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，以下是 C++ 实现程序的代码，注释中有详细说明：

#include <iostream>
#include <fstream>
#include <vector>
#include <algorithm>
#include <math.h>

using namespace std;

// 定义坐标点类
class Point {
public:
    double x, y;
    Point() {}
    Point(double a, double b) { x = a; y = b; }
    // 重载小于符号，用于排序
    bool operator<(const Point& rhs) const { return x < rhs.x; }
};

// 定义文件读取函数
vector<Point> readFile(string filename) {
    vector<Point> points;
    ifstream fin(filename);
    if (!fin) {
        cerr << "Failed to open file: " << filename << endl;
        exit(1);
    }
    double x, y;
    while (fin >> x >> y) {
        points.push_back(Point(x, y));
    }
    fin.close();
    return points;
}

// 定义输出所有坐标函数
void printPoints(vector<Point>& points) {
    for (int i = 0; i < points.size(); i++) {
        cout << "(" << points[i].x << ", " << points[i].y << ")" << endl;
    }
}

// 定义按 x 排序输出函数
void sortByX(vector<Point>& points) {
    sort(points.begin(), points.end());
    printPoints(points);
}

// 定义按 y 排序输出函数
void sortByY(vector<Point>& points) {
    sort(points.begin(), points.end(), [](const Point& a, const Point& b) { return a.y < b.y; });
    printPoints(points);
}

// 定义输出坐标数目函数
void printNumOfPoints(vector<Point>& points) {
    cout << "Number of points: " << points.size() << endl;
}

// 定义输出质心位置函数
void printCenterOfGravity(vector<Point>& points) {
    double cx = 0, cy = 0;
    for (int i = 0; i < points.size(); i++) {
        cx += points[i].x;
        cy += points[i].y;
    }
    cx /= points.size();
    cy /= points.size();
    cout << "Center of gravity: (" << cx << ", " << cy << ")" << endl;
}

// 定义最小二乘法拟合函数
void leastSquaresFitting(vector<Point>& points) {
    double sumX = 0, sumY = 0, sumXY = 0, sumXX = 0;
    for (int i = 0; i < points.size(); i++) {
        sumX += points[i].x;
        sumY += points[i].y;
        sumXY += points[i].x * points[i].y;
        sumXX += points[i].x * points[i].x;
    }
    double n = points.size();
    double a = (n * sumXY - sumX * sumY) / (n * sumXX - sumX * sumX);
    double b = (sumY - a * sumX) / n;
    double err = 0;
    for (int i = 0; i < points.size(); i++) {
        err += pow(points[i].y - a * points[i].x - b, 2);
    }
    err = sqrt(err / n);
    cout << "Slope: " << a << endl;
    cout << "Intercept: " << b << endl;
    cout << "Error: " << err << endl;
}

// 定义按序号输出函数
void printPointByIndex(vector<Point>& points) {
    int index;
    cout << "Please enter the index: ";
    cin >> index;
    if (index < 1 || index > points.size()) {
        cerr << "Invalid index." << endl;
        return;
    }
    cout << "(" << points[index - 1].x << ", " << points[index - 1].y << ")" << endl;
}

// 定义 x 轴镜像变换函数
void mirrorByXAxis(vector<Point>& points) {
    for (int i = 0; i < points.size(); i++) {
        points[i].y = -points[i].y;
    }
    printPoints(points);
}

// 定义 y 轴镜像变换函数
void mirrorByYAxis(vector<Point>& points) {
    for (int i = 0; i < points.size(); i++) {
        points[i].x = -points[i].x;
    }
    printPoints(points);
}

// 定义旋转函数
void rotate(vector<Point>& points) {
    double angle;
    cout << "Please enter the angle (in degrees): ";
    cin >> angle;
    double rad = angle * M_PI / 180;
    for (int i = 0; i < points.size(); i++) {
        double x = points[i].x * cos(rad) - points[i].y * sin(rad);
        double y = points[i].x * sin(rad) + points[i].y * cos(rad);
        points[i].x = x;
        points[i].y = y;
    }
    printPoints(points);
}

// 定义平移函数
void translate(vector<Point>& points) {
    double x, y;
    cout << "Please enter the x and y translation: ";
    cin >> x >> y;
    for (int i = 0; i < points.size(); i++) {
        points[i].x += x;
        points[i].y += y;
    }
    printPoints(points);
}

int main() {
    // 读取文件
    vector<Point> points = readFile("input.txt");
    char command;
    while (true) {
        cout << "Please enter a command: ";
        cin >> command;
        switch (command) {
        case 's':
            printPoints(points);
            break;
        case 'x':
            sortByX(points);
            break;
        case 'y':
            sortByY(points);
            break;
        case 'n':
            printNumOfPoints(points);
            break;
        case 'c':
            printCenterOfGravity(points);
            break;
        case 'l':
            leastSquaresFitting(points);
            break;
        case 'i':
            printPointByIndex(points);
            break;
        case 'v':
            mirrorByXAxis(points);
            break;
        case 'h':
            mirrorByYAxis(points);
            break;
        case 'r':
            rotate(points);
            break;
        case 'm':
            translate(points);
            break;
        case 'e':
            return 0;
        default:
            cerr << "Unknown command." << endl;
            break;
        }
    }
    return 0;
}