DDA Line generation Algorithm in Computer Graphics

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 the 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;
}

Python3

# Python program for DDA line generation
from matplotlib import pyplot as plt

# DDA Function for line generation
def DDA(x0, y0, x1, y1):

    # find absolute differences
    dx = abs(x0 - x1)
    dy = abs(y0 - y1)

    # find maximum difference
    steps = max(dx, dy)

    # calculate the increment in x and y
    xinc  = dx/steps
    yinc = dy/steps

    # start with 1st point
    x = float(x0)
    y = float(y0)

    # make a list for coordinates
    x_coorinates = []
    y_coorinates = []

    for i in range(steps):
        # append the x,y coordinates in respective list
        x_coorinates.append(x)
        y_coorinates.append(y)

        # increment the values
        x = x + xinc
        y = y + yinc

    # plot the line with coordinates list
    plt.plot(x_coorinates, y_coorinates, marker = "o", markersize = 1, markerfacecolor = "green")
    plt.show()


if __name__ == "__main__":

    # coordinates of 1st point
    x0, y0 =  20, 20

    # coordinates of 2nd point
    x1, y1 = 60, 50
    DDA(x0, y0, x1, y1)

    # This code is contributed by 111arpit1

C++

#include <iostream>
//#include<graphics.h>
//#include<time.h>
using namespace std;

//function for rounding off the pixels
int round(float n) {
    if (n - (int)n < 0.5)
        return (int)n;
    return (int)(n + 1);
}

//function for line generation
void DDALine(int x0, int y0, int x1, int y1) {

      //calculate dx and dy
      int dx = x1 - x0;
    int dy= y1 - y0;

    int step;

      //if dx > dy we will take step as dx
      //else we will take step as dy to draw the complete line
    if (abs(dx) > abs(dy))
        step = abs(dx);
    else
        step = abs(dy);

      //calculate x-increment and y-increment for each step
    float x_incr = (float)dx / step;
    float y_incr = (float)dy / step;

      //take the initial points as x and y
    float x = x0;
    float y = y0;

    for (int i = 0; i < step; i ++) {
        //putpixel(round(x), round(y), WHITE);
        cout << round(x) << " " << round(y) << "\n";
        x += x_incr;
        y += y_incr;
        //delay(10);
    }
}

//driver function
int main() {
    //initwindow(3000,1000);
    int x0 = 200, y0 = 180, x1 = 180, y1 = 160;

    DDALine(x0, y0, x1, y1);
    //getch();
    //closegraph();

    return 0;
}

//all functions regarding to graphichs.h are commented out
//contributed by hopelessalexander

Output: 

200 180
199 179
198 178
197 177
196 176
195 175
194 174
193 173
192 172
191 171
190 170
189 169
188 168
187 167
186 166
185 165
184 164
183 163
182 162
181 161

Advantages :

• It is a simple and easy-to-implement algorithm.
• It avoids 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 a 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 write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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