The Digital Differential Analyzer (DDA) algorithm is one of the simplest line-drawing algorithms in computer graphics. It is an incremental method that determines intermediate points between two given endpoints of a line. In this blog post, we will explore the DDA algorithm, understand its working, and implement it using C++.

What is the DDA Algorithm?

The DDA (Digital Differential Analyzer) algorithm is a rasterization algorithm used to draw lines on a pixel-based display. It works by calculating the intermediate points that form a straight line between two given points and plotting them sequentially. The algorithm uses floating-point arithmetic to incrementally determine the next pixel position.

Steps of the DDA Algorithm:

1. Calculate the change in x (dx) and y (dy) between the starting and ending points.
2. Determine the number of steps required for the line. This is the greater value between dx and dy.
3. Compute the increment values dx/steps and dy/steps to determine how much x and y should increase per step.
4. Start from the initial point and iteratively plot the next points by adding the increment values.
5. Stop when the endpoint is reached.

C++ Implementation of DDA Algorithm

Here is a simple C++ program to implement the DDA line drawing algorithm using the graphics.h library:

//DDA
#include <graphics.h>
#include <stdlib.h>
#include <stdio.h>
#include <conio.h>
#include <iostream.h>

int main(void) {
  /* request auto detection */
  int gdriver = DETECT, gmode, errorcode;

  /* initialize graphics and local variables */
  initgraph( & gdriver, & gmode, "C:\\tc\\bgi");

  cout << "\n Enter X1,Y1,X2,Y2";
  int x1, y1, x2, y2;
  cin >> x1 >> y1 >> x2 >> y2;

  int dx = x2 - x1;
  int dy = y2 - y1;
  int length;
  if (dx >= dy)
    length = dx;
  else
    length = dy;
  dx = dx / length;
  dy = dy / length;
  int sx;
  if (dx >= 0)
    sx = 1;
  else
    sx = -1;
  int sy;
  if (dy >= 0)
    sy = 1;
  else
    sy = -1;
  float x = x1 + 0.5 * (sx);
  float y = y1 + 0.5 * (sy);
  int i = 0;
  while (i <= length) {
    putpixel(int(x), int(y), 15);
    x = x + dx;
    y = y + dy;
    i = i + 1;
  }

  /* clean up */
  getch();
  closegraph();
  return 0;
}

Explanation of the Code

• The program begins by initializing the graphics mode using initgraph().
• It prompts the user to enter the starting and ending coordinates of the line.
• The change in x (dx) and y (dy) is calculated.
• The number of steps needed to draw the line is determined.
• The increments dx/steps and dy/steps are computed.
• A loop is used to plot the points on the screen using the putpixel() function.
• The program waits for user input (getch()) before closing the graphics window.

Output

When you run this program and enter the coordinates of a line, the graphics window will display a line drawn using the DDA algorithm.

The DDA algorithm is a simple and effective method for drawing lines in computer graphics. It provides smooth and precise results and is an essential concept for graphics programming. If you are interested in learning more, you can explore Bresenham’s Line Drawing Algorithm, which is another efficient method for line rasterization.

Happy coding!