Dda Circle Drawing Algorithm in Computer Graphics Using C

The mid-betoken circle drawing algorithm is an algorithm used to decide the points needed for rasterizing a circumvolve.

We use the mid-point algorithm to summate all the perimeter points of the circle in the first octant and then print them along with their mirror points in the other octants. This volition work because a circumvolve is symmetric nearly its center.

The algorithm is very similar to the Mid-Indicate Line Generation Algorithm. Hither, only the boundary condition is different.

For any given pixel (ten, y), the next pixel to be plotted is either (ten, y+one) or (x-one, y+1). This can be decided by following the steps below.

1. Detect the mid-point p of the two possible pixels i.e (x-0.5, y+ane)
2. If p lies inside or on the circle perimeter, we plot the pixel (x, y+ane), otherwise if it's outside we plot the pixel (x-1, y+1)

Boundary Status : Whether the mid-point lies within or outside the circumvolve can be decided by using the formula:-

Given a circle centered at (0,0) and radius r and a betoken p(x,y)
F(p) = xⁱⁱ + yⁱⁱ – r^two
if F(p)<0, the point is inside the circumvolve
F(p)=0, the bespeak is on the perimeter
F(p)>0, the point is exterior the circle

In our programme, nosotros denote F(p) with P. The value of P is calculated at the mid-bespeak of the 2 contending pixels i.eastward. (x-0.v, y+1). Each pixel is described with a subscript k.

P_chiliad = (Ten_grand — 0.5)ⁱⁱ + (y_k + ane)² – r²
Now,
ten₁₀₀₀₊₁ = x_m or ten_k-1 , y₁₀₀₀₊₁= y_grand +1
∴ P_k+1 = (10_k+i – 0.5)ⁱⁱ + (y_chiliad+1 +one)^two – r²
= (ten_g+ane – 0.5)² + [(y_k +i) + 1]^two – r²
= (x_thou+i – 0.5)² + (y_thou +1)² + 2(y_k + 1) + 1 – r^two
= (x_k+1 – 0.v)² + [ – (ten_k – 0.5)² +(x_k – 0.v)^two ] + (y_grand + 1)ⁱⁱ – r² + ii(y_k + 1) + 1
= P_k + (10_k+i – 0.five)ⁱⁱ – (10_chiliad – 0.5)ⁱⁱ + two(y_thou + 1) + i
= P_g + (xⁱⁱ _k+i – x² _k) – (10_k+1 – x_k) + 2(y_k + 1) + ane
= P_yard + 2(y_thousand +1) + i, when P_k <=0 i.e the midpoint is within the circle
(x_k+1 = x_k)
P_{one thousand} + 2(y_k +1) – ii(ten_k – 1) + one, when P_chiliad>0 I.east the mid betoken is outside the circle(x_k+1 = x_grand-1)

The first point to be plotted is (r, 0) on the x-axis. The initial value of P is calculated every bit follows:-

P1 = (r – 0.v)² + (0+1)^two – r^two
= 1.25 – r
= 1 -r (When rounded off)

Examples:

          Input :          Heart -> (0, 0), Radius -> 3          Output :          (3, 0) (3, 0) (0, 3) (0, iii)          (3, 1) (-3, 1) (3, -1) (-3, -one)          (ane, 3) (-1, 3) (1, -3) (-i, -iii)          (2, two) (-2, 2) (2, -ii) (-ii, -2)

          Input :          Centre -> (4, iv), Radius -> 2          Output :          (6, four) (6, 4) (4, half dozen) (4, half dozen)          (6, 5) (2, five) (6, 3) (2, 3)          (five, 6) (3, 6) (5, 2) (3, two)

CPP

#include<iostream>

using namespace std;

void midPointCircleDraw( int x_centre, int y_centre, int r)

{

int x = r, y = 0;

cout << "(" << ten + x_centre << ", " << y + y_centre << ") " ;

if (r > 0)

{

cout << "(" << ten + x_centre << ", " << -y + y_centre << ") " ;

cout << "(" << y + x_centre << ", " << x + y_centre << ") " ;

cout << "(" << -y + x_centre << ", " << x + y_centre << ")\n" ;

