OpenCV C++ Tutorial for drawing a Star

In the previous tutorial we learnt about drawing a LINE:
http://opencv-code.blogspot.in/2016/12/how-to-draw-line-opencv-cplusplus-example.html

Thus this opencv tutorial will be an extension of that tutorial with some added mathematical logic for drawing a star.

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To begin with we first start by drawing a pentagon:
And name the vertex as a ,b ,c ,d, e.
The co-ordinates of which can be obtained by mathematical rules as explained before:

a=( 2*r*cos(36)*cos(72) , x )
b=( x-2*r*cos(36)*cos(72) , x )
c=( x , 2*r*cos(36)*sin(72) )
d=( x/2 , 0 )
e=( 0 , 2*r*cos(36)*sin(72) )

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Now, The magic begins. 1. Join vertex a with d. 2. Join vertex d with b. 3. Join vertex b with e. 4. Join vertex e with c. 5. Join vertex c with a.

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Here is the opencv code for drawing a Star:

//Opencv Example of drawing a Star 
#include <opencv2/core/core.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <iostream>
#include <math.h>
using namespace cv;
using namespace std;
  
int main( )
{    
  double pi=3.14;
  int a=500/(1+cos(pi*54/180));
  
  // Create black empty images
  Mat image = Mat::zeros( 500, 500, CV_8UC3 );
   
  line( image, Point((a*cos(pi*72/180)), 500),  Point(250, 0), Scalar( 255, 255, 0 ), 2, 8 );
  imshow("Image",image); 
  waitKey( 500 );
 
  line( image, Point(250, 0), Point(500-(a*cos(pi*72/180)),500), Scalar( 255, 255, 0 ), 2, 8 );
  imshow("Image",image); 
  waitKey( 500 ); 
 
  line( image, Point(500-(a*cos(pi*72/180)),500), Point(0, 500-(a*sin(pi*72/180))), Scalar( 255, 255, 0 ), 2, 8 );
  imshow("Image",image); 
  waitKey( 500 );
 
  line( image, Point(0, 500-(a*sin(pi*72/180))), Point( 500, 500-(a*sin(pi*72/180)) ), Scalar( 255, 255, 0 ), 2, 8 );
  imshow("Image",image); 
  waitKey( 500 );
 
  line( image, Point( 500, 500-(a*sin(pi*72/180)) ), Point((a*cos(pi*72/180)), 500), Scalar( 255, 255, 0 ), 2, 8 );
  imshow("Image",image); 
  waitKey( 0 );
  return(0);
}

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Output:-