C++小例子——01向量类myVectormeiguanhua的博客-

向量（vector）
$vec a=[x,y,z]$

a=[x,y,z]应用较广，比如节点的坐标
$vec x=[x,y,z]$

x=[x,y,z]、面的面积矢量
$vec{S}_f=[Sf_x,Sf_y,Sf_z]$

Sf​=[Sfx​,Sfy​,Sfz​]，面空间速度矢量
$vec u=[u,v,w]$

u=[u,v,w]等，都离不开它。同时，向量还有点乘、叉乘、求模（也称为幅值或二范数）的运算，以及向量与向量或标量的加减操作、向量与标量的乘除运算等。那么，咱们可以用C++定义一个向量类myVector，其包含三个成员变量
$x,y,z$

x,y,z，可通过三个分量来构造，也可通过另一个myVector对象来构造，重载操作符+、-、*、/来完成相关运算，重载赋值符=，重载输出流<<来实现输出，定义友元函数dotProduct、crossProduct、norm来计算点乘、叉乘、求模……写好的程序如下：

注意：这里的myVector和C++里自带的库文件vector不同，这里只是含3个分量的空间矢量，而C++中的vector则更类似于一维变长度数组。

myVector.h头文件

// 2020-06-09 // class myVector - head file // Author: Guanhua Mei // definition and functions of a myVector [x, y, z] // can be used for points, velocity, etc. in CFD #include <iostream> class myVector { private: double m_dX; double m_dY; double m_dZ; public: // construct with input x, y and z, default 0 myVector(double x = 0.0, double y = 0.0, double z = 0.0); // construct with another myVector myVector(const myVector &); // destructor, do nothing ~myVector(); // print void print() const; // get x, y, z double getX() const; double getY() const; double getZ() const; // set x, y, z void setX(double x = 0.0); void setY(double y = 0.0); void setZ(double z = 0.0); // set total value void setVal(double x = 0.0, double y = 0.0, double z = 0.0); // overload =  myVector & operator=(const myVector &); // overload operators  // +: (x1, y1, z1) + (x2, y2, z2) = (x1 + x2, y1 + y2, z1 + z2) friend myVector operator+(const myVector &, const myVector &); // +: (x1, y1, z1) + b = (x1 + b, y1 + b, z1 + b) friend myVector operator+(const myVector &, double); // -: (x1, y1, z1) - (x2, y2, z2) = (x1 - x2, y1 - y2, z1 - z2) friend myVector operator-(const myVector &, const myVector &); // -: (x1, y1, z1) - b = (x1 - b, y1 - b, z1 - b) friend myVector operator-(const myVector &, double); // +=  myVector & operator+=(const myVector &);  myVector & operator+=(double); // -=  myVector & operator-=(const myVector &);  myVector & operator-=(double); // multiply // *: (x1, y1, z1) * b = (x1 * b, y1 * b, z1 * b) friend myVector operator*(const myVector &, double); // *: b * (x1, y1, z1) = (x1, y1, z1) * b friend myVector operator*(double, const myVector &); // divide // /: (x1, y1, z1) / b = (x1 / b, y1 / b, z1 / b) friend myVector operator/(const myVector &, double); // dot product // (x1, y1, z1) dot (x2, y2, z2) = x1 * x2 + y1 * y2 + z1 * z2 friend double dotProduct(const myVector &, const myVector &); // cross product // (x1, y1, z1) cross (x2, y2, z2) =  //     |  i  j  k | //     | x1 y1 z1 | //     | x2 y2 z2 | friend myVector crossProduct(const myVector &, const myVector &); // output << friend std::ostream & operator<<(std::ostream & os, const myVector &); // magnitude // norm([x, y, z]) = sqrt(x^2 + y^2 + z^2) friend double norm(const myVector &); }; 

