#include "SG_baseDataType.h"
#include "SG_baseAlgo_Export.h"
#include <vector>
#ifdef  __WIN32
#include <corecrt_math_defines.h>
#endif //  __WIN32

#include <cmath>
#include <unordered_map>
#include <Eigen/dense>

void lineFitting(std::vector< SVzNL3DPoint>& inliers, double* _k, double* _b)
{
	//最小二乘拟合直线参数
	double xx_sum = 0;
	double x_sum = 0;
	double y_sum = 0;
	double xy_sum = 0;
	int num = 0;
	for (int i = 0; i < inliers.size(); i++)
	{
		x_sum += inliers[i].x; //x的累加和
		y_sum += inliers[i].y; //y的累加和
		xx_sum += inliers[i].x * inliers[i].x; //x的平方累加和
		xy_sum += inliers[i].x * inliers[i].y; //x，y的累加和
		num++;
	}
	*_k = (num * xy_sum - x_sum * y_sum) / (num * xx_sum - x_sum * x_sum); //根据公式求解k
	*_b = (-x_sum * xy_sum + xx_sum * y_sum) / (num * xx_sum - x_sum * x_sum);//根据公式求解b
}

//拟合成通用直线方程ax+by+c=0，包括垂直
void lineFitting_abc(std::vector< SVzNL3DPoint>& inliers, double* _a, double* _b, double* _c)
{
	//判断是否为垂直
	int dataSize = (int)inliers.size();
	if (dataSize < 2)
		return;

	double deltaX = abs(inliers[0].x - inliers[dataSize - 1].x);
	double deltaY = abs(inliers[0].y - inliers[dataSize - 1].y);
	std::vector< SVzNL3DPoint> fittingData;
	if (deltaX < deltaY)
	{
		//x=ky+b 拟合
		for (int i = 0; i < dataSize; i++)
		{
			SVzNL3DPoint a_fitPt;
			a_fitPt.x = inliers[i].y;
			a_fitPt.y = inliers[i].x;
			a_fitPt.z = inliers[i].z;
			fittingData.push_back(a_fitPt);
		}
		double k = 0, b = 0;
		lineFitting(fittingData, &k, &b);
		//ax+by+c
		*_a = 1.0;
		*_b = -k;
		*_c = -b;
	}
	else
	{
		//y = kx+b拟合
		double k = 0, b = 0;
		lineFitting(inliers, &k, &b);
		//ax+by+c
		*_a = k;
		*_b = -1;
		*_c = b;
	}
	return;
}

//圆最小二乘拟合
double fitCircleByLeastSquare(
	const std::vector<SVzNL3DPoint>& pointArray,
	SVzNL3DPoint& center,
	double& radius)
{
	int N = pointArray.size();
	if (N < 3) {
		return std::numeric_limits<double>::max();
	}

	double sumX = 0.0;
	double sumY = 0.0;
	double sumX2 = 0.0;
	double sumY2 = 0.0;
	double sumX3 = 0.0;
	double sumY3 = 0.0;
	double sumXY = 0.0;
	double sumXY2 = 0.0;
	double sumX2Y = 0.0;

	for (int pId = 0; pId < N; ++pId) {
		sumX += pointArray[pId].x;
		sumY += pointArray[pId].y;

		double x2 = pointArray[pId].x * pointArray[pId].x;
		double y2 = pointArray[pId].y * pointArray[pId].y;
		sumX2 += x2;
		sumY2 += y2;

		sumX3 += x2 * pointArray[pId].x;
		sumY3 += y2 * pointArray[pId].y;
		sumXY += pointArray[pId].x * pointArray[pId].y;
		sumXY2 += pointArray[pId].x * y2;
		sumX2Y += x2 * pointArray[pId].y;
	}

	double C, D, E, G, H;
	double a, b, c;

	C = N * sumX2 - sumX * sumX;
	D = N * sumXY - sumX * sumY;
	E = N * sumX3 + N * sumXY2 - (sumX2 + sumY2) * sumX;
	G = N * sumY2 - sumY * sumY;
	H = N * sumX2Y + N * sumY3 - (sumX2 + sumY2) * sumY;

	a = (H * D - E * G) / (C * G - D * D);
	b = (H * C - E * D) / (D * D - G * C);
	c = -(a * sumX + b * sumY + sumX2 + sumY2) / N;

	center.x = -a / 2.0;
	center.y = -b / 2.0;
	radius = sqrt(a * a + b * b - 4 * c) / 2.0;

	double err = 0.0;
	double e;
	double r2 = radius * radius;
	for (int pId = 0; pId < N; ++pId) {
		e = pow(pointArray[pId].x - center.x, 2) + pow(pointArray[pId].y - center.y, 2) - r2;
		if (e > err) {
			err = e;
		}
	}
	return err;
}

