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# DDA Line generation Algorithm in Computer Graphics

• Difficulty Level : Easy
• Last Updated : 20 Dec, 2022

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) :
Output: we need (3, 3) (4, 4) and (5, 5) as our intermediate points.

Input: For line segment between (0, 2) and (0, 6) :
Output: 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;
}

Below is the implementation of the above approach:

## C

 `// C program for DDA line generation`   `#include ` `#include ` `#include ` `// 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;`   `    ``// Function call` `    ``DDA(2, 2, 14, 16);` `    ``return` `0;` `}`

## C++

 `// C++ program for DDA line generation`   `#include ` `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 code` `int` `main()` `{`   `    ``int` `x0 = 200, y0 = 180, x1 = 180, y1 = 160;`   `    ``// Function call` `    ``DDALine(x0, y0, x1, y1);`   `    ``return` `0;` `}`   `// all functions regarding to graphichs.h are commented out` `// contributed by hopelessalexander`

## Java

 `// Java Code for DDA line generation ` `public` `class` `Solution {`   `  ``// function for rounding off the pixels` `  ``public` `static` `int` `round(``float` `n) {` `    ``if` `(n - (``int``) n < ``0.5``)` `      ``return` `(``int``) n;` `    ``return` `(``int``) (n + ``1``);` `  ``}`   `  ``// Function for line generation` `  ``public` `static` `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` `(Math.abs(dx) > Math.abs(dy))` `      ``step = Math.abs(dx);` `    ``else` `      ``step = Math.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);` `      ``System.out.println(round(x) + ``" "` `+ round(y));` `      ``x += x_incr;` `      ``y += y_incr;` `      ``// delay(10);` `    ``}` `  ``}`   `  ``// Driver code` `  ``public` `static` `void` `main(String[] args) {`   `    ``int` `x0 = ``200``, y0 = ``180``, x1 = ``180``, y1 = ``160``;`   `    ``// Function call` `    ``DDALine(x0, y0, x1, y1);`   `  ``}` `}`   `// This code is contributed by ishankhandelwals.`

## 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()`     `# Driver code` `if` `__name__ ``=``=` `"__main__"``:`   `    ``# coordinates of 1st point` `    ``x0, y0 ``=` `20``, ``20`   `    ``# coordinates of 2nd point` `    ``x1, y1 ``=` `60``, ``50`   `    ``# Function call` `    ``DDA(x0, y0, x1, y1)`   `    ``# This code is contributed by 111arpit1`

## C#

 `// C# code for DDA line generation` `using` `System;` `public` `class` `Solution ` `{` `  `  `  ``// function for rounding off the pixels` `  ``public` `static` `int` `Round(``float` `n)` `  ``{` `    ``if` `(n - (``int``)n < 0.5)` `      ``return` `(``int``)n;` `    ``return` `(``int``)(n + 1);` `  ``}`   `  ``// Function for line generation` `  ``public` `static` `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` `(Math.Abs(dx) > Math.Abs(dy))` `      ``step = Math.Abs(dx);` `    ``else` `      ``step = Math.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);` `      ``Console.WriteLine(Round(x) + ``" "` `+ Round(y));` `      ``x += x_incr;` `      ``y += y_incr;` `      ``// delay(10);` `    ``}` `  ``}`   `  ``// Driver code` `  ``public` `static` `void` `Main(``string``[] args)` `  ``{`   `    ``int` `x0 = 200, y0 = 180, x1 = 180, y1 = 160;`   `    ``// Function call` `    ``DDALine(x0, y0, x1, y1);` `  ``}` `}`   `// This code is contributed by ishankhandelwals`

## Javascript

 `// JS program for DDA Line generation`   `function` `round(n) {` `    ``if` `(n - Math.floor(n) < 0.5)` `        ``return` `Math.floor(n);` `    ``return` `Math.floor(n + 1);` `};`   `function` `DDALine(x0, y0, x1, y1) {` `    ``let dx = x1 - x0;` `    ``let dy = y1 - y0;` `    ``let step;`   `    ``if` `(Math.abs(dx) > Math.abs(dy))` `        ``step = Math.abs(dx);` `    ``else` `        ``step = Math.abs(dy);`   `    ``let x_incr = (dx / step);` `    ``let y_incr = (dy / step);`   `    ``let x = x0;` `    ``let y = y0;`   `    ``for` `(let i = 0; i < step; i++) {` `        ``console.log(round(x) + ``" "` `+ round(y));` `        ``x += x_incr;` `        ``y += y_incr;` `    ``}` `};`   `let x0 = 200, y0 = 180, x1 = 180, y1 = 160;` `DDALine(x0, y0, x1, y1);`   `// This code is contributed by ishankhandelwals.`

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```

• 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.

• 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.

Bresenhamâ€™s Line Generation Algorithm