myVector.cpp文件

// 2020-06-09 // class myVector - cpp file // Author: Guanhua Mei #include "myVector.h" // construct with input x, y and z, default 0 myVector::myVector(double x, double y, double z) {  m_dX = x;  m_dY = y;  m_dZ = z; } // construct with another myVector myVector::myVector(const myVector & vct) {  m_dX = vct.m_dX;  m_dY = vct.m_dY;  m_dZ = vct.m_dZ; } // destructor, do nothing myVector::~myVector() { } // print void myVector::print() const {  std::cout << "(" << m_dX << ", " << m_dY << ", " << m_dZ << ")" << std::endl; } // get x, y, z double myVector::getX() const { return m_dX; } double myVector::getY() const { return m_dY; } double myVector::getZ() const { return m_dZ; } // set x, y, z void myVector::setX(double x) {  m_dX = x; } void myVector::setY(double y) {  m_dY = y; } void myVector::setZ(double z) {  m_dZ = z; } void myVector::setVal(double x, double y, double z) {  m_dX = x;  m_dY = y;  m_dZ = z; } // overload = myVector & myVector::operator=(const myVector & vct) {  m_dX = vct.m_dX;  m_dY = vct.m_dY;  m_dZ = vct.m_dZ; return *this; } // +: (x1, y1, z1) + (x2, y2, z2) = (x1 + x2, y1 + y2, z1 + z2) myVector operator+(const myVector & vct1, const myVector & vct2) {  myVector tmp(vct1.m_dX + vct2.m_dX,    vct1.m_dY + vct2.m_dY, vct1.m_dZ + vct2.m_dZ); return tmp; } // +: (x1, y1, z1) + b = (x1 + b, y1 + b, z1 + b) myVector operator+(const myVector & vct1, double dbl) {  myVector tmp(vct1.m_dX + dbl,    vct1.m_dY + dbl, vct1.m_dZ + dbl); return tmp; } // -: (x1, y1, z1) - (x2, y2, z2) = (x1 - x2, y1 - y2, z1 - z2) myVector operator-(const myVector & vct1, const myVector & vct2) {  myVector tmp(vct1.m_dX - vct2.m_dX,    vct1.m_dY - vct2.m_dY, vct1.m_dZ - vct2.m_dZ); return tmp; } // -: (x1, y1, z1) - b = (x1 - b, y1 - b, z1 - b) myVector operator-(const myVector & vct1, double dbl) {  myVector tmp(vct1.m_dX - dbl,    vct1.m_dY - dbl, vct1.m_dZ - dbl); return tmp; } // += myVector & myVector::operator+=(const myVector & vct) {  m_dX += vct.m_dX;  m_dY += vct.m_dY;  m_dZ += vct.m_dZ; return *this; }  myVector & myVector::operator+=(double dbl) {  m_dX += dbl;  m_dY += dbl;  m_dZ += dbl; return *this; } // -= myVector & myVector::operator-=(const myVector & vct) {  m_dX -= vct.m_dX;  m_dY -= vct.m_dY;  m_dZ -= vct.m_dZ; return *this; }  myVector & myVector::operator-=(double dbl) {  m_dX -= dbl;  m_dY -= dbl;  m_dZ -= dbl; return *this; } // multiply // *: (x1, y1, z1) * b = (x1 * b, y1 * b, z1 * b) myVector operator*(const myVector & vct, double dbl) {  myVector tmp(vct.m_dX * dbl, vct.m_dY * dbl, vct.m_dZ * dbl); return tmp; } // *: b * (x1, y1, z1) = (x1, y1, z1) * b myVector operator*(double dbl, const myVector & vct) { return (vct * dbl); } // divide // /: (x1, y1, z1) / b = (x1 / b, y1 / b, z1 / b) myVector operator/(const myVector & vct, double dbl) { // if dbl equals 0, it will return INF return (vct * (1.0 / dbl)); } // dot product // (x1, y1, z1) dot (x2, y2, z2) = x1 * x2 + y1 * y2 + z1 * z2 double dotProduct(const myVector & vct1, const myVector & vct2) { return (vct1.m_dX * vct2.m_dX + vct1.m_dY * vct2.m_dY   + vct1.m_dZ * vct2.m_dZ); } // cross product // (x1, y1, z1) cross (x2, y2, z2) =  // |  i  j  k | // | x1 y1 z1 | // | x2 y2 z2 | myVector crossProduct  (const myVector & vct1, const myVector & vct2) {  myVector tmp;  tmp.m_dX = vct1.m_dY * vct2.m_dZ - vct1.m_dZ * vct2.m_dY;  tmp.m_dY = vct1.m_dZ * vct2.m_dX - vct1.m_dX * vct2.m_dZ;  tmp.m_dZ = vct1.m_dX * vct2.m_dY - vct1.m_dY * vct2.m_dX; return tmp; } // output stream << std::ostream & operator<<(std::ostream & os, const myVector & vct) {  os << "(" << vct.m_dX << ", " << vct.m_dY << ", " << vct.m_dZ << ")"; return os; } // magnitude // norm([x, y, z]) = sqrt(x^2 + y^2 + z^2) double norm(const myVector & vct) { double tmp;  tmp = std::sqrt(vct.m_dX * vct.m_dX   + vct.m_dY * vct.m_dY + vct.m_dZ * vct.m_dZ); return tmp; } 

测试主函数main.cpp

// 2020-06-09 // test class myVector // Author: Guanhua Mei #include <iostream> #include "myVector.h" using namespace std; int main() { // test constructor  myVector a;  myVector b(1.2);  myVector c(2.3, 3.4, 5.6);  myVector d(5.6, 6.7, 7.8); // test print()  cout << "a:"; a.print(); // test <<  cout << "b:" << b << endl;  cout << "c:" << c << endl;  cout << "d:" << d << endl;  myVector e; // test =  e = d;  cout << "After e = d, e =:" << e << endl; // test setVal  e.setVal(1, 2, 3);  cout << "After e.setVal(1,2,3), e: " << e << endl; // test +  cout << "d + c:" << d + c << endl;  cout << "d + 1:" << d + 1 << endl; // test -  cout << "d - c:" << d - c << endl;  cout << "d - 1:" << d - 1 << endl; // test *  cout << "d * 2.0:" << d * 2.0 << endl;  cout << "2.0 * d:" << 2.0 * d << endl; // test /  cout << "d / 2.0:" << d / 2.0 << endl;  cout << "d / 0.0:" << d / 0.0 << endl; // test dotProduct  cout << "dotProduct(d, c):" << dotProduct(d, c) << endl; // test crossProduct  cout << "crossProduct(d, c):" << crossProduct(d,c) << endl; // test norm 2  cout  << "norm(d):" << norm(d) << endl; // test +=  d += c;  cout << "After d += c, d = :" << d << endl; // test -=  d -= c;  cout << "After d -= c, d = :" << d << endl; return 0; } 

测试结果，表明所有函数均实现了其功能。