C++ Math Challenge(Circle in Asterisks)

Well we all have seen the common questions on creating squares and hollow squares out of asterisks in C++, but how about creating a program that prints out a circle in asterisks? Obviously this would look like an oval due to line adjustment, but it would be quite interesting to see if someone could do it.

I have tried myself and I must admit it is a fairly decent challenge.

If you figure it out, post your code here!

Hint: r^2 = x^2 + y^2

restrictment

Posting Whiz in Training

228 posts since Oct 2009

Reputation Points: 102

Solved Threads: 17

9 Months Ago

Show Comments

Piece of cake, kinda crude approximation tho.

#include <iostream>
#include <cmath>
#include <string>
#include <vector>

using namespace std;

const unsigned CANVAS_WIDTH = 20;
const unsigned CANVAS_HEIGHT = 20;
const unsigned char BACKGROUND_FILL = '#';
const char POINT = '*';
const float PI = 3.14159265f;
const float DEGREE_TO_RADIAN_FACTOR = 0.0174532925f;

typedef std::vector<std::string> Canvas;

float toRadians(const float deg){ return deg * DEGREE_TO_RADIAN_FACTOR;}
int roundPositive(const float n){ return int(n + 0.5f); }

Canvas createDefaultCanvas(){
 return Canvas(CANVAS_HEIGHT, std::string(CANVAS_WIDTH,BACKGROUND_FILL) );
}
void fillCircle(Canvas& canvas,const unsigned radius){

 const int canvasMidX = canvas[0].size() / 2; //assume same width for each height
 const int canvasMidY = canvas.size() / 2;
 const int STEP_SIZE = 1;
 for(int deg = 0; deg < 360; deg += STEP_SIZE){
     float radian = toRadians(deg);
     float x = cos(radian) * radius + canvasMidX;
     float y = sin(radian) * radius + canvasMidY;
     x = roundPositive(x);
     y = roundPositive(y);
     canvas[y][x] = POINT;
 }
}

void showCanvas(const Canvas& canvas){
 for(unsigned height = 0; height < canvas.size(); ++height){
  for(unsigned width = 0; width < canvas[height].size(); ++width){
   cout << canvas[height][width];
  }
  cout << endl;
 }
}
int main(){
 using namespace std;

 const unsigned RADIUS = 5;
 Canvas canvas = createDefaultCanvas();

 fillCircle(canvas,RADIUS);

 showCanvas(canvas);

 return 0;
}

example output :

####################
####################
####################
####################
####################
########*****#######
######***###***#####
######*#######*#####
#####**#######**####
#####*#########*####
#####*#########*####
#####*#########*####
#####**#######**####
######*#######*#####
######***###***#####
########*****#######
####################
####################
####################
####################

firstPerson

Senior Poster

3,923 posts since Dec 2008

Reputation Points: 841

Solved Threads: 608

9 Months Ago

Show Comments

Would look more like a circle if the characters were square and line spacing was the same as character spacing.

#include <iostream>
using namespace std;

int main()
{
	double r = 1.2;

	for( double y = -r-0.1; y <= r+0.2; y += 0.1 )
	{
		for( double x = -r-0.1; x <= r+0.2; x += 0.1 )
		{
			if( (x*x + y*y <= (r*r)*1.1) && (x*x + y*y >= (r*r)*0.9) )
				cout << "*";
			else
				cout << "#";
		}
		cout << endl;
	}
	return 0;
}

Output:

###########################
##########*******##########
#######****#####****#######
######**###########**######
#####**#############**#####
####*#################*####
###**#################**###
##**###################**##
##*#####################*##
##*#####################*##
#**#####################**#
#*#######################*#
#*#######################*#
#*#######################*#
#*#######################*#
#*#######################*#
#**#####################**#
##*#####################*##
##*#####################*##
##**###################**##
###**#################**###
####*#################*####
#####**#############**#####
######**###########**######
#######****#####****#######
##########*******##########
###########################

sfuo

Practically a Master Poster

656 posts since Jul 2009

Reputation Points: 164

Solved Threads: 99

9 Months Ago

Very Cool. Now how about a solid circle? =o

restrictment

Posting Whiz in Training

228 posts since Oct 2009

Reputation Points: 102

Solved Threads: 17

9 Months Ago

C'mon, lets address the aspect ratio.

