向量叉乘求多变形面积

CODE

#include <iostream>
#include <algorithm>
#include <vector>
#include <fstream>
#include <cmath>
using namespace std;
struct Point 
{ 
double x, y;
};
double cross(const Point &A, const Point &B, const Point &C) 
{
    return (B.x - A.x) * (C.y - A.y) - (B.y - A.y) * (C.x - A.x);
}
double polygon_area(vector<Point>& v)
{
    double area=0;
    auto it=v.begin();
    for(;it<v.end();++it)
    {
        area+=cross({0,0},*it,*(it+1));
    }
    return abs(area/2);
}
int main()
{
    fstream fs("C:\Documents and Settings\Administrator\桌面\poly.txt");
    Point tmp;
    vector<Point> v;
    while(!fs.eof())
    {
        fs>>tmp.x>>tmp.y;
        v.push_back(tmp);
    }
    double area=polygon_area(v);
    cout<<"多边形面积为："<<area<<endl;
    return 0;
}