#if 0
bool leastSquareParabolaFit(const std::vector<cv::Point2d>& points,
	double& a, double& b, double& c,
	double& mse, double& max_err)
{
	// 校验点集数量（至少3个点才能拟合抛物线）
	int n = points.size();
	if (n < 3) {
		return false;
	}

	// 初始化各项求和参数
	double sum_x = 0.0, sum_x2 = 0.0, sum_x3 = 0.0, sum_x4 = 0.0;
	double sum_y = 0.0, sum_xy = 0.0, sum_x2y = 0.0;

	// 计算各项求和
	for (const auto& p : points) {
		double x = p.x;
		double y = p.y;
		double x2 = x * x;
		double x3 = x2 * x;
		double x4 = x3 * x;

		sum_x += x;
		sum_x2 += x2;
		sum_x3 += x3;
		sum_x4 += x4;
		sum_y += y;
		sum_xy += x * y;
		sum_x2y += x2 * y;
	}

	// 构建线性方程组 M * [a,b,c]^T = N
	// M矩阵：3x3
	double M[3][3] = {
		{sum_x4, sum_x3, sum_x2},
		{sum_x3, sum_x2, sum_x},
		{sum_x2, sum_x, (double)n}
	};

	// N向量：3x1
	double N[3] = { sum_x2y, sum_xy, sum_y };

	// 高斯消元法求解线性方程组（3元一次方程组）
	// 步骤1：将M转化为上三角矩阵
	for (int i = 0; i < 3; i++) {
		// 选主元（避免除数为0）
		int pivot = i;
		for (int j = i; j < 3; j++) {
			if (fabs(M[j][i]) > fabs(M[pivot][i])) {
				pivot = j;
			}
		}
		// 交换行
		std::swap(M[i], M[pivot]);
		std::swap(N[i], N[pivot]);

		// 归一化主元行
		double div = M[i][i];
		if (fabs(div) < 1e-10) {
			return false;
		}
		for (int j = i; j < 3; j++) {
			M[i][j] /= div;
		}
		N[i] /= div;

		// 消去下方行
		for (int j = i + 1; j < 3; j++) {
			double factor = M[j][i];
			for (int k = i; k < 3; k++) {
				M[j][k] -= factor * M[i][k];
			}
			N[j] -= factor * N[i];
		}
	}

	// 步骤2：回代求解
	c = N[2];
	b = N[1] - M[1][2] * c;
	a = N[0] - M[0][1] * b - M[0][2] * c;

	// 计算拟合误差
	mse = 0.0;
	max_err = 0.0;
	for (const auto& p : points) {
		double y_fit = a * p.x * p.x + b * p.x + c;
		double err = y_fit - p.y;
		double err_abs = fabs(err);
		mse += err * err;
		if (err_abs > max_err) {
			max_err = err_abs;
		}
	}
	mse /= n; // 均方误差

	return true;
}
#endif
//抛物线最小二乘拟合 y=ax^2 + bx + c
bool leastSquareParabolaFitEigen(
	const std::vector<cv::Point2d>& points,
	double& a, double& b, double& c,
	double& mse, double& max_err)
{
	int n = points.size();
	if (n < 3) {
		return false;
	}

	// 构建系数矩阵A和目标向量B
	Eigen::MatrixXd A(n, 3);
	Eigen::VectorXd B(n);
	for (int i = 0; i < n; i++) {
		double x = points[i].x;
		A(i, 0) = x * x;
		A(i, 1) = x;
		A(i, 2) = 1.0;
		B(i) = points[i].y;
	}

	// 最小二乘求解：Ax = B，直接调用Eigen的求解器
	Eigen::Vector3d coeffs = A.bdcSvd(Eigen::ComputeThinU | Eigen::ComputeThinV).solve(B);
	a = coeffs(0);
	b = coeffs(1);
	c = coeffs(2);

	// 计算误差
	mse = 0.0;
	max_err = 0.0;
	for (const auto& p : points) {
		double y_fit = a * p.x * p.x + b * p.x + c;
		double err = y_fit - p.y;
		double err_abs = fabs(err);
		mse += err * err;
		if (err_abs > max_err) {
			max_err = err_abs;
		}
	}
	mse /= n;
	return true;
}

