(三角剖分)三角形和矩形的面积交 2016湖南省赛

// (三角剖分)三角形和矩形的面积交 2016湖南省赛

#include <iostream>
#include <cstdio>
#include <cstring>
#include <stack>
#include <queue>
#include <cmath>
#include <algorithm>
using namespace std;

const int maxn = 555;
const int maxisn = 10;
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 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 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);
    }
};

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 PolygonArea(Point p[], int n) {
    if(n < 3) return 0.0;
    double s = p[0].y * (p[n - 1].x - p[1].x);
    p[n] = p[0];
    for(int i = 1; i < n; ++ i)
        s += p[i].y * (p[i - 1].x - p[i + 1].x);
    return fabs(s * 0.5);
}

double CPIA(Point a[], Point b[], int na, int nb) { //ConvexPolygonIntersectArea
    Point p[maxisn], tmp[maxisn];
    int i, j, tn, sflag, eflag;
    a[na] = a[0], b[nb] = b[0];
    memcpy(p, b, sizeof(Point) * (nb + 1));
    for(i = 0; i < na && nb > 2; ++ i) {
        sflag = dcmp(a[i].cross(a[i + 1], p[0]));
        for(j = tn = 0; j < nb; ++ j, sflag = eflag) {
            if(sflag >= 0) tmp[tn ++] = p[j];
            eflag = dcmp(a[i].cross(a[i + 1], p[j + 1]));
            if((sflag ^ eflag) == -2)
                tmp[tn ++] = LineCross(a[i], a[i + 1], p[j], p[j + 1]);
        }
        memcpy(p, tmp, sizeof(Point) * tn);
        nb = tn, p[nb] = p[0];
    }
    if(nb < 3) return 0.0;
    return PolygonArea(p, nb);
}

double SPIA(Point a[], Point b[], int na, int nb) { //SimplePolygonIntersectArea
    int i, j;
    Point t1[4], t2[4];
    double res = 0, if_clock_t1, if_clock_t2;
    a[na] = t1[0] = a[0], b[nb] = t2[0] = b[0];
    for(i = 2; i < na; ++ i) {
        t1[1] = a[i - 1], t1[2] = a[i];
        if_clock_t1 = dcmp(t1[0].cross(t1[1], t1[2]));
        if(if_clock_t1 < 0) std::swap(t1[1], t1[2]);
        for(j = 2; j < nb; ++ j) {
            t2[1] = b[j - 1], t2[2] = b[j];
            if_clock_t2 = dcmp(t2[0].cross(t2[1], t2[2]));
            if(if_clock_t2 < 0) std::swap(t2[1], t2[2]);
            res += CPIA(t1, t2, 3, 3) * if_clock_t1 * if_clock_t2;
        }
    }
    return fabs(res);
}

Point p1[maxn], p2[maxn];
int n1, n2;

int main() {
    double x1,x2,x3,x4,y1,y2,y3,y4;
    while(~scanf("%lf%lf%lf%lf",&x1,&y1,&x2,&y2)){
        scanf("%lf%lf%lf%lf",&x3,&y3,&x4,&y4);
        p1[0].x=x1,p1[0].y=y1;
        p1[1].x=x1,p1[1].y=y2;
        p1[2].x=x2,p1[2].y=y1;
        p2[0].x=x3,p2[0].y=y3;
        p2[1].x=x3,p2[1].y=y4;
        p2[2].x=x4,p2[2].y=y4;
        p2[3].x=x4,p2[3].y=y3;
        double ans=SPIA(p1,p2,3,4);
        printf("%.6f
",ans);
    }
    return 0;
}