计算几何 多边形的交与并

admin1

/*
* 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 <bits/stdc++.h>
using namespace std;

const int maxn = //300;
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[maxn], p2[maxn];
int n1, n2;
int main()
{
    while(cin>>n1>>n2)
    {
        for(int i = 0; i < n1; i++) scanf("%lf%lf", &p1[i].x, &p1[i].y);
        for(int i = 0; i < n2; i++) scanf("%lf%lf", &p2[i].x, &p2[i].y);
        double Area = SPIA(p1, p2, n1, n2);
    }
    return 0;
}