C++如何实现一个简单的向量数学库_为C++图形学编程编写Vec3和Mat4类

class Vec3 { public: float x, y, z;

// 构造函数
Vec3() : x(0), y(0), z(0) {}
Vec3(float x, float y, float z) : x(x), y(y), z(z) {}

// 向量加法
Vec3 operator+(const Vec3& other) const {
    return Vec3(x + other.x, y + other.y, z + other.z);
}

// 向量减法
Vec3 operator-(const Vec3& other) const {
    return Vec3(x - other.x, y - other.y, z - other.z);
}

// 数乘
Vec3 operator*(float scalar) const {
    return Vec3(x * scalar, y * scalar, z * scalar);
}

// 点积
float dot(const Vec3& other) const {
    return x * other.x + y * other.y + z * other.z;
}

// 叉积
Vec3 cross(const Vec3& other) const {
    return Vec3(
        y * other.z - z * other.y,
        z * other.x - x * other.z,
        x * other.y - y * other.x
    );
}

// 向量长度
float length() const {
    return std::sqrt(x*x + y*y + z*z);
}

// 单位化
Vec3 normalize() const {
    float len = length();
    return len != 0 ? *this * (1.0f / len) : Vec3(0, 0, 0);
}

};

// 支持 scalar vector inline Vec3 operator(float scalar, const Vec3& v) { return v * scalar; }

class Transform { public: // 平移矩阵 static Mat4 translate(float x, float y, float z) { Mat4 mat; mat.set(0, 3, x); mat.set(1, 3, y); mat.set(2, 3, z); return mat; }

// 缩放矩阵
static Mat4 scale(float x, float y, float z) {
    Mat4 mat;
    mat.set(0, 0, x);
    mat.set(1, 1, y);
    mat.set(2, 2, z);
    return mat;
}

// 绕X轴旋转
static Mat4 rotateX(float rad) {
    Mat4 mat;
    float c = cosf(rad);
    float s = sinf(rad);
    mat.set(1, 1, c); mat.set(1, 2, -s);
    mat.set(2, 1, s); mat.set(2, 2, c);
    return mat;
}

// 绕Y轴旋转
static Mat4 rotateY(float rad) {
    Mat4 mat;
    float c = cosf(rad);
    float s = sinf(rad);
    mat.set(0, 0, c); mat.set(0, 2, s);
    mat.set(2, 0, -s); mat.set(2, 2, c);
    return mat;
}

// 绕Z轴旋转
static Mat4 rotateZ(float rad) {
    Mat4 mat;
    float c = cosf(rad);
    float s = sinf(rad);
    mat.set(0, 0, c); mat.set(0, 1, -s);
    mat.set(1, 0, s); mat.set(1, 1, c);
    return mat;
}

// 透视投影矩阵（简化版）
static Mat4 perspective(float fov, float aspect, float near, float far) {
    Mat4 mat;
    float f = 1.0f / tanf(fov * 0.5f);
    mat.set(0, 0, f / aspect);
    mat.set(1, 1, f);
    mat.set(2, 2, (far + near) / (near - far));
    mat.set(2, 3, (2 * far * near) / (near - far));
    mat.set(3, 2, -1);
    mat.set(3, 3, 0);
    return mat;
}

};