C++中使用复数的几何套装2

在上一篇文章中，我们知道什么是复数，以及如何使用它们来模拟笛卡尔平面中的点。现在，我们将了解如何在C++中使用STL中的复杂类。

要使用STL中的复杂类，请使用#include

定义点类别

我们可以通过typedef complex point定义我们的点类。在程序开始时。该点的X和Y坐标分别是复数的实部和虚部。要访问我们的X和Y坐标，我们可以使用#define来对real()和imag()函数进行宏处理，如下所示：

# include 
typedef complex point;
# define x real()
# define y imag()

缺点：由于x和y已用作宏，因此它们不能用作变量。但是，此缺点并不代表其所具有的许多优点。

// CPP program to illustrate 
// the definition of point class
#include 
#include 
  
using namespace std;
  
typedef complex point;
  
// X-coordinate is equivalent to the real part
// Y-coordinate is equivalent to the imaginary part
#define x real()
#define y imag()
  
int main()
{
    point P(2.0, 3.0);
    cout << "The X-coordinate of point P is: " << P.x << endl;
    cout << "The Y-coordinate of point P is: " << P.y << endl;
  
    return 0;
}

输出：

The X-coordinate of point P is: 2
The Y-coordinate of point P is: 3

关于平面中P个单点P的属性的实现：

1. P的X坐标： Px
2. P的Y坐标： Py
3. P距原点(0，0)的距离： abs(P)
4. OP与X轴的夹角，其中O为原点： arg(z)
5. P绕原点旋转： P *极坐标(r，θ)

   // CPP program to illustrate
   // the implementation of single point attributes
   #include 
   #include 
     
   using namespace std;
     
   typedef complex point;
   #define x real()
   #define y imag()
     
   // The constant PI for providing angles in radians
   #define PI 3.1415926535897932384626
     
   // Function used to display X and Y coordiantes of a point
   void displayPoint(point P)
   {
       cout << "(" << P.x << ", " << P.y << ")" << endl;
   }
     
   int main()
   {
       point P(4.0, 3.0);
     
       // X-Coordinate and Y-coordinate
       cout << "The X-coordinate of point P is: " << P.x << endl;
       cout << "The Y-coordinate of point P is: " << P.y << endl;
     
       // Distances of P from origin
       cout << "The distance of point P from orgin is: " << abs(P) <

   输出：

   The X-coordinate of point P is: 4
   The Y-coordinate of point P is: 3
   The distance of point P from orgin is: 5
   The squared distance of point P from orgin is: 25
   The angle made by OP with the X-Axis is: 0.643501 radians
   The angle made by OP with the X-Axis is: 36.8699 degrees
   The point P on rotating 90 degrees anti-clockwise becomes: P_rotated(-3, 4)
   

   让我们考虑欧几里得平面上的点P(a，b)和Q(c，d)。
   关于P和Q的属性的实现。

6. 向量加法： P + Q
7. 矢量减法： P – Q
8. 欧氏距离： abs(P – Q)
9. PQ线的斜率： tan(arg(Q – P))

   point A = conj(P) * Q

10. 点积：斧头
11. 叉乘幅度： abs(Ay)

// CPP program to illustrate 
// the implementation of two point attributes
#include 
#include 
  
using namespace std;
  
typedef complex point;
#define x real()
#define y imag()
  
// Constant PI for providing angles in radians
#define PI 3.1415926535897932384626
  
// Function used to display X and Y coordiantes of a point
void displayPoint(point P)
{
    cout << "(" << P.x << ", " << P.y << ")" << endl;
}
  
int main()
{
    point P(2.0, 3.0);
    point Q(3.0, 4.0);
  
    // Addition and Subtraction
    cout << "Addition of P and Q is: P+Q"; displayPoint(P+Q);
    cout << "Subtraction of P and Q is: P-Q"; displayPoint(P-Q);
  
    // Distances between points P and Q
    cout << "The distance between point P ans Q is: " << abs(P-Q) <

输出：

Addition of P and Q is: P+Q(5, 7)
Subtraction of P and Q is: P-Q(-1, -1)
The distance between point P ans Q is: 1.41421
The squared distance between point P ans Q is: 2
The angle of elevation for line PQ is: 45 degrees
The slope of line PQ is: 1
The dot product P.Q is: 18
The magnitude of cross product PxQ is: 1