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今天无事水一水,结果就看到这个水题了!
题意思是 有俩个区域如图
求在俩个圆之间的运动时间 给出 初始的开始点和速度的矢量式;而且这个点 不再俩个圆之间的区域,且碰到内测园会反弹:
在大大物实验的时候记得学过为了减少误差 和简易计算可以:把这个小圆看成质点,并把固定园的半径加上小圆的半径。
其实就是求 与俩个圆与射线的交点! 代码如下:()
#include <cstring>
#include <cmath>
#include <algorithm>
#include <cstdlib>
#include <cstdio>
using namespace std;
struct point
{
double x,y;
point (double x=0,double y=0):x(x),y(y){}
};
typedef point Vector;
const double eps=1e-8;
int dcmp(double x)
{
if(fabs(x)<eps) return 0;
return x<0?-1:1;
}
Vector operator + (Vector a,Vector b){return Vector(a.x+b.x,a.y+b.y);}
Vector operator - (Vector a,Vector b){return Vector(a.x-b.x,a.y-b.y);}
Vector operator * (Vector a,double b){return Vector(a.x*b,a.y*b);} double det(Vector a,Vector b){return a.x*b.y-a.y*b.x;}
double dot(Vector a,Vector b){return a.x*b.x+a.y*b.y;}
double lenth(Vector a){return sqrt(dot(a,a));}
struct line
{
point p;
Vector v;
double angle;
line(){}
line(point p,Vector v):p(p),v(v){}
bool operator <(const line &rht)const
{
return angle<rht.angle;
}
};
struct circle
{
point c;
double r;
circle(){c=point(0.0,0.0);}
circle(point c,double r):c(c),r(r){}
point Point(double rad)
{
return point(c.x+cos(rad)*r,c.y+sin(rad)*r);
}
};
int get_circle_intersection(line L,circle C,double &t1,double &t2)
{
t1=t2=0;
double a=L.v.x, b=L.p.x-C.c.x,c=L.v.y,d=L.p.y-C.c.y; double e=a*a+c*c,f=2*(a*b+c*d),g=b*b+d*d-C.r*C.r; double detle = f*f-4*e*g; if(dcmp(detle)<0) return 0;
if(dcmp(detle)==0) {t1=t2=-f/(2*e);return 1;}
t1=(-f-sqrt(detle)) /(2*e);
t2=(-f+sqrt(detle)) /(2*e);
if(dcmp(t1)<0 || dcmp(t2)<0) return 0;//按照速度的反方向才可以和圆相交
return 2;
}
int main()
{
double t1,t2;
double x1,x2;
line tmp;
circle tmp1;
circle tmp2;
double Rm, R, r;
while(~scanf("%lf %lf %lf %lf %lf %lf %lf",&Rm,&R,&r,&tmp.p.x,&tmp.p.y,&tmp.v.x,&tmp.v.y))
{
Rm+=r;R+=r;
tmp1.r=Rm;
tmp2.r=R;
int count1=get_circle_intersection(tmp,tmp1,t1,t2);
int count2=get_circle_intersection(tmp,tmp2,x1,x2);
if(count2==0)printf("0.00\n");
else
printf("%.3lf\n",fabs(x2-x1)-fabs(t1-t2));// 因为直线式点+向量(和速度一样)所以减法就可以了
}
return 0;
}