坐标系转换的7参数的求解的c++代码

以下是一个用于坐标系转换的7参数求解的C++代码示例：

#include <iostream>
#include <cmath>

using namespace std;

const double PI = 3.14159265358979323846;

// 定义一个7参数的结构体
struct SevenParams {
    double dx, dy, dz;    // 平移参数
    double rx, ry, rz;    // 旋转角度（弧度）
    double k;             // 尺度因子
};

// 将角度转换为弧度
double toRadian(double degree) {
    return degree * PI / 180.0;
}

// 计算旋转矩阵
void calcRotationMatrix(double rx, double ry, double rz, double r[3][3]) {
    double sx = sin(rx);
    double cx = cos(rx);
    double sy = sin(ry);
    double cy = cos(ry);
    double sz = sin(rz);
    double cz = cos(rz);

    r[0][0] = cy * cz;
    r[0][1] = -cy * sz;
    r[0][2] = sy;
    r[1][0] = cz * sx * sy + cx * sz;
    r[1][1] = cx * cz - sx * sy * sz;
    r[1][2] = -cy * sx;
    r[2][0] = -cx * cz * sy + sx * sz;
    r[2][1] = cz * sx + cx * sy * sz;
    r[2][2] = cx * cy;
}

// 计算坐标系转换的7参数
SevenParams calc7Params(double x1[], double y1[], double z1[],
                         double x2[], double y2[], double z2[], int n) {
    double mx1 = 0, my1 = 0, mz1 = 0;
    double mx2 = 0, my2 = 0, mz2 = 0;
    for (int i = 0; i < n; i++) {
        mx1 += x1[i];
        my1 += y1[i];
        mz1 += z1[i];
        mx2 += x2[i];
        my2 += y2[i];
        mz2 += z2[i];
    }
    mx1 /= n;
    my1 /= n;
    mz1 /= n;
    mx2 /= n;
    my2 /= n;
    mz2 /= n;

    double M[7][7] = {0};
    double V[7] = {0};
    for (int i = 0; i < n; i++) {
        double X = x1[i] - mx1;
        double Y = y1[i] - my1;
        double Z = z1[i] - mz1;
        double X2 = x2[i] - mx2;
        double Y2 = y2[i] - my2;
        double Z2 = z2[i] - mz2;

        double r[3][3];
        calcRotationMatrix(toRadian(rx), toRadian(ry), toRadian(rz), r);

        double X1_ = r[0][0] * X + r[0][1] * Y + r[0][2] * Z;
        double Y1_ = r[1][0] * X + r[1][1] * Y + r[1][2] * Z;
        double Z1_ = r[2][0] * X + r[2][1] * Y + r[2][2] * Z;

        double kX1_ = k * X1_;
        double kY1_ = k * Y1_;
        double kZ1_ = k * Z1_;

        M[0][0] += kX1_ * kX1_;
        M[0][1] += kX1_ * kY1_;
        M[0][2] += kX1_ * kZ1_;
        M[0][3] += kX1_;
        M[1][1] += kY1_ * kY1_;
        M[1][2] += kY1_ * kZ1_;
        M[1][3] += kY1_;
        M[2][2] += kZ1_ * kZ1_;
        M[2][3] += kZ1_;
        M[3][3] += 1;
        V[0] += kX1_ * X2;
        V[1] += kY1_ * X2;
        V[2] += kZ1_ * X2;
        V[3] += X2;
        V[4] += kX1_ * Y2;
        V[5] += kY1_ * Y2;
        V[6] += kZ1_ * Y2;
    }
    M[1][0] = M[0][1];
    M[2][0] = M[0][2];
    M[2][1] = M[1][2];
    M[4][0] = M[0][4];
    M[5][0] = M[0][5];
    M[5][1] = M[1][5];
    M[6][0] = M[0][6];
    M[6][1] = M[1][6];
    M[6][2] = M[2][6];

    for (int i = 0; i < 7; i++) {
        for (int j = i + 1; j < 7; j++) {
            M[j][i] = M[i][j];
        }
    }

    double det = M[0][0] * (M[1][1] * M[2][2] - M[1][2] * M[2][1])
               - M[0][1] * (M[1][0] * M[2][2] - M[1][2] * M[2][0])
               + M[0][2] * (M[1][0] * M[2][1] - M[1][1] * M[2][0]);

    double inv[7][7];
    inv[0][0] = (M[1][1] * M[2][2] - M[1][2] * M[2][1]) / det;
    inv[0][1] = (M[0][2] * M[2][1] - M[0][1] * M[2][2]) / det;
    inv[0][2] = (M[0][1] * M[1][2] - M[0][2] * M[1][1]) / det;
    inv[0][3] = 0;
    inv[1][0] = (M[1][2] * M[2][0] - M[1][0] * M[2][2]) / det;
    inv[1][1] = (M[0][0] * M[2][2] - M[0][2] * M[2][0]) / det;
    inv[1][2] = (M[0][2] * M[1][0] - M[0][0] * M[1][2]) / det;
    inv[1][3] = 0;
    inv[2][0] = (M[1][0] * M[2][1] - M[1][1] * M[2][0]) / det;
    inv[2][1] = (M[0][1] * M[2][0] - M[0][0] * M[2][1]) / det;
    inv[2][2] = (M[0][0] * M[1][1] - M[0][1] * M[1][0]) / det;
    inv[2][3] = 0;
    inv[3][0] = 0;
    inv[3][1] = 0;
    inv[3][2] = 0;
    inv[3][3] = 1;

    SevenParams params;
    params.dx = inv[0][0] * V[0] + inv[0][1] * V[1] + inv[0][2] * V[2] + inv[0][3] * V[3];
    params.dy = inv[1][0] * V[0] + inv[1][1] * V[1] + inv[1][2] * V[2] + inv[1][3] * V[3];
    params.dz = inv[2][0] * V[0] + inv[2][1] * V[1] + inv[2][2] * V[2] + inv[2][3] * V[3];
    params.rx = toRadian(rx);
    params.ry = toRadian(ry);
    params.rz = toRadian(rz);
    params.k = k;

    return params;
}

int main() {
    double x1[] = { 1, 2, 3, 4, 5 };     // 原始坐标系的X坐标
    double y1[] = { 2, 3, 4, 5, 6 };     // 原始坐标系的Y坐标
    double z1[] = { 3, 4, 5, 6, 7 };     // 原始坐标系的Z坐标
    double x2[] = { 1.5, 2.5, 3.5, 4.5, 5.5 };  // 目标坐标系的X坐标
    double y2[] = { 2.5, 3.5, 4.5, 5.5, 6.5 };  // 目标坐标系的Y坐标
    double z2[] = { 3.5, 4.5, 5.5, 6.5, 7.5 };  // 目标坐标系的Z坐标

    SevenParams params = calc7Params(x1, y1, z1, x2, y2, z2, 5);

    cout << "平移参数：dx=" << params.dx << ", dy=" << params.dy << ", dz=" << params.dz << endl;
    cout << "旋转角度：rx=" << params.rx << ", ry=" << params.ry << ", rz=" << params.rz << endl;
    cout << "尺度因子：k=" << params.k << endl;

    return 0;
}

这段代码实现了一个基本的坐标系转换的7参数求解过程，输入原始坐标系和目标坐标系的坐标，输出平移参数、旋转角度和尺度因子。但需要注意的是，该代码中的计算结果可能存在误差，且不一定适用于所有场景。在实际应用中，需要根据具体情况进行调整和优化。