#include <iostream>

int foo(double a, double b, double x, double y) {
    return ((x*x)/(a*a) + (y*y)/(b*b));
}

int main () {
    int b = 4, a = 10;
    const int min = -15, max = 15;
    int x = min, y = min;
    for (; y < max; ++y) {
        for (x = min; x < max; ++x)
            std::cout << (foo(a,b,x,y) == 1 ? '*' : '#');
        std::cout << std::endl;
    }
    return 0;
}

##############################
##############################
##############################
##############################
##############################
##############################
##############################
##############################
##############################
##############################
#########*************########
######*******************#####
####*****#############*****###
##*****#################*****#
##****###################****#
#*****###################*****
##****###################****#
##*****#################*****#
####*****#############*****###
######*******************#####
#########*************########
##############################
##############################
##############################
##############################
##############################
##############################
##############################
##############################
##############################

L7Sqr

Practically a Master Poster

657 posts since Feb 2011

Reputation Points: 201

Solved Threads: 124

9 Months Ago

#include <iostream>
#include <cmath>
#include <sstream>

int pth (int x,int y)  {
	return std::sqrt (std::pow(x,2)+std::pow(y,2));
 }

int main (int argc,char* argv[])  {
	int c=0;
	int r;
	std::istringstream i(argv[1]);
        i >> r;
	
	const int width=r;
	const int length=r*1.5;

	for (int y=width;y >= -width;y-=2)  {
		for (int x=-length;x <= length;x++)  {
			if ((int) pth(x,y)==r) std::cout << "*";
			else std::cout << " ";
		 }
		std::cout << "\n";
	 }
	std::cin.get();
 }
                                      ***************                                      
                                ***                     ***                                
                             **                             **                             
                          **                                   **                          
                        *                                         *                        
                      *                                             *                      
                    **                                               **                    
                   *                                                   *                   
                  *                                                     *                  
                 *                                                       *                 
                *                                                         *                
                *                                                         *                
               *                                                           *               
               *                                                           *               
               *                                                           *               
               *                                                           *               
               *                                                           *               
               *                                                           *               
               *                                                           *               
                *                                                         *                
                *                                                         *                
                 *                                                       *                 
                  *                                                     *                  
                   *                                                   *                   
                    **                                               **                    
                      *                                             *                      
                        *                                         *                        
                          **                                   **                          
                             **                             **                             
                                ***                     ***                                
                                      ***************

caut_baia

Posting Whiz

387 posts since Apr 2010

Reputation Points: 25

Solved Threads: 49

9 Months Ago

#include <iostream>
#include <cmath>
#include <sstream>

int pth (int x,int y)  {
	return std::sqrt (std::pow(x,2)+std::pow(y,2));
 }

int main (int argc,char* argv[1])  {
	if (argv[1]==NULL) argv[1]="30";
	int c=0;
	int r;
	std::istringstream i(argv[1]);
        i >> r;
	
	const int width=r;
	const int length=r*1.5;
	bool in=1;

	for (int y=width;y >= -width;y-=2)  {
		for (int x=-length;x <= length;x++)  {
			if (pth(x,y)==r && pth(x-1,y)!=r)  {
				std::cout << "*";
				in^=1; 
			 }
			else if (in) std::cout << "*";
			else std::cout << " ";
		 }
		std::cout << "\n";
	 }
	std::cin.get();
 }
***************************************                                                    
                                *************************                                  
                             ********************************                              
                          **************************************                           
                        *******************************************                        
                      ***********************************************                      
                    **************************************************                     
                   *****************************************************                   
                  *******************************************************                  
                 *********************************************************                 
                ***********************************************************                
                ***********************************************************                
               *************************************************************               
               *************************************************************               
               *************************************************************               
               *************************************************************               
               *************************************************************               
               *************************************************************               
               *************************************************************               
                ***********************************************************                
                ***********************************************************                
                 *********************************************************                 
                  *******************************************************                  
                   *****************************************************                   
                    **************************************************                     
                      ***********************************************                      
                        *******************************************                        
                          **************************************                           
                             ********************************                              
                                *************************                                  
                                      *****************************************************

caut_baia

Posting Whiz

387 posts since Apr 2010

Reputation Points: 25

Solved Threads: 49

9 Months Ago

Using midpoint circle algorithm:

