使用 C++设计一个程序，功能如下: 从文件“input.txt”中读入数据(一组二维坐标(x，y))，文件格式如下: 大 34.1 45,44 -323.67 493.56 42.55 -89.22 34.11 99.56 ...... 每行第一个数为 x，第二个数为y。 读取数据后，通过按键控制程序: 1.输入字符为's’时，在屏幕上显示所有坐标; 2.输入字符为'x’时，依据x对所有坐标进行排序并输出到屏幕; 3.输入字符为'y’时，依据y对所有坐标进行排序并输出到屏幕; 4.输入字符为'n’时，在屏幕上输出坐标数目; 5.输入字符为'c’时，在屏幕上输出所有点的质心位置(假设每个点质量相同); 6.输入字符为'l’时，对坐标进行最小二乘法拟合，输出拟合的斜率、截距 和误差; 7.输入字符为'i’时，要求用户再输入一个整数 n，输入后屏幕显示第n个 发给 坐标值; 8.输入字符为'v’时，所有坐标沿x轴进行镜像变换，并将变换后的坐标屏幕上输出; 9.输入字符为'h’时，所有坐标沿y轴进行镜像变换，并将变换后的坐标在屏幕上输出; 10.输入字符为'r’时，要求用户再输入一个数 a，输入后所有坐标绕原点旋转a度; 11.输入字符为'm’时，要求用户再输入两个数 x0，y0，输入后将所有坐标沿 x和y轴分别平移 x0，y0，并在屏幕上输出所有坐标;12.输入字符为'e’时，退出程序。

好的，我会根据您的要求进行回答，以下是C++代码实现：

#include <iostream>
#include <fstream>
#include <vector>
#include <algorithm>
#include <cmath>

using namespace std;

//定义二维坐标结构体
struct Point {
    double x;
    double y;
};

//按照x进行排序
bool cmp_x(Point a, Point b) {
    return a.x < b.x;
}

//按照y进行排序
bool cmp_y(Point a, Point b) {
    return a.y < b.y;
}

//计算质心
Point center_of_mass(vector<Point> points) {
    Point center;
    center.x = 0;
    center.y = 0;
    int n = points.size();
    for (int i = 0; i < n; i++) {
        center.x += points[i].x;
        center.y += points[i].y;
    }
    center.x /= n;
    center.y /= n;
    return center;
}

//计算最小二乘法拟合的斜率、截距和误差
void least_square_method(vector<Point> points, double& k, double& b, double& error) {
    int n = points.size();
    double sum_x = 0, sum_y = 0, sum_xy = 0, sum_xx = 0;
    for (int i = 0; i < n; i++) {
        sum_x += points[i].x;
        sum_y += points[i].y;
        sum_xy += points[i].x * points[i].y;
        sum_xx += points[i].x * points[i].x;
    }
    double x_mean = sum_x / n;
    double y_mean = sum_y / n;
    k = (sum_xy - n * x_mean * y_mean) / (sum_xx - n * x_mean * x_mean);
    b = y_mean - k * x_mean;
    error = 0;
    for (int i = 0; i < n; i++) {
        error += pow(points[i].y - k * points[i].x - b, 2);
    }
    error = sqrt(error / n);
}

//沿x轴进行镜像变换
void mirror_x(vector<Point>& points) {
    int n = points.size();
    for (int i = 0; i < n; i++) {
        points[i].y = -points[i].y;
    }
}

//沿y轴进行镜像变换
void mirror_y(vector<Point>& points) {
    int n = points.size();
    for (int i = 0; i < n; i++) {
        points[i].x = -points[i].x;
    }
}

//绕原点旋转
void rotate(vector<Point>& points, double a) {
    int n = points.size();
    double radian = a * M_PI / 180.0;
    for (int i = 0; i < n; i++) {
        double x = points[i].x;
        double y = points[i].y;
        points[i].x = x * cos(radian) - y * sin(radian);
        points[i].y = x * sin(radian) + y * cos(radian);
    }
}

//平移
void translate(vector<Point>& points, double x0, double y0) {
    int n = points.size();
    for (int i = 0; i < n; i++) {
        points[i].x += x0;
        points[i].y += y0;
    }
}

int main() {
    //从文件中读取数据
    ifstream fin("input.txt");
    vector<Point> points;
    double x, y;
    while (fin >> x >> y) {
        Point p;
        p.x = x;
        p.y = y;
        points.push_back(p);
    }
    fin.close();

    //循环控制程序
    char ch;
    while (true) {
        cout << "请输入指令：";
        cin >> ch;
        switch (ch) {
            case 's':
                //显示所有坐标
                for (int i = 0; i < points.size(); i++) {
                    cout << "(" << points[i].x << ", " << points[i].y << ")" << endl;
                }
                break;
            case 'x':
                //依据x进行排序
                sort(points.begin(), points.end(), cmp_x);
                for (int i = 0; i < points.size(); i++) {
                    cout << "(" << points[i].x << ", " << points[i].y << ")" << endl;
                }
                break;
            case 'y':
                //依据y进行排序
                sort(points.begin(), points.end(), cmp_y);
                for (int i = 0; i < points.size(); i++) {
                    cout << "(" << points[i].x << ", " << points[i].y << ")" << endl;
                }
                break;
            case 'n':
                //输出坐标数目
                cout << "坐标数目为：" << points.size() << endl;
                break;
            case 'c':
                //输出质心位置
                Point center = center_of_mass(points);
                cout << "质心位置为：(" << center.x << ", " << center.y << ")" << endl;
                break;
            case 'l':
                //最小二乘法拟合
                double k, b, error;
                least_square_method(points, k, b, error);
                cout << "斜率为：" << k << endl;
                cout << "截距为：" << b << endl;
                cout << "误差为：" << error << endl;
                break;
            case 'i':
                //输出第n个坐标值
                int n;
                cout << "请输入n：";
                cin >> n;
                if (n >= 1 && n <= points.size()) {
                    cout << "第" << n << "个坐标为：" << "(" << points[n-1].x << ", " << points[n-1].y << ")" << endl;
                }
                else {
                    cout << "输入错误！" << endl;
                }
                break;
            case 'v':
                //沿x轴进行镜像变换
                mirror_x(points);
                for (int i = 0; i < points.size(); i++) {
                    cout << "(" << points[i].x << ", " << points[i].y << ")" << endl;
                }
                break;
            case 'h':
                //沿y轴进行镜像变换
                mirror_y(points);
                for (int i = 0; i < points.size(); i++) {
                    cout << "(" << points[i].x << ", " << points[i].y << ")" << endl;
                }
                break;
            case 'r':
                //绕原点旋转
                double a;
                cout << "请输入a：";
                cin >> a;
                rotate(points, a);
                for (int i = 0; i < points.size(); i++) {
                    cout << "(" << points[i].x << ", " << points[i].y << ")" << endl;
                }
                break;
            case 'm':
                //沿x和y轴分别平移
                double x0, y0;
                cout << "请输入x0和y0：";
                cin >> x0 >> y0;
                translate(points, x0, y0);
                for (int i = 0; i < points.size(); i++) {
                    cout << "(" << points[i].x << ", " << points[i].y << ")" << endl;
                }
                break;
            case 'e':
                //退出程序
                return 0;
            default:
                cout << "输入错误！" << endl;
                break;
        }
    }
    return 0;
}

代码中实现了上述功能，您可以根据需要进行调整或扩展。