多边形面积交模板

/* 
 * 多边形的交，多边形的边一定是要按逆时针方向给出 
 * 还要判断是凸包还是凹包，调用相应的函数 
 * 面积并，只要和面积减去交即可 
 */
#include 

using namespace std;

const double eps = 1e-8;

int dcmp(double x) {
    if (x > eps) return 1;
    return x < -eps ? -1 : 0;
}

struct Point {
    double x, y;
};

double cross(Point a, Point b, Point c) ///叉积
{
    return (a.x - c.x) * (b.y - c.y) - (b.x - c.x) * (a.y - c.y);
}

Point intersection(Point a, Point b, Point c, Point d) {
    Point p = a;
    double t = ((a.x - c.x) * (c.y - d.y) - (a.y - c.y) * (c.x - d.x)) /
               ((a.x - b.x) * (c.y - d.y) - (a.y - b.y) * (c.x - d.x));
    p.x += (b.x - a.x) * t;
    p.y += (b.y - a.y) * t;
    return p;
}

//计算多边形面积
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[20], tmp[20];
    int tn, sflag, eflag;
    a[na] = a[0], b[nb] = b[0];
    memcpy(p, b, sizeof(Point) * (nb + 1));
    for (int i = 0; i < na && nb > 2; i++) {
        sflag = dcmp(cross(a[i + 1], p[0], a[i]));
        for (int j = tn = 0; j < nb; j++, sflag = eflag) {
            if (sflag >= 0) tmp[tn++] = p[j];
            eflag = dcmp(cross(a[i + 1], p[j + 1], a[i]));
            if ((sflag ^ eflag) == -2)
                tmp[tn++] = intersection(a[i], a[i + 1], p[j], p[j + 1]); ///求交点  
        }
        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 调用此函数
{
    int i, j;
    Point t1[4], t2[4];
    double res = 0, num1, num2;
    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];
        num1 = dcmp(cross(t1[1], t1[2], t1[0]));
        if (num1 < 0) swap(t1[1], t1[2]);
        for (j = 2; j < nb; j++) {
            t2[1] = b[j - 1], t2[2] = b[j];
            num2 = dcmp(cross(t2[1], t2[2], t2[0]));
            if (num2 < 0) swap(t2[1], t2[2]);
            res += CPIA(t1, t2, 3, 3) * num1 * num2;
        }
    }
    return res;
}

Point p1[3], p2[4];
int X[5], Y[5];

int main() {
    //freopen("in", "r", stdin);
    while (scanf("%d%d%d%d%d%d%d%d", &X[1], &Y[1], &X[2], &Y[2], &X[3], &Y[3], &X[4], &Y[4]) != EOF) {
        p1[2].x = X[1], p1[2].y = Y[1];
        p1[1].x = X[1], p1[1].y = Y[2];
        p1[0].x = X[2], p1[0].y = Y[1];
        p2[3].x = X[3], p2[3].y = Y[3];
        p2[2].x = X[3], p2[2].y = Y[4];
        p2[1].x = X[4], p2[1].y = Y[4];
        p2[0].x = X[4], p2[0].y = Y[3];
        printf("%.8lf\n", fabs(SPIA(p1, p2, 3, 4)));
    }
    return 0;
}