#pragma comment(linker, "/STACK:1024000000,1024000000") #include #include #include #include #include #include #include #include #include #include #include #define FIR first #define SEC second #define MP make_pair #define inf 0x3f3f3f3f #define LL long long #define CLR(a, b) memset(a, b, sizeof(a)) using namespace std; struct Point { double x, y; Point(double x = 0, double y = 0) :x(x), y(y) {} }; double EP = 0; double x_mult(Point sp, Point ep, Point op){ return (sp.x-op.x)*(ep.y-op.y)-(sp.y-op.y)*(ep.x-op.x); } double cross(Point a,Point b,Point c){ return (a.x-c.x)*(b.x-c.x)+(a.y-c.y)*(b.y-c.y); } double dist(Point a,Point b){ return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y)); } double cal_area(Point a,Point b,Point c,double r){ double A,B,C,x,y,tS; A=dist(b,c); B=dist(a,c); C=dist(b,a); if(A=r){ x=(cross(a,c,b)+sqrt(r*r*C*C-x_mult(a,c,b)*x_mult(a,c,b)))/C; tS=x_mult(a,b,c)/2; return asin(tS*(1-x/C)*2/r/B*(1-EP))*r*r/2+tS*x/C; } else if(A>=r&&B=r*C||cross(b,c,a)<=0||cross(a,c,b)<=0){ if(cross(a,b,c)<0) if(x_mult(a,b,c)<0) return (-acos(-1.0)-asin(x_mult(a,b,c)/A/B*(1-EP)))*r*r/2; else return (acos(-1.0)-asin(x_mult(a,b,c)/A/B*(1-EP)))*r*r/2; else return asin(x_mult(a,b,c)/A/B*(1-EP))*r*r/2; } else{ x=(cross(a,c,b)+sqrt(r*r*C*C-x_mult(a,c,b)*x_mult(a,c,b)))/C; y=(cross(b,c,a)+sqrt(r*r*C*C-x_mult(b,c,a)*x_mult(b,c,a)))/C; tS=x_mult(a,b,c)/2; return (asin(tS*(1-x/C)*2/r/B*(1-EP))+asin(tS*(1-y/C)*2/r/A*(1-EP)))*r*r/2+tS*((y+x)/C-1); } } double solve(Point p[], int n, Point cir, double r){ double area=0; for(int i=0;i> v0 >> v1 >> D >> T) { printf("Case %d: ", cas ++); Point cir = Point(-D, 0); double r = v0 * T; if(v0 * T <= D) { printf("%.7f\n", pi * r * r); continue; } double lft = D / v0, rgt = T; for(int i = 0; i < 100; i ++) { double mid = (lft + rgt) / 2; double midmid = (mid + rgt) / 2; double _mid = sqrt((v0 * mid) * (v0 * mid) - D * D) + v1 * (T - mid); double _midmid = sqrt((v0 * midmid) * (v0 * midmid) - D * D) + v1 * (T - midmid); if(_mid > _midmid) rgt = midmid; else lft = mid; } double t = (lft + rgt) / 2; double y = sqrt((v0 * t) * (v0 * t) - D * D) + v1 * (T - t); double x1 = T / t * D, y1 = sqrt(v0 * T * v0 * T - x1 * x1); x1 -= D; Point p[8]; p[0] = Point(0, y); p[1] = Point(x1, y1); p[2] = Point(x1, -y1); p[3] = Point(0, -y); p[4] = Point(-x1, -y1); p[5] = Point(-x1, y1); p[6] = p[0]; double ans = solve(p, 6, cir, r); ans = pi * r * r + x1 * y1 * 4 + x1 * (y - y1) * 2 - fabs(ans); printf("%.7f\n", ans); } }