求取多边形面积与周长

支持任意多边形，凹、凸皆可
多边形顶点输入时按顺时针顺序排列

面积法一：

//**函数部分**

struct Point2i
{
double x;
double y;
}
//  面积   (Shoelace formula)鞋带公式S=|(x2-x1)(y3-y1)-(x3-x1)(y2-y1)|
double cross1(Point2i pi, Point2i pj, Point2i pk)
{
	return (pj.x - pi.x) * (pk.y - pi.y) - (pj.y - pi.y) * (pk.x - pi.x);
}

//vector<Point>存储多边形顶点
double polygon_area(vector<Point2i>& polygon)
{
	double area = 0.0;
	Point2i temp;
	temp.x = 0;
	temp.y = 0;
	for (int i = 0; i < polygon.size(); i++)
	{
		area += cross1(temp, polygon.data()[(i)], polygon.data()[((i + 1) % polygon.size())]);
	}
	return fabs(area / 2);
}

面积法二：

//polygon：多变形顶点数组
//N：多边形顶点数目

double polygonarea(vector<Point2i>& polygon, int N)//N表示多边形的边数
{
	int m, n;
	double area = 0;
	for (m = 0; m < N; m++) {
		n = (m + 1) % N;
		area += polygon[m].x * polygon[n].y;
		area -= polygon[m].y * polygon[n].x;
	}
	area /= 2;
	return(area < 0 ? -area : area);
}

求周长方法：

inline double calDis2_2(double x1, double y1, double x2, double y2)
{
	return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}

double polygon_length(vector<Point2i>& polygon)
{
	double len = 0;
	Point2i pt1, pt2;
	long npt = polygon.size();
	for (int i = 0; i < npt; i++)
	{
		pt1 = polygon.at(i);
		pt2 = polygon.at((i + 1) % npt);
		len += calDis2_2(pt1.x, pt1.y, pt2.x, pt2.y);
	}
	return len;
}