DDA Line generation Algorithm in Computer Graphics

Difficulty Level : Easy
Last Updated : 19 Feb, 2021

In any 2-Dimensional plane if we connect two points (x0, y0) and (x1, y1), we get a line segment. But in the case of computer graphics, we can not directly join any two coordinate points, for that we should calculate intermediate points’ coordinates and put a pixel for each intermediate point, of the desired color with help of functions like putpixel(x, y, K) in C, where (x,y) is our co-ordinate and K denotes some color.
Examples:

Input: For line segment between (2, 2) and (6, 6) :
we need (3, 3) (4, 4) and (5, 5) as our intermediate
points.

Input: For line segment between (0, 2) and (0, 6) :
we need (0, 3) (0, 4) and (0, 5) as our intermediate
points.

For using graphics functions, our system output screen is treated as a coordinate system where the coordinate of the top-left corner is (0, 0) and as we move down our y-ordinate increases and as we move right our x-ordinate increases for any point (x, y).
Now, for generating any line segment we need intermediate points and for calculating them we can use a basic algorithm called DDA(Digital differential analyzer) line generating algorithm.

DDA Algorithm :
Consider one point of the line as (X0,Y0) and the second point of the line as (X1,Y1).

// calculate dx , dy
dx = X1 - X0;
dy = Y1 - Y0;

// Depending upon absolute value of dx & dy
// choose number of steps to put pixel as
// steps = abs(dx) > abs(dy) ? abs(dx) : abs(dy)
steps = abs(dx) > abs(dy) ? abs(dx) : abs(dy);

// calculate increment in x & y for each steps
Xinc = dx / (float) steps;
Yinc = dy / (float) steps;

// Put pixel for each step
X = X0;
Y = Y0;
for (int i = 0; i <= steps; i++)
{
    putpixel (round(X),round(Y),WHITE);
    X += Xinc;
    Y += Yinc;
}

C

// C program for DDA line generation
#include<stdio.h>
#include<graphics.h>
#include<math.h>
//Function for finding absolute value
int abs (int n)
{
    return ( (n>0) ? n : ( n * (-1)));
}
 
//DDA Function for line generation
void DDA(int X0, int Y0, int X1, int Y1)
{
    // calculate dx & dy
    int dx = X1 - X0;
    int dy = Y1 - Y0;
 
    // calculate steps required for generating pixels
    int steps = abs(dx) > abs(dy) ? abs(dx) : abs(dy);
 
    // calculate increment in x & y for each steps
    float Xinc = dx / (float) steps;
    float Yinc = dy / (float) steps;
 
    // Put pixel for each step
    float X = X0;
    float Y = Y0;
    for (int i = 0; i <= steps; i++)
    {
        putpixel (round(X),round(Y),RED);  // put pixel at (X,Y)
        X += Xinc;           // increment in x at each step
        Y += Yinc;           // increment in y at each step
        delay(100);          // for visualization of line-
                             // generation step by step
    }
}
 
// Driver program
int main()
{
    int gd = DETECT, gm;
 
    // Initialize graphics function
    initgraph (&gd, &gm, "");   
 
    int X0 = 2, Y0 = 2, X1 = 14, Y1 = 16;
    DDA(2, 2, 14, 16);
    return 0;
} 

Output:

Advantages :

It is simple and easy to implement algorithm.
It avoid using multiple operations which have high time complexities.
It is faster than the direct use of the line equation because it does not use any floating point multiplication and it calculates points on the line.

Disadvantages :

It deals with the rounding off operation and floating point arithmetic so it has high time complexity.
As it is orientation dependent, so it has poor endpoint accuracy.
Due to the limited precision in the floating point representation it produces cumulative error.

Bresenham’s Line Generation Algorithm
This article is contributed by Shivam Pradhan (anuj_charm). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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