hdu 4404 Worms（多边形与圆的交）

求出爆炸点的坐标，就成了多边形与圆相交面积的模板题了。。。

 

#include<algorithm>

#include<iostream>

#include<cstring>

#include<fstream>

#include<sstream>

#include<vector>

#include<string>

#include<cstdio>

#include<bitset>

#include<queue>

#include<stack>

#include<cmath>

#include<map>

#include<set>

#define FF(i, a, b) for(int i=a; i<b; i++)

#define FD(i, a, b) for(int i=a; i>=b; i--)

#define REP(i, n) for(int i=0; i<n; i++)

#define CLR(a, b) memset(a, b, sizeof(a))

#define LL long long

#define PB push_back

#define eps 1e-10

#define debug puts("**debug**")

using namespace std;



const int maxn = 110;

const double PI = acos(-1);

struct Point

{

    double x, y;

    Point (double x=0, double y=0):x(x), y(y) {}

};

typedef Point Vector;

struct Circle

{

   Point c;

   double r;

   Circle() {}

   Circle(Point c, double r) : c(c), r(r) {}

   Point point(double a) { return Point(c.x+cos(a)*r, c.y+sin(a)*r); }

};

struct Line

{

    Point p;

    Vector v;

    double ang;

    Line(){}

    Line(Point p, Vector v) : p(p), v(v) {ang = atan2(v.y, v.x); }

    Point point(double t)

    {

        return Point(p.x + t*v.x, p.y + t*v.y);

    }

    bool operator < (const Line& L) const

    {

        return ang < L.ang;

    }

};



template <class T> T sqr(T x) { return x * x;}

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 p) { return Vector(A.x*p, A.y*p); }

Vector operator / (Vector A, double p) { return Vector(A.x/p, A.y/p); }

bool operator < (const Point& a, const Point& b) { return a.x < b.x || (a.x == b.x && a.y < b.y); }

int dcmp(double x)

{

    if(fabs(x) < eps) return 0;

    return x < 0 ? -1 : 1;

}

bool operator == (const Point& a, const Point& b){ return dcmp(a.x-b.x) == 0 && dcmp(a.y-b.y) == 0;}



double Dot(Vector A, Vector B) { return A.x*B.x + A.y*B.y; }

double Length(Vector A) { return sqrt(Dot(A, A)); }

double Angel(Vector A, Vector B) { return acos(Dot(A, B) / Length(A) / Length(B)); }

double Cross(Vector A, Vector B) { return A.x*B.y - A.y*B.x; }

double torad(double d) { return (d/180)*PI; }

Vector vecunit(Vector x){ return x / Length(x);} //单位向量

Vector normal(Vector x) { return Point(-x.y, x.x) / Length(x);} //垂直法向量

Point GetIntersection(Line a, Line b) //线段交点

{

    Vector u = a.p-b.p;

    double t = Cross(b.v, u) / Cross(a.v, b.v);

    return a.p + a.v*t;

}

bool OnSegment(Point p, Point a1, Point a2)

{

    return dcmp(Cross(a1-p, a2-p)) == 0 && dcmp(Dot(a1-p, a2-p)) < 0;

}



bool InCircle(Point x, Circle c) { return dcmp(sqr(c.r) - sqr(Length(c.c - x))) >= 0;}

bool OnCircle(Point x, Circle c) { return dcmp(sqr(c.r) - sqr(Length(c.c - x))) == 0;}

double angle(Vector x) { return atan2(x.y, x.x);}



//直线与圆交点

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.PB(L.point(t1));

        return 1;

    }

    t1 = (-f-sqrt(delta))/(2*e); sol.PB(L.point(t1));

    t2 = (-f+sqrt(delta))/(2*e); sol.PB(L.point(t2));

    return 2;

}



//线段与圆的焦点

int getSegCircleIntersection(Line L, Circle C, Point* sol) 

{

    Vector nor = normal(L.v);

    Line pl = Line(C.c, nor);

    Point ip = GetIntersection(pl, L);

    double dis = Length(ip - C.c);

    if (dcmp(dis - C.r) > 0) return 0;

    Point dxy = vecunit(L.v) * sqrt(sqr(C.r) - sqr(dis));

    int ret = 0;

    sol[ret] = ip + dxy;

    if (OnSegment(sol[ret], L.p, L.point(1))) ret++;

    sol[ret] = ip - dxy;

    if (OnSegment(sol[ret], L.p, L.point(1))) ret++;

    return ret;

}



double SegCircleArea(Circle C, Point a, Point b) //线段切割圆

{

    double a1 = angle(a - C.c);

    double a2 = angle(b - C.c);

    double da = fabs(a1 - a2);

    if (da > PI) da = PI * 2.0 - da;

    return dcmp(Cross(b - C.c, a - C.c)) * da * sqr(C.r) / 2.0;

}



double PolyCiclrArea(Circle C, Point *p, int n)//多边形与圆相交面积

{

    double ret = 0.0;

    Point sol[2];

    p[n] = p[0];

    REP(i, n)

    {

        double t1, t2;

        int cnt = getSegCircleIntersection(Line(p[i], p[i+1]-p[i]), C, sol);

        if (cnt == 0)

        {

            if (!InCircle(p[i], C) || !InCircle(p[i+1], C)) ret += SegCircleArea(C, p[i], p[i+1]);

            else ret += Cross(p[i+1] - C.c, p[i] - C.c) / 2.0;

        }

        if (cnt == 1)

        {

            if (InCircle(p[i], C) && !InCircle(p[i+1], C)) ret += Cross(sol[0] - C.c, p[i] - C.c) / 2.0, ret += SegCircleArea(C, sol[0], p[i+1]);

            else ret += SegCircleArea(C, p[i], sol[0]), ret += Cross(p[i+1] - C.c, sol[0] - C.c) / 2.0;

        }

        if (cnt == 2)

        {

            if ((p[i] < p[i + 1]) ^ (sol[0] < sol[1])) swap(sol[0], sol[1]);

            ret += SegCircleArea(C, p[i], sol[0]);

            ret += Cross(sol[1] - C.c, sol[0] - C.c) / 2.0;

            ret += SegCircleArea(C, sol[1], p[i+1]);

        }

    }

    return fabs(ret);

}



int n;

double x, y, v, ang, t, g, r;

Circle C;

Point p[maxn];



int main()

{

    while (scanf("%lf%lf%lf%lf%lf%lf%lf", &x, &y, &v, &ang, &t, &g, &r))

    {

      if(x == 0 && y == 0 && v == 0 && ang == 0 && t == 0 &&  g == 0 && r == 0) break;

      ang = torad(ang);

      C = Circle(Point(x + v*cos(ang)*t, y + v*sin(ang)*t - 0.5*g*t*t), r);



      scanf("%d", &n);

      REP(i, n) scanf("%lf%lf", &p[i].x, &p[i].y);

      printf("%.2f\n", PolyCiclrArea(C, p, n));

    }

    return 0;

}