csu1812求两多边形的交面积

本文介绍了一种计算两个多边形交集面积的方法,包括处理凸包和凹包的情况,并提供了完整的C++代码实现。

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/*
 * 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 <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
const int maxn = 300;
const double eps = 1e-8;
struct Point//点 向量
{
    double x,y;
    Point(double x=0,double y=0):x(x),y(y) {}
};
typedef  Point  Vector;
//向量使用点作为表示方法 结构相同 为了代码清晰

int dcmp(double x) //三态函数 处理与double零有关的精度问题
{
    if(fabs(x) < eps)    return 0;
    return x<0 ? -1 : 1;
}
//向量运算
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 Vector& A, const Vector& B)
{
    return dcmp(A.x-B.x)==0 && dcmp(A.y-B.y)==0;
}
bool operator < (const Point&a,const Point &b)
{
    return a.x<b.x||(a.x==b.x&&a.y<b.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()
{
    double x1,x2,x3,x4,y1,y2,y3,y4;
    while(~scanf("%lf %lf %lf %lf %lf %lf %lf %lf",&x1,&y1,&x2,&y2,&x3,&y3,&x4,&y4))
    {
        p1[0]=Point(x1,y1);
        p1[1]=Point(x1,y2);
        p1[2]=Point(x2,y1);
        p2[0]=Point(x3,y3);
         p2[1]=Point(x3,y4);
          p2[2]=Point(x4,y4);
           p2[3]=Point(x4,y3);
             double Area = SPIA(p1, p2, 3, 4);
             printf("%.8lf\n",fabs(Area));
    }
}



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