string.h>
#include <stdio.h>
#include <algorithm>
#include <cmath>
#define eps 1e-8
using namespace std;
struct point
{
double x;
double y;
}circle,a,b,c,d;
double r;
double dis(point &a,point &b)
{
return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
int main()
{
int t;
scanf("%d",&t);
point temp;
while(t--)
{
scanf("%lf%lf%lf%lf%lf%lf%lf",&circle.x,&circle.y,&r,&a.x,&a.y,&b.x,&b.y);
if(a.x > b.x)
temp=a,a=b,b=temp;
// if(((circle.x >= min(a.x,b.x)) && (circle.x <=max(a.x,b.x))) && ((circle.y <=max(a.y,b.y)) && (circle.y>=min(a.y,b.y))))
// { printf("YES\n");continue;}
c.x=a.x,c.y=b.y;
d.x=b.x,d.y=a.y;
if(dis(a,circle)<r && dis(b,circle) <r && dis(c,circle)<r && dis(d,circle) <r)
{printf("NO\n");continue;}
if(circle.x>=a.x && circle.x<=b.x)
{
if(fabs(circle.y-a.y) <= r || fabs(circle.y-b.y) <= r)
{printf("YES\n");continue;}
}
if((circle.y >= a.y && circle.y <=b.y) || (circle.y>=b.y && circle.y<=a.y))
{
if(fabs(circle.x-a.x) <=r || fabs(circle.x-b.x) <=r)
{printf("YES\n");continue;}
}
if(dis(a,circle)<=r || dis(b,circle) <=r || dis(c,circle)<=r || dis(d,circle) <=r)
{printf("YES\n");continue;}
printf("NO\n");
}
return 0;
}
1、如果矩形的四个顶点到圆心的距离全部大于半径,那么显然不会相交(很多人都死在这里)
2、把圆圆心按照矩形的边滚一圈,圆所覆盖的区域,只要圆心在这个区域内部就符合相交的条件
具体判断见下面代码三种情况,离横边距离,竖边距离,和四个顶点的距离
#include <iostream>
#include <string.h>
#include <stdio.h>
#include <algorithm>
#include <cmath>
#define eps 1e-8
using namespace std;
struct point
{
double x;
double y;
}circle,a,b,c,d;
double r;
double dis(point &a,point &b)
{
return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
int main()
{
int t;
scanf("%d",&t);
point temp;
while(t--)
{
scanf("%lf%lf%lf%lf%lf%lf%lf",&circle.x,&circle.y,&r,&a.x,&a.y,&b.x,&b.y);
if(a.x > b.x)
temp=a,a=b,b=temp;
// if(((circle.x >= min(a.x,b.x)) && (circle.x <=max(a.x,b.x))) && ((circle.y <=max(a.y,b.y)) && (circle.y>=min(a.y,b.y))))
// { printf("YES\n");continue;}
c.x=a.x,c.y=b.y;
d.x=b.x,d.y=a.y;
if(dis(a,circle)<r && dis(b,circle) <r && dis(c,circle)<r && dis(d,circle) <r)
{printf("NO\n");continue;}
if(circle.x>=a.x && circle.x<=b.x)
{
if(fabs(circle.y-a.y) <= r || fabs(circle.y-b.y) <= r)
{printf("YES\n");continue;}
}
if((circle.y >= a.y && circle.y <=b.y) || (circle.y>=b.y && circle.y<=a.y))
{
if(fabs(circle.x-a.x) <=r || fabs(circle.x-b.x) <=r)
{printf("YES\n");continue;}
}
if(dis(a,circle)<=r || dis(b,circle) <=r || dis(c,circle)<=r || dis(d,circle) <=r)
{printf("YES\n");continue;}
printf("NO\n");
}
return 0;
}
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