}

int P = i - r;

while (10 > y)

{

y++;

if (P <= 0)

P = P + 2*y + i;

else

{

10--;

P = P + 2*y - 2*10 + 1;

}

if (x < y)

break ;

cout << "(" << x + x_centre << ", " << y + y_centre << ") " ;

cout << "(" << -x + x_centre << ", " << y + y_centre << ") " ;

cout << "(" << 10 + x_centre << ", " << -y + y_centre << ") " ;

cout << "(" << -x + x_centre << ", " << -y + y_centre << ")\n" ;

if (10 != y)

{

cout << "(" << y + x_centre << ", " << 10 + y_centre << ") " ;

cout << "(" << -y + x_centre << ", " << x + y_centre << ") " ;

cout << "(" << y + x_centre << ", " << -x + y_centre << ") " ;

cout << "(" << -y + x_centre << ", " << -10 + y_centre << ")\n" ;

}

}

}

int principal()

{

midPointCircleDraw(0, 0, three);

return 0;

}

C

#include<stdio.h>

void midPointCircleDraw( int x_centre, int y_centre, int r)

{

int ten = r, y = 0;

printf ( "(%d, %d) " , 10 + x_centre, y + y_centre);

if (r > 0)

{

printf ( "(%d, %d) " , x + x_centre, -y + y_centre);

printf ( "(%d, %d) " , y + x_centre, 10 + y_centre);

printf ( "(%d, %d)\north" , -y + x_centre, x + y_centre);

}

int P = 1 - r;

while (x > y)

{

y++;

if (P <= 0)

P = P + 2*y + 1;

else

{

x--;

P = P + 2*y - ii*x + 1;

}

if (ten < y)

pause ;

printf ( "(%d, %d) " , x + x_centre, y + y_centre);

printf ( "(%d, %d) " , -x + x_centre, y + y_centre);

printf ( "(%d, %d) " , 10 + x_centre, -y + y_centre);

printf ( "(%d, %d)\n" , -x + x_centre, -y + y_centre);

if (10 != y)

{

printf ( "(%d, %d) " , y + x_centre, x + y_centre);

printf ( "(%d, %d) " , -y + x_centre, x + y_centre);

printf ( "(%d, %d) " , y + x_centre, -10 + y_centre);

printf ( "(%d, %d)\due north" , -y + x_centre, -ten + y_centre);

}

}

}

int main()

{

midPointCircleDraw(0, 0, three);

return 0;

}

Java

class GFG {

static void midPointCircleDraw( int x_centre,

int y_centre, int r)

{

int x = r, y = 0 ;

System.out.print( "(" + (10 + x_centre)

+ ", " + (y + y_centre) + ")" );

if (r > 0 ) {

System.out.impress( "(" + (x + x_centre)

+ ", " + (-y + y_centre) + ")" );

System.out.impress( "(" + (y + x_centre)

+ ", " + (x + y_centre) + ")" );

System.out.println( "(" + (-y + x_centre)

+ ", " + (ten + y_centre) + ")" );

}

int P = 1 - r;

while (x > y) {

y++;

if (P <= 0 )

P = P + 2 * y + 1 ;

else {

ten--;

P = P + ii * y - two * x + 1 ;

}

if (ten < y)

break ;

Arrangement.out.print( "(" + (ten + x_centre)

+ ", " + (y + y_centre) + ")" );

Organisation.out.print( "(" + (-x + x_centre)

+ ", " + (y + y_centre) + ")" );

Organisation.out.print( "(" + (x + x_centre) +

", " + (-y + y_centre) + ")" );

Organization.out.println( "(" + (-10 + x_centre)

+ ", " + (-y + y_centre) + ")" );

if (ten != y) {

System.out.impress( "(" + (y + x_centre)

+ ", " + (x + y_centre) + ")" );

System.out.print( "(" + (-y + x_centre)

+ ", " + (x + y_centre) + ")" );

Organization.out.print( "(" + (y + x_centre)