#include <stack>
#include <string>
#include <iostream>
#include <vector>
#include <string>
#include <algorithm>

using namespace std;

typedef std::vector<std::string> Canvas;

void setPixel(int x, int y, Canvas& canvas){
	canvas[y][x] = '*';
}
//midpoint circle algorithm -- src via wiki
void renderCircle(const int x0, const int y0, const int radius,Canvas& c){
  int f = 1 - radius;
  int ddF_x = 1;
  int ddF_y = -2 * radius;
  int x = 0;
  int y = radius;
 
  setPixel(x0, y0 + radius, c);
  setPixel(x0, y0 - radius, c);
  setPixel(x0 + radius, y0, c);
  setPixel(x0 - radius, y0, c);
 
  while(x < y)
  {
    // ddF_x == 2 * x + 1;
    // ddF_y == -2 * y;
    // f == x*x + y*y - radius*radius + 2*x - y + 1;
    if(f >= 0) 
    {
      y--;
      ddF_y += 2;
      f += ddF_y;
    }
    x++;
    ddF_x += 2;
    f += ddF_x;    
    setPixel(x0 + x, y0 + y, c);
    setPixel(x0 - x, y0 + y, c);
    setPixel(x0 + x, y0 - y, c);
    setPixel(x0 - x, y0 - y, c);
    setPixel(x0 + y, y0 + x, c);
    setPixel(x0 - y, y0 + x, c);
    setPixel(x0 + y, y0 - x, c);
    setPixel(x0 - y, y0 - x, c);
  }
}

void show(const Canvas& c){
	struct _show{
		void operator()(const std::string& str){ cout << str << endl; }
	};
	std::for_each(c.begin(),c.end(),_show());
}
int main(){
	const unsigned RADIUS = 10;
	Canvas c = Canvas(50,string(50,' ') );
	renderCircle(25,25,RADIUS,c);
	show(c);
 return 0;
}

*******
                    **       **
                   *           *
                  *             *
                 *               *
                *                 *
                *                 *
               *                   *
               *                   *
               *                   *
               *                   *
               *                   *
               *                   *
               *                   *
                *                 *
                *                 *
                 *               *
                  *             *
                   *           *
                    **       **
                      *******

firstPerson

Senior Poster

3,923 posts since Dec 2008

Reputation Points: 841

Solved Threads: 608

8 Months Ago

C'mon, lets address the aspect ratio.

#include <iostream>

int foo(double a, double b, double x, double y) {
    return ((x*x)/(a*a) + (y*y)/(b*b));
}

int main () {
    int b = 4, a = 10;
    const int min = -15, max = 15;
    int x = min, y = min;
    for (; y < max; ++y) {
        for (x = min; x < max; ++x)
            std::cout << (foo(a,b,x,y) == 1 ? '*' : '#');
        std::cout << std::endl;
    }
    return 0;
}

##############################
##############################
##############################
##############################
##############################
##############################
##############################
##############################
##############################
##############################
#########*************########
######*******************#####
####*****#############*****###
##*****#################*****#
##****###################****#
#*****###################*****
##****###################****#
##*****#################*****#
####*****#############*****###
######*******************#####
#########*************########
##############################
##############################
##############################
##############################
##############################
##############################
##############################
##############################
##############################

@L7Sqr: Cool program man, could be please also comment the code so that beginners like me would know what is happening in every line of code, thanks in advance!

hasnain2009

Newbie Poster

1 post since Sep 2011

Reputation Points: 10

Solved Threads: 0

8 Months Ago

You can read about the equation here - that is what the foo function does. The rest of the program just loops over the bounds of our drawing area evaluating that formula and drawing a * when it evaluates to 1.

L7Sqr

Practically a Master Poster

657 posts since Feb 2011

Reputation Points: 201

Solved Threads: 124

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