背景知识：
在数学中，向量（也称为欧几里得向量、几何向量、矢量），指具有大小（magnitude）和方向的量.
百度百科--向量
本例实现一个二维向量。二维向量通常表示的方法有 直角坐标（x,y）和极坐标(a,m) // (a为长度，m为角度)。
创建一个类首先考虑类包含的数据。
一个向量(Vector)可以使用两个double表示直角坐标的x,y；用两个double表示极坐标的a,m。
还需要则有：
public: enum Mode{RECT,POL};
private: double x; double y; double mag; double ang; Mode mode;
接着考虑对向量的操作，一个类最基本的 应该有构造函数和析构函数。
在创建构造函数时，我们遇到了一个问题，由于同一个向量有两个形式，那么创建时应该怎么做呢？
最容易想到的办法就是选择其一，如直角坐标。那么，构造函数应该像是这种形式，
Vector(double n1, double n2);
然后让x=n1,y=n2;这样就可以设置向量的直角坐标，但是，极坐标就被忽略了。
考虑到向量的直角坐标和极坐标是一一对应的，于是想让程序自动设置对应的极坐标。
在Vector类中添加函数(在private中，因为不需要给外部提供接口)
void set_mag(); void set_ang();
具体实现为：
void Vector::set_mag() { mag = sqrt(x*x + y * y); } void Vector::set_ang() { if (x == 0.0 && y == 0.0) ang = 0.0; else ang = atan2(y, x); }
然而，如果用户想要用极坐标形式输入向量，当前的构造函数无法满足需求。
于是，改造构造函数，添加一个参数 form 用来选择形式。
Vector(double n1, double n2, Mode form= RECT);
相应的，构造函数的实现改为：
Vector::Vector(double n1, double n2, Mode form ) { mode = form; if (form == RECT) { x = n1; y = n2; set_mag(); set_ang(); } else if (form == POL) { mag = n1; ang = n2/Rad_to_deg; set_x(); set_y(); } else { cout << "Incorrect 3rd argument to Vector() --"; cout << "Vector set to 0"; x = y = mag = ang = 0; mode = RECT; } }
相应的，在Vector类添加set_x();set_t()方法。
void set_x(); void set_y();
void Vector::set_x() { x = mag * cos(ang); } void Vector::set_y() { y = mag * sin(ang); }
如此，完成了构造函数。
析构函数使用默认的即可。或者自己加上一个构造函数 ~Vector(); 然后在对应的实现函数函数体中留下空格即可。
Vector::~Vector() { }
完成了构造函数和析构函数，考虑向量需要的其他功能/接口。
两个向量相加减，向量的数乘，改变向量的坐标。输出向量。
获取向量的坐标值(提供接口才可访问，否则在private中不能访问)
设置向量的形式
......
