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 #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;     DDA(2, 2, 14, 16);     return 0; }

Output:

• 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.

• 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