+ ", " + (-10 + y_centre) + ")" );

System.out.println( "(" + (-y + x_centre)

+ ", " + (-x + y_centre) + ")" );

}

}

}

public static void master(String[] args) {

midPointCircleDraw( 0 , 0 , 3 );

}

}

Python3

def midPointCircleDraw(x_centre, y_centre, r):

x = r

y = 0

impress ( "(" , x + x_centre, ", " ,

y + y_centre, ")" ,

sep = " ", end = " ")

if (r > 0 ) :

impress ( "(" , 10 + x_centre, ", " ,

- y + y_centre, ")" ,

sep = " ", end = " ")

print ( "(" , y + x_centre, ", " ,

x + y_centre, ")" ,

sep = " ", end = " ")

print ( "(" , - y + x_centre, ", " ,

x + y_centre, ")" , sep = "")

P = 1 - r

while x > y:

y + = 1

if P < = 0 :

P = P + 2 * y + 1

else :

10 - = one

P = P + 2 * y - 2 * ten + 1

if (x < y):

intermission

print ( "(" , x + x_centre, ", " , y + y_centre,

")" , sep = " ", end = " ")

print ( "(" , - x + x_centre, ", " , y + y_centre,

")" , sep = " ", end = " ")

print ( "(" , 10 + x_centre, ", " , - y + y_centre,

")" , sep = " ", end = " ")

print ( "(" , - ten + x_centre, ", " , - y + y_centre,

")" , sep = "")

if x ! = y:

print ( "(" , y + x_centre, ", " , x + y_centre,

")" , sep = " ", end = " ")

print ( "(" , - y + x_centre, ", " , ten + y_centre,

")" , sep = " ", end = " ")

print ( "(" , y + x_centre, ", " , - 10 + y_centre,

")" , sep = " ", finish = " ")

print ( "(" , - y + x_centre, ", " , - x + y_centre,

")" , sep = "")

if __name__ = = '__main__' :

midPointCircleDraw( 0 , 0 , three )

C#

using System;

class GFG {

static void midPointCircleDraw( int x_centre,

int y_centre, int r)

{

int x = r, y = 0;

Console.Write( "(" + (x + x_centre)

+ ", " + (y + y_centre) + ")" );

if (r > 0)

{

Console.Write( "(" + (x + x_centre)

+ ", " + (-y + y_centre) + ")" );

Console.Write( "(" + (y + x_centre)

+ ", " + (ten + y_centre) + ")" );

Console.WriteLine( "(" + (-y + x_centre)

+ ", " + (ten + y_centre) + ")" );

}

int P = 1 - r;

while (x > y)

{

y++;

if (P <= 0)

P = P + 2 * y + i;

else

{

ten--;

P = P + 2 * y - 2 * 10 + one;

}

if (ten < y)

break ;

Console.Write( "(" + (ten + x_centre)

+ ", " + (y + y_centre) + ")" );

Panel.Write( "(" + (-ten + x_centre)

+ ", " + (y + y_centre) + ")" );

Console.Write( "(" + (ten + x_centre) +

", " + (-y + y_centre) + ")" );

Panel.WriteLine( "(" + (-x + x_centre)

+ ", " + (-y + y_centre) + ")" );

if (x != y)

{

Console.Write( "(" + (y + x_centre)

+ ", " + (10 + y_centre) + ")" );

Console.Write( "(" + (-y + x_centre)

+ ", " + (x + y_centre) + ")" );

Console.Write( "(" + (y + x_centre)

+ ", " + (-10 + y_centre) + ")" );

Console.WriteLine( "(" + (-y + x_centre)

+ ", " + (-x + y_centre) + ")" );

}

}

}

public static void Main()

{

midPointCircleDraw(0, 0, 3);

}

}

PHP

<?php

function midPointCircleDraw( $x_centre ,

$y_centre ,

$r )

{

$ten = $r ;

$y = 0;

echo "(" , $ten + $x_centre , "," , $y + $y_centre , ")" ;

if ( $r > 0)

