Draw A Circle Without Floating Point Arithmetic In C++

Algorithms that solely rely on integer operations are essential for rendering circles without utilizing floating-point calculations. Bresenham's algorithm for drawing circles is a popular choice in such scenarios, where only integer arithmetic is employed to efficiently and effectively generate circle shapes.

A variation of Bresenham's line algorithm, employed for drawing lines on a raster display, is Bresenham's circle plotting algorithm. This technique determines the precise points to be marked along the circle's boundary through a smart decision-making process that relies solely on integer computations. By avoiding floating-point arithmetic, this approach accurately determines the pixel positions to mimic a circle with great precision.

The decision factor is employed to ascertain the next C++ tutorial to be displayed, and it serves as the central idea behind Bresenham's technique for drawing circles. This method efficiently sketches the circle using solely integer operations by meticulously adjusting the decision factor according to the previous selection and the mathematical attributes of the circle. This approach is suitable for situations or environments where using floating-point calculations may not be preferred or feasible due to this particular attribute.

Although Bresenham's algorithm provides a fast method for rendering circles without relying on floating-point calculations, it's important to note that the resulting circles may lack the precision and smoothness of those generated by algorithms utilizing floating-point operations. Nevertheless, Bresenham's method serves as a valuable resource for various applications, especially in computer graphics on devices with limited resources, enabling the creation of circles and other shapes without the need for floating-point arithmetic.

Code:

#include <stdio.h>
void Draw_Circle(int radius)
{
    // Think of a rectangle with dimensions N*N.
    int N = 2*radius+1;
    int xyz, pqr;  
    // inside-rectangle coordinates
    // Make a square with sides of N*N.
    for (int k = 0; k < N; k++)
    {
        for (int l = 0; l < N; l++)
        {
            // begin from the position in the corner of the left.
            xyz = k-radius;
            pqr = l-radius;
            // Print it if this point falls inside the circle.
            if (xyz*xyz + pqr*pqr <= radius*radius+1 )
            {
                printf(".");
            }
             else 
             //If outside of the circle, print space
                printf(" ");
            printf(" ");
        }
        printf("\n");
    }
}
int  main()
{
    Draw_Circle(10);
    return 0;
}

Output:

. . .                   
            . . . . . . . . .             
        . . . . . . . . . . . . .         
      . . . . . . . . . . . . . . .       
    . . . . . . . . . . . . . . . . .     
    . . . . . . . . . . . . . . . . .     
  . . . . . . . . . . . . . . . . . . .   
  . . . . . . . . . . . . . . . . . . .   
  . . . . . . . . . . . . . . . . . . .   
. . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . 
  . . . . . . . . . . . . . . . . . . .   
  . . . . . . . . . . . . . . . . . . .   
  . . . . . . . . . . . . . . . . . . .   
    . . . . . . . . . . . . . . . . .     
    . . . . . . . . . . . . . . . . .     
      . . . . . . . . . . . . . . .       
        . . . . . . . . . . . . .         
            . . . . . . . . .             
                  . . .

Explanation:

• ✅ In this example, when given an integer radius as an input, the Draw_Circle function utilizes that radius to calculate the size of the square grid and draw the circle inside of it.
• ✅ The square grid's dimensions are specified by the variable N , which is set to 2 * radius + 1 . The grid will have N rows and N columns , forming a square with N units on each side.
• ✅ The rows and columns of the square grid are iterated over using two nested loops. The variables k and l are responsible for these loops.
• ✅ The nested loops contain calculations for the variables xyz and pqr . The coordinates of the currencpp tutorial concerning the grid's center are shown by these variables.
• ✅ The if statement determines if the currencpp tutorial, denoted by the variables xyz and pqr, is inside the circle. It is accomplished by comparing the point's squared distance from the center to the circle's squared radius (using the Pythagorean theorem). It prints a period (. ), which symbolizes a filled point if the point is inside the circle. In the absence of that, a space , which stands for an empty point, is printed.
• ✅ A newline character (n) , which signals the transition to the following row of the grid, is displayed after iterating through each point in a row.
• ✅ Draw_Circle is called by the main function with a radius of 10, and it returns 0.