具体如下：
void reset(double n1, double n2, Mode form = RECT); double xval()const { return x; } double yval()const { return y; } double magval()const { return mag; } double angval()const { return ang; } void polar_mode(); void rect_mode(); //operator Vector operator+(const Vector&b)const; Vector operator-(const Vector&b)const; Vector operator-()const; Vector operator*(double n)const; //friends friend Vector operator*(double n, const Vector &a); friend std::ostream & operator<<(std::ostream &os, const Vector &v);
实现：
void Vector::reset(double n1, double n2, Mode form ) { mode = form; if (form == RECT) { x = n1; y = n2; set_mag(); set_ang(); } else if (form == POL) { mag = n1; ang = n2 / Rad_to_deg; set_x(); set_y(); } else { cout << "Incorrect 3rd argument to Vector() --"; cout << "Vector set to 0"; x = y = mag = ang = 0; mode = RECT; } } void Vector::polar_mode() { mode = POL; } void Vector::rect_mode() { mode = RECT; } //operator Vector Vector::operator+(const Vector&b)const { return Vector(x + b.x, y + b.y ); } Vector Vector::operator-(const Vector&b)const { return Vector(x - b.x, y - b.y); } Vector Vector::operator-()const { return Vector(-x, -y); } Vector Vector::operator*(double n)const { return Vector(x*n, y*n); } //friends Vector operator*(double n, const Vector &a) { return a * n; } std::ostream & operator<<(std::ostream &os, const Vector &v) { if (v.mode == Vector::RECT) os << "(x,y) = (" << v.x << ", " << v.y << ")"; else if (v.mode == Vector::POL) { os << "(m,a) = (" << v.mag << ", " << v.ang*Rad_to_deg << ")"; } else os << "Vector Object mode is invalid"; return os; }
至此已经完成了Vector类的定义。（借助了cmath库进行了坐标两种形式转换）
完整代码：
//vector.h #pragma once #include<iostream> namespace VECTOR { class Vector { public: enum Mode{RECT,POL}; private: double x; double y; double mag; double ang; Mode mode; void set_mag(); void set_ang(); void set_x(); void set_y(); public: Vector(); Vector(double n1, double n2, Mode form= RECT); ~Vector(); void reset(double n1, double n2, Mode form = RECT); double xval()const { return x; } double yval()const { return y; } double magval()const { return mag; } double angval()const { return ang; } void polar_mode(); void rect_mode(); //operator Vector operator+(const Vector&b)const; Vector operator-(const Vector&b)const; Vector operator-()const; Vector operator*(double n)const; //friends friend Vector operator*(double n, const Vector &a); friend std::ostream & operator<<(std::ostream &os, const Vector &v); }; }
#include<cmath> #include"vector.h" using std::sqrt; using std::sin; using std::cos; using std::atan; using std::atan2; using std::cout; namespace VECTOR { const double Rad_to_deg = 45.0 / atan(1.0); //private methods void Vector::set_mag() { mag = sqrt(x*x + y * y); } void Vector::set_ang() { if (x == 0.0 && y == 0.0) ang = 0.0; else ang = atan2(y, x); } void Vector::set_x() { x = mag * cos(ang); } void Vector::set_y() { y = mag * sin(ang); } //public methods Vector::Vector() { x = y = mag = ang = 0.0; mode = RECT; } Vector::Vector(double n1, double n2, Mode form ) { mode = form; if (form == RECT) { x = n1; y = n2; set_mag(); set_ang(); } else if (form == POL) { mag = n1; ang = n2/Rad_to_deg; set_x(); set_y(); } else { cout << "Incorrect 3rd argument to Vector() --"; cout << "Vector set to 0"; x = y = mag = ang = 0; mode = RECT; } } Vector::~Vector() { } void Vector::reset(double n1, double n2, Mode form ) { mode = form; if (form == RECT) { x = n1; y = n2; set_mag(); set_ang(); } else if (form == POL) { mag = n1; ang = n2 / Rad_to_deg; set_x(); set_y(); } else { cout << "Incorrect 3rd argument to Vector() --"; cout << "Vector set to 0"; x = y = mag = ang = 0; mode = RECT; } } void Vector::polar_mode() { mode = POL; } void Vector::rect_mode() { mode = RECT; } //operator Vector Vector::operator+(const Vector&b)const { return Vector(x + b.x, y + b.y ); } Vector Vector::operator-(const Vector&b)const { return Vector(x - b.x, y - b.y); } Vector Vector::operator-()const { return Vector(-x, -y); } Vector Vector::operator*(double n)const { return Vector(x*n, y*n); } //friends Vector operator*(double n, const Vector &a) { return a * n; } std::ostream & operator<<(std::ostream &os, const Vector &v) { if (v.mode == Vector::RECT) os << "(x,y) = (" << v.x << ", " << v.y << ")"; else if (v.mode == Vector::POL) { os << "(m,a) = (" << v.mag << ", " << v.ang*Rad_to_deg << ")"; } else os << "Vector Object mode is invalid"; return os; } }
