直角坐标与极坐标互相转换（Python&C++实现）

在直角坐标系中$P$点坐标可表示为$(X,Y)$，在极坐标系中$P$点坐标可表示为$(R,\theta )$。

直角坐标转极坐标

已知$(x,y)$，
$$R=\sqrt{X^2+Y^2}$$
$$\theta =arctan(\frac{Y}{X})$$
Python代码为：

import numpy as np


def Rectangular_to_Polar(x, y):  # 直角坐标转极坐标，输出的thata为角度值
    r = np.sqrt(np.square(x) + np.square(y))
    theta = np.degrees(np.arctan(y / x))
    return round(r, 2), round(theta, 2)

C++代码为：

#include
#include
#define PAI acos(-1)

using namespace std;
int main() 
{
//	double x = 1;
//	double y = 1;

	double x, y;
	cout << "请输入x坐标值：";
	cin >> x;
	cout << "请输入y坐标值：";
	cin >> y;
	
	double r = pow(pow(x, 2) + pow(y, 2), 0.5);
	double theta = atan(y / x) * (180 / PAI);
	
	cout << "r:" << r << endl;
	cout << "theta:" << theta << "°" << endl;
	
	return 0;
}

极坐标转直角坐标

已知$(R,\theta )$，
$$X=R\times cos(\theta )$$
$$Y=R\times sin(\theta )$$
Python代码为：

import numpy as np


def Polar_to_Rectangular(r, theta):  # 极坐标转直角坐标，输入的thata需为角度值
	theta = theta * (np.pi / 180)
    x = r * np.cos(theta)
    y = r * np.sin(theta)
    return round(x, 2), round(y, 2)

C++代码为：

#include
#include
#define PAI acos(-1)

using namespace std;
int main() 
{
//	double r = 1.41;
//	double theta = 45*(PAI/180);
	double x_1, y_1, theta_1;
	cout << "请输入X：";
	cin >> x_1;
	cout << "请输入y：";
	cin >> y_1;
	cout << "请输入Theta(°)：";
	cin >> theta_1;
	
	double r = pow(pow(x_1, 2) + pow(y_1, 2), 0.5);
	double theta = theta_1 * (PAI / 180);
	double x = r * cos(theta);
	double y = r * sin(theta);
	
	cout << "x:" << x << endl;
	cout << "y:" << y << endl;
	
	return 0;
}