hdoj.2892 area【计算几何+圆与多边形相交面积】 2015/08/17
2015-08-17 17:43
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area
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 743 Accepted Submission(s): 289
[align=left]Problem Description[/align]
小白最近被空军特招为飞行员,参与一项实战演习。演习的内容是轰炸某个岛屿。。。
作为一名优秀的飞行员,任务是必须要完成的,当然,凭借小白出色的操作,顺利地将炸弹投到了岛上某个位置,可是长官更关心的是,小白投掷的炸弹到底摧毁了岛上多大的区域?
岛是一个不规则的多边形,而炸弹的爆炸半径为R。
小白只知道自己在(x,y,h)的空间坐标处以(x1,y1,0)的速度水平飞行时投下的炸弹,请你计算出小白所摧毁的岛屿的面积有多大. 重力加速度G = 10.
[align=left]Input[/align]
首先输入三个数代表小白投弹的坐标(x,y,h);
然后输入两个数代表飞机当前的速度(x1, y1);
接着输入炸弹的爆炸半径R;
再输入一个数n,代表岛屿由n个点组成;
最后输入n行,每行输入一个(x',y')坐标,代表岛屿的顶点(按顺势针或者逆时针给出)。(3<= n < 100000)
[align=left]Output[/align]
输出一个两位小数,表示实际轰炸到的岛屿的面积。
[align=left]Sample Input[/align]
0 0 2000 100 0 100 4 1900 100 2000 100 2000 -100 1900 -100
[align=left]Sample Output[/align]
15707.96
[align=left]Source[/align]
2009 Multi-University Training Contest 10 - Host by NIT
注:圆与多边形相交面积模板题,根据题中信息可以求出导弹落到岛上时的坐标,即爆炸圆心
#include<iostream> #include<cstdio> #include<cmath> #include<cstdlib> using namespace std; const double eps = 1e-8; const double PI = acos(-1.0); int dcmp(double x){ if( x > eps ) return 1; return x < -eps ? -1 : 0; } struct Point{ double x,y; Point(){ x = y = 0; } Point(double a,double b){ x = a;y = b; } inline void input(){ scanf("%lf%lf",&x,&y); } inline Point operator-(const Point &b)const{ return Point(x - b.x,y - b.y); } inline Point operator+(const Point &b)const{ return Point(x + b.x,y + b.y); } inline Point operator*(const double &b)const{ return Point(x * b,y * b); } inline double dot(const Point &b)const{ return x * b.x + y * b.y; } inline double cross(const Point &b,const Point &c)const{ return (b.x - x) * (c.y - y) - (c.x - x) * (b.y - y); } inline double Dis(const Point &b)const{ return sqrt((*this-b).dot(*this-b)); } inline bool InLine(const Point &b,const Point &c)const{ //三点共线 return !dcmp(cross(b,c)); } inline bool OnSeg(const Point &b,const Point &c)const{ //点在线段上,包括端点 return InLine(b,c) && (*this - c).dot(*this - b) < eps; } }; inline double min(double a,double b){ return a < b ? a : b; } inline double max(double a,double b){ return a > b ? a : b; } inline double Sqr(double x){ return x * x; } inline double Sqr(const Point &p){ return p.dot(p); } Point LineCross(const Point &a,const Point &b,const Point &c,const Point &d){ double u = a.cross(b,c) , v = b.cross(a,d); return Point((c.x * v + d.x * u) / (u + v) , (c.y * v + d.y * u) / (u + v)); } double LineCrossCircle(const Point &a,const Point &b,const Point &r, double R,Point &p1,Point & p2){ Point fp = LineCross(r , Point(r.x+a.y-b.y , r.y+b.x-a.x) , a , b); double rtol = r.Dis(fp); double rtos = fp.OnSeg(a , b) ? rtol : min(r.Dis(a) , r.Dis(b)); double atob = a.Dis(b); double fptoe = sqrt(R * R - rtol * rtol) / atob; if( rtos > R - eps ) return rtos; p1 = fp + (a - b) * fptoe; p2 = fp + (b - a) * fptoe; return rtos; } double SectorArea(const Point &r,const Point &a,const Point &b,double R){ //不大于180度扇形面积,r->a->b逆时针 double A2 = Sqr(r - a) , B2 = Sqr(r - b) , C2 = Sqr(a - b); return R * R * acos( (A2 + B2 - C2) * 0.5 / sqrt(A2) / sqrt(B2)) * 0.5; } double TACIA(const Point &r,const Point &a,const Point &b,double R){ double adis = r.Dis(a) , bdis = r.Dis(b); if( adis < R + eps && bdis < R + eps ) return r.cross(a , b) * 0.5; Point ta , tb; if( r.InLine(a,b) ) return 0.0; double rtos = LineCrossCircle(a, b, r, R, ta, tb); if( rtos > R - eps ) return SectorArea(r, a, b, R); if( adis < R + eps ) return r.cross(a, tb) * 0.5 + SectorArea(r, tb, b, R); if( bdis < R + eps ) return r.cross(ta, b) * 0.5 + SectorArea(r, a, ta, R); return r.cross(ta, tb) * 0.5 + SectorArea(r, tb, b, R) + SectorArea(r, a, ta, R); } const int MAXN = 100010; Point p[MAXN]; double SPICA(int n,Point r,double R){ int i; double ret = 0 , if_clock_t; for( i = 0 ; i < n ; ++i ){ if_clock_t = dcmp(r.cross(p[i], p[(i + 1) % n])); if( if_clock_t < 0 ) ret -= TACIA(r, p[(i + 1) % n], p[i], R); else ret += TACIA(r, p[i], p[(i + 1) % n], R); } return fabs(ret); } int main(){ double xa,xb,ya,yb,h,r; int n,i; while( ~scanf("%lf%lf%lf",&xa,&ya,&h) ){ scanf("%lf%lf",&xb,&yb); double t = sqrt(h/5.0); Point circle = Point( (xa+t*xb) , (ya+t*yb) ); scanf("%lf",&r); scanf("%d",&n); for( i = 0 ; i < n ; ++i ) p[i].input(); printf("%.2lf\n",SPICA(n,circle,r)); } return 0; }
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