csu 1812（半平面交求面积）

题目链接：

http://acm.csu.edu.cn/csuoj/problemset/problem?pid=1812

题解：

用半平面交求出三角形和矩形的交的点集，然后用叉积就可以求出面积了，注意需要逆时针输入多边形的点

AC代码：

#include 
using namespace std;

typedef complex<double> Point;
typedef pair Halfplane;
typedef vector Convex;//多边形

const double EPS = 1e-10;

inline int sgn(double n) { return fabs(n) < EPS ? 0 : (n < 0 ? -1 : 1); }
inline double det(Point a, Point b) { return (conj(a)*b).imag(); }
inline double dot(Point a, Point b) { return (conj(a)*b).real(); }
inline double onLeft(Point a, Halfplane p) {
    return sgn(det(a - p.first, p.second - p.first)) <= 0;
}

Point crossPoint(const Halfplane& a, const Halfplane& b) {
    double k = det(b.first - b.second, a.first - b.second);
    k = k / (k - det(b.first - b.second, a.second - b.second));
    return a.first + (a.second - a.first) * k;
}

bool cmp(const Halfplane& a, const Halfplane& b) {
    int res = sgn(arg(a.second - a.first) - arg(b.second - b.first));
    return res == 0 ? onLeft(a.first, b) : res < 0;
}

vector halfplaneIntersection(vector v) {
    sort(v.begin(), v.end(), cmp);
    deque ans; deque q;
    q.push_back(v[0]);
    for(int i = 1; i < int(v.size()); ++i) {
        if(sgn(arg(v[i].second - v[i].first) - arg(v[i-1].second - v[i-1].first)) == 0) continue;
        while(ans.size() > 0 && !onLeft(ans.back(), v[i])) ans.pop_back(), q.pop_back();
        while(ans.size() > 0 && !onLeft(ans.front(), v[i])) ans.pop_front(), q.pop_front();
        ans.push_back(crossPoint(q.back(), v[i]));
        q.push_back(v[i]);
    }
    while(ans.size() > 0 && !onLeft(ans.back(), q.front())) ans.pop_back(), q.pop_back();
    while(ans.size() > 0 && !onLeft(ans.front(), q.back())) ans.pop_front(), q.pop_front();
    ans.push_back(crossPoint(q.back(), q.front()));
    return vector(ans.begin(), ans.end());
}

double x1,yy1,x2,y2;
double x3,y3,x4,y4;

int main()
{
    while(~scanf("%lf %lf %lf %lf", &x1, &yy1, &x2, &y2))
    {
        Convex tri,rect;
        tri.push_back(Point(x1,yy1));
        if((x2 >= x1 && y2 >= yy1) || (x2 <= x1 && y2 <= yy1))
        {
            tri.push_back(Point(x2,yy1));
            tri.push_back(Point(x1,y2));
        }
        else
        {
            tri.push_back(Point(x1,y2));
            tri.push_back(Point(x2,yy1));
        }
        scanf("%lf %lf %lf %lf", &x3, &y3, &x4, &y4);
        rect.push_back(Point(x3,y3));
        if((x4 >= x3 && y4 >= y3) || (x4 <= x3 && y4 <= y3))
        {
            rect.push_back(Point(x4,y3));
            rect.push_back(Point(x4,y4));
            rect.push_back(Point(x3,y4));
        }
        else
        {
            rect.push_back(Point(x3,y4));
            rect.push_back(Point(x4,y4));
            rect.push_back(Point(x4,y3));
        }
        vector  ans;
        for(int i = 0; i < tri.size(); i++)ans.push_back(Halfplane(tri[i], tri[(i+1) % tri.size()]));
        for(int i = 0; i < rect.size(); i++)ans.push_back(Halfplane(rect[i], rect[(i+1) % rect.size()]));
        vector ansans = halfplaneIntersection(ans);
        double ansarea = 0;
        for(int i = 1; i < ansans.size(); i++)
        {
            //cout << ansans[i] << " " <
            ansarea += det(ansans[i], ansans[i-1]);
        }
        //cout << ansans[0] << " " <
        ansarea += det(ansans[0], ansans[ansans.size()-1]);
        printf("%.8f\n", fabs(ansarea)/2);
    }
    return 0;
}