//计算面参数: z = Ax + By + C
//res: [0]=A, [1]= B, [2]=-1.0, [3]=C,
void vzCaculateLaserPlane(std::vector<cv::Point3f> Points3ds, std::vector<double>& res)
{
	//最小二乘法拟合平面
	//获取cv::Mat的坐标系以纵向为x轴，横向为y轴，而cvPoint等则相反
	//系数矩阵
	cv::Mat A = cv::Mat::zeros(3, 3, CV_64FC1);
	//
	cv::Mat B = cv::Mat::zeros(3, 1, CV_64FC1);
	//结果矩阵
	cv::Mat X = cv::Mat::zeros(3, 1, CV_64FC1);
	double x2 = 0, xiyi = 0, xi = 0, yi = 0, zixi = 0, ziyi = 0, zi = 0, y2 = 0;
	for (int i = 0; i < Points3ds.size(); i++)
	{
		x2 += (double)Points3ds[i].x * (double)Points3ds[i].x;
		y2 += (double)Points3ds[i].y * (double)Points3ds[i].y;
		xiyi += (double)Points3ds[i].x * (double)Points3ds[i].y;
		xi += (double)Points3ds[i].x;
		yi += (double)Points3ds[i].y;
		zixi += (double)Points3ds[i].z * (double)Points3ds[i].x;
		ziyi += (double)Points3ds[i].z * (double)Points3ds[i].y;
		zi += (double)Points3ds[i].z;
	}
	A.at<double>(0, 0) = x2;
	A.at<double>(1, 0) = xiyi;
	A.at<double>(2, 0) = xi;
	A.at<double>(0, 1) = xiyi;
	A.at<double>(1, 1) = y2;
	A.at<double>(2, 1) = yi;
	A.at<double>(0, 2) = xi;
	A.at<double>(1, 2) = yi;
	A.at<double>(2, 2) = (double)((int)Points3ds.size());
	B.at<double>(0, 0) = zixi;
	B.at<double>(1, 0) = ziyi;
	B.at<double>(2, 0) = zi;
	//计算平面系数
	X = A.inv() * B;
	//A
	res.push_back(X.at<double>(0, 0));
	//B
	res.push_back(X.at<double>(1, 0));
	//Z的系数为-1
	res.push_back(-1.0);
	//C
	res.push_back(X.at<double>(2, 0));
	return;
}

/**
 * @brief 空间直线最小二乘拟合
 * @param points 输入的三维点集（至少2个点，否则无意义）
 * @param center 输出：拟合直线的质心（基准点P0）
 * @param direction 输出：拟合直线的方向向量v（单位化）
 * @return 拟合是否成功（点集有效返回true）
 */
bool fitLine3DLeastSquares(const std::vector<SVzNL3DPoint>& points, SVzNL3DPoint& center, SVzNL3DPoint& direction)
{
	// 检查点集有效性
	if (points.size() < 2) {
		std::cerr << "Error: 点集数量必须大于等于2！" << std::endl;
		return false;
	}

	int n = points.size();
	Eigen::MatrixXd A(n, 3); // 点集矩阵：每行一个点的(x,y,z)

	// 1. 计算质心（center）
	double cx = 0.0, cy = 0.0, cz = 0.0;
	for (const auto& p : points) {
		cx += p.x;
		cy += p.y;
		cz += p.z;
		A.row(points.size() - n) << p.x, p.y, p.z; // 填充点集矩阵
		n--;
	}
	cx /= points.size();
	cy /= points.size();
	cz /= points.size();
	center = { cx, cy, cz };

	// 2. 构造去中心化的协方差矩阵（3x3）
	// 关键修复：使用RowVector3d（行向量）做rowwise减法，匹配维度
	Eigen::RowVector3d centroid_row(cx, cy, cz);
	Eigen::MatrixXd centered = A.rowwise() - centroid_row; // 维度匹配，无报错

	// 协方差矩阵计算（n-1为无偏估计，工程中也可直接用n）
	Eigen::Matrix3d cov = centered.transpose() * centered; // / (points.size() - 1);
	// 3. 特征值分解：求协方差矩阵的特征值和特征向量
	Eigen::SelfAdjointEigenSolver<Eigen::Matrix3d> eigensolver(cov);
	if (eigensolver.info() != Eigen::Success) {
		std::cerr << "Error: 特征值分解失败！" << std::endl;
		return false;
	}

	// 最大特征值对应的特征向量即为方向向量（Eigen默认按特征值升序排列，取最后一个）
	Eigen::Vector3d dir = eigensolver.eigenvectors().col(2);
	// 单位化方向向量（可选，但工程中通常标准化）
	dir.normalize();

	direction = { dir(0), dir(1), dir(2) };
	return true;
}