{

repeat "(" , $x + $x_centre , "," , - $y + $y_centre , ")" ;

echo "(" , $y + $x_centre , "," , $ten + $y_centre , ")" ;

echo "(" ,- $y + $x_centre , "," , $x + $y_centre , ")" , "\n" ;

}

$P = 1 - $r ;

while ( $10 > $y )

{

$y ++;

if ( $P <= 0)

$P = $P + 2 * $y + 1;

else

{

$x --;

$P = $P + two * $y -

2 * $x + 1;

}

if ( $x < $y )

suspension ;

echo "(" , $x + $x_centre , "," , $y + $y_centre , ")" ;

echo "(" ,- $x + $x_centre , "," , $y + $y_centre , ")" ;

repeat "(" , $x + $x_centre , "," , - $y + $y_centre , ")" ;

repeat "(" ,- $10 + $x_centre , "," , - $y + $y_centre , ")" , "\northward" ;

if ( $x != $y )

{

repeat "(" , $y + $x_centre , "," , $x + $y_centre , ")" ;

echo "(" ,- $y + $x_centre , "," , $x + $y_centre , ")" ;

echo "(" , $y + $x_centre , "," , - $ten + $y_centre , ")" ;

echo "(" ,- $y + $x_centre , "," , - $ten + $y_centre , ")" , "\n" ;

}

}

}

midPointCircleDraw(0, 0, three);

?>

Javascript

<script>

office midPointCircleDraw(x_centre , y_centre , r) {

var 10 = r, y = 0;

certificate.write( "(" + (x + x_centre) + ", " + (y + y_centre) + ")" );

if (r > 0) {

document.write( "(" + (ten + x_centre) + ", " + (-y + y_centre) + ")" );

certificate.write( "(" + (y + x_centre) + ", " + (x + y_centre) + ")" );

document.write( "(" + (-y + x_centre) + ", " + (x + y_centre) + ")<br/>" );

}

var P = 1 - r;

while (10 > y) {

y++;

if (P <= 0)

P = P + ii * y + 1;

else {

x--;

P = P + 2 * y - 2 * ten + one;

}

if (x < y)

break ;

document.write( "(" + (x + x_centre) + ", " + (y + y_centre) + ")" );

document.write( "(" + (-x + x_centre) + ", " + (y + y_centre) + ")" );

document.write( "(" + (x + x_centre) + ", " + (-y + y_centre) + ")" );

document.write( "(" + (-x + x_centre) + ", " + (-y + y_centre) + ")<br/>" );

if (10 != y) {

document.write( "(" + (y + x_centre) + ", " + (ten + y_centre) + ")" );

document.write( "(" + (-y + x_centre) + ", " + (x + y_centre) + ")" );

document.write( "(" + (y + x_centre) + ", " + (-x + y_centre) + ")" );

certificate.write( "(" + (-y + x_centre) + ", " + (-10 + y_centre) + ")<br/>" );

}

}

}

midPointCircleDraw(0, 0, 3);

</script>

Output:

(3, 0) (3, 0) (0, 3) (0, 3) (3, 1) (-3, 1) (3, -1) (-3, -ane) (1, 3) (-1, iii) (1, -3) (-1, -3) (ii, ii) (-2, 2) (2, -2) (-2, -two)

Fourth dimension Complication: O(ten – y)
Auxiliary Space: O(1)
References : Midpoint Circle Algorithm
Epitome References : Octants of a circle, Rasterised Circumvolve, the other images were created for this article by the geek
Thanks Tuhina Singh and Teva Zanker for improving this article.
This article is contributed by Nabaneet Roy. If you lot like GeeksforGeeks and would like to contribute, you can also write an commodity using write.geeksforgeeks.org or postal service your commodity to review-squad@geeksforgeeks.org. See your article appearing on the GeeksforGeeks chief page and assistance other Geeks.
Please write comments if you observe anything incorrect, or you want to share more than information about the topic discussed above.

bromananceend.blogspot.com

Source: https://www.geeksforgeeks.org/mid-point-circle-drawing-algorithm/

Share this post