在平面上0,0点,有一个半径为R的圆形区域,并且在0,0点固定着一个半径为RM(<R)的圆形障碍物,现在圆形区域外x,y,有一个半径为r的,并且速度为vx,vy的硬币,如果硬币碰到了障碍物,将会保持原有的速度向反射的方向继续前进,现在给出R,RM,r,x,y,vx,vy,问硬币的任意部分在圆形区域中滑行多少时间?
首先把R,RM加上r,就可以把硬币看做一个点来讨论了,然后算一下射线与这两个圆交点的个数,记作C1,C2,CM1,CM2,若与两个圆的交点数都是2,答案就是dis(c1,c2)-dis(cm1,cm2)之后再除以合成后的速度,若与大圆的交点数为2,小圆的交点数是0或者1,答案就是dis(c1,c2)/合成后的速度,否则肯定是0了.
#include<iostream> #include<cstdio> #include<cstring> #include<string> #include<algorithm> #include<map> #include<queue> #include<set> #include<stack> #include<cmath> #include<vector> #define inf 0x3f3f3f3f #define Inf 0x3FFFFFFFFFFFFFFFLL #define eps 1e-9 #define pi acos(-1.0) using namespace std; typedef long long ll; int dcmp(double x) { return (x>eps)-(x<-eps);} typedef struct Point { double x, y; Point(double x = 0, double y = 0) : x(x), y(y){} Point operator+(const Point& p) const { return Point(x+p.x, y+p.y );} Point operator-(const Point& p) const { return Point(x-p.x, y-p.y );} Point operator*(const double d) const { return Point(x*d, y*d );} Point operator/(const double d) const { return Point(x/d, y/d );} void read() { scanf("%lf%lf", &x, &y);} }Vector; inline double Dis(const Point& a, const Point& b) { return sqrt((a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y)); } struct Line { Point P; Vector v; double ang; Line(){} Line(const Point& P, const Vector& v):P(P),v(v){ang = atan2(v.y,v.x);} bool operator<(const Line& L) const { return ang<L.ang; } Point point(double t) { return P+v*t; } }; struct Circle { Point c; double r; Circle(){} }; int GetLineCircleIntersection(Line L, Circle C, double &t1, double &t2, vector<Point> &sol) { 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 delta = f*f-4*e*g; if(dcmp(delta)<0) return 0; if(dcmp(delta)==0) { t1 = t2 = -f/(2*e); sol.push_back(L.point(t1)); return 1; } t1 = (-f-sqrt(delta))/(2*e);sol.push_back(L.point(t1)); t2 = (-f+sqrt(delta))/(2*e);sol.push_back(L.point(t2)); if(dcmp(t1)<0 || dcmp(t2)<0) return 0; return 2; } double R,RM,r,x,y,vx,vy; int n,m,k; int main() { // freopen("in.txt","r",stdin); while(~scanf("%lf%lf%lf%lf%lf%lf%lf",&RM,&R,&r,&x,&y,&vx,&vy)) { Line l1(Point(x,y),Point(vx,vy)); Circle c1,c2; c1.r=RM+r; c1.c.x=c1.c.y=0.0; c2.c.x=c2.c.y=0.0; c2.r=R+r; double db1=0.0,db2=0.0; vector<Point> crs1; vector<Point> crs2; int num2=GetLineCircleIntersection(l1,c1,db1,db2,crs2); int num1=GetLineCircleIntersection(l1,c2,db1,db2,crs1); double len=0.0,ans=0.0; double vv=sqrt(vx*vx+vy*vy); if (num1==2 && num2==2) { len=Dis(crs1[0],crs1[1])-Dis(crs2[0],crs2[1]); printf("%.4lf\n",len/vv); } else if (num1==2) { len=Dis(crs1[0],crs1[1]); printf("%.4lf\n",len/vv); } else { puts("0.0000"); } } return 0; }