判断一组点是否可以近似成一个球体

// 计算两个点之间的距离
double distance(const vector<int>& p1, const vector<int>& p2) 
{
	double sum = 0;
	for (int i = 0; i < p1.size(); ++i)
	{
		sum += pow(p1[i]*1.0 - p2[i] * 1.0, 2);
	}
	return sqrt(sum);
}

// 判断一组点是否近似为一个球体
bool isApproxSphere(const vector<vector<int>>& points) 
{
	int n = points.size();
	vector<double> distances;
	for (int i = 0; i < n; ++i)
	{
		for (int j = i + 1; j < n; ++j) 
		{
			distances.push_back(distance(points[i], points[j]));
		}
	}
	double meanDist = accumulate(distances.begin(), distances.end(), 0.0) / distances.size();
	double varDist = 0;
	for (double d : distances) 
	{
		varDist += pow(d - meanDist, 2);
	}
	varDist /= distances.size() - 1;
	double stdDevDist = sqrt(varDist);
	return stdDevDist / meanDist < 0.42; // 根据经验值设定偏差阈值为0.42
}

0.42 是经验值，可调