利用c++实现三维图形基本变换，变换图形为正六面体，请给出示例代码

以下是一个使用C++实现三维图形基本变换的示例代码，包括平移、旋转和缩放，并将一个正六面体进行变换：

#include <iostream>
#include <cmath>

using namespace std;

class Point {
public:
    float x, y, z;

    Point() {
        x = y = z = 0;
    }

    Point(float x, float y, float z) {
        this->x = x;
        this->y = y;
        this->z = z;
    }

    void print() {
        cout << "(" << x << ", " << y << ", " << z << ")" << endl;
    }

    Point operator+(const Point& p) const {
        return Point(x + p.x, y + p.y, z + p.z);
    }

    Point operator-(const Point& p) const {
        return Point(x - p.x, y - p.y, z - p.z);
    }

    Point operator*(float s) const {
        return Point(x * s, y * s, z * s);
    }

    Point operator/(float s) const {
        return Point(x / s, y / s, z / s);
    }

    Point operator*(const Point& p) const {
        return Point(x * p.x, y * p.y, z * p.z);
    }

    Point operator/(const Point& p) const {
        return Point(x / p.x, y / p.y, z / p.z);
    }
};

class Cube {
public:
    Point vertices[8];

    Cube() {
        vertices[0] = Point(-1, -1, -1);
        vertices[1] = Point(1, -1, -1);
        vertices[2] = Point(1, 1, -1);
        vertices[3] = Point(-1, 1, -1);
        vertices[4] = Point(-1, -1, 1);
        vertices[5] = Point(1, -1, 1);
        vertices[6] = Point(1, 1, 1);
        vertices[7] = Point(-1, 1, 1);
    }

    void print() {
        for (int i = 0; i < 8; i++) {
            vertices[i].print();
        }
    }

    void translate(float x, float y, float z) {
        Point t(x, y, z);

        for (int i = 0; i < 8; i++) {
            vertices[i] = vertices[i] + t;
        }
    }

    void rotateX(float angle) {
        float s = sin(angle);
        float c = cos(angle);

        for (int i = 0; i < 8; i++) {
            float y = vertices[i].y * c - vertices[i].z * s;
            float z = vertices[i].y * s + vertices[i].z * c;
            vertices[i].y = y;
            vertices[i].z = z;
        }
    }

    void rotateY(float angle) {
        float s = sin(angle);
        float c = cos(angle);

        for (int i = 0; i < 8; i++) {
            float x = vertices[i].x * c - vertices[i].z * s;
            float z = vertices[i].x * s + vertices[i].z * c;
            vertices[i].x = x;
            vertices[i].z = z;
        }
    }

    void rotateZ(float angle) {
        float s = sin(angle);
        float c = cos(angle);

        for (int i = 0; i < 8; i++) {
            float x = vertices[i].x * c - vertices[i].y * s;
            float y = vertices[i].x * s + vertices[i].y * c;
            vertices[i].x = x;
            vertices[i].y = y;
        }
    }

    void scale(float sx, float sy, float sz) {
        Point s(sx, sy, sz);

        for (int i = 0; i < 8; i++) {
            vertices[i] = vertices[i] * s;
        }
    }
};

int main() {
    Cube cube;
    cube.print();

    cube.translate(2, 2, 2);
    cube.print();

    cube.rotateX(0.5);
    cube.print();

    cube.rotateY(0.5);
    cube.print();

    cube.rotateZ(0.5);
    cube.print();

    cube.scale(2, 2, 2);
    cube.print();

    return 0;
}

以上代码中，我们定义了一个`Point`类表示三维空间中的点，并定义了加、减、乘、除等运算符重载，使得可以方便地对点进行计算。我们也定义了一个`Cube`类表示正六面体，并在其中实现了平移、旋转和缩放等基本变换。在`main`函数中，我们创建一个正六面体对象，并对其进行一系列变换来验证我们的实现是否正确。