What is the Bresenham line tracer algorithm?

There are many algorithms which, rather than giving an alphanumeric output, give you a graphical output. Line drawing algorithms are among these types of algorithms. Moreover, the Bresenham Line Tracer Algorithm is one of the fastest algorithms to draw straight lines on a digital display whose pixels are based on an x-y axis graph-like setting. 

However, the algorithm originally is known as the Bresenham line drawing algorithm, but for some reason, it is known more for tracing the line rather than drawing it. So, let's know everything about the Bresenham Line Tracer Algorithm in detail. 

What is the Bresenham Line Drawing Algorithm?

The Bresenham line drawing algorithm is popular for drawing a straight line on a digital screen. The Bresenham line drawing algorithm was developed by Jack Elton back in 1962. 

Brenham line drawing algorithm is one of the most efficient algorithms for line drawing compared to others. Moreover, it is also known as the Bresenham line tracer algorithm, as it is used to trace lines and find out the number of pixels the line has made up of or crossed through. 

How Does Bresenham Line Drawing Algorithm Work?

1. Firstly, the Bresenham line drawing algorithm needs the input of the initial and final point of the line. This input is in the form of coordinates. So, you should first enter the coordinates of the starting and ending points of the line. For example, x1,y1 and x2,y2 are a given line's initial and final coordinates, respectively. 

1. The algorithm will first subtract the corresponding coordinates to get a difference to follow. So, there will be a simple subtraction operation: (x2-x1) and (y2-y1). It will give the algorithm a difference that the line is following. 

1. In the next step, there is a decision parameter which you'll have to create. It will follow the decision parameter to decide to take every step further from the starting point. The decision parameter (P) is '2* (y2-y1) - (x2-x1)'. 

1. Now, if the decision parameter is smaller than zero, then It will choose (x+1, y) as the next pixel and after moving to the (x+1, y) pixel, the parameter P will be updated to P + 2*(y2-y1). 

However, if the parameter is greater than or equal to zero, the algorithm will move to (x+1, y+1) pixel from the starting point. Moreover, the parameter P this time will get updated to P + 2*(y2 - y1) - 2*(x2 -x1). 

1. The fourth step will be continuously executed until the last or the final coordinates are reached. Once the final coordinates are reached, all the pixels encountered during the process will be calculated and represented.

How is the Bresenham line drawing algorithm better than other line drawing algorithms for line tracing?

The Bresenham line drawing algorithm avoids three main things while working. Firstly, It doesn't use real numbers but only integers, meaning no number with decimals is included in the calculation. That is why the second thing is also avoided in the Bresenham line drawing algorithm, which is the floating point calculation. 

Floating point calculation is rounding off the decimal to the nearest integer. However, no floating point calculation is included since no division occurs in the Bresenham line drawing algorithm. It makes this algorithm faster than other line drawing algorithms like the Digital Differential Algorithm.

But there is a point to notice that it is not as accurate as the DDA in drawing the line. So, the efficiency lies in tracing the line, not drawing. So, if you want to draw smooth lines, then the DDA is better than the Bresenham line drawing algorithm. 

Let's see the difference between the working of the Bresenham line drawing algorithm and the DDA that makes the Bresenham line drawing algorithm faster but more accurate in drawing smooth lines. 

How does the Digital Differential Algorithm work?

1. Firstly, the slope is found in the DDA. To find the slope; the difference of corresponding x coordinates is subtracted and divided by the difference between the corresponding y coordinates. Here's what the calculation looks like: slope (m) = (x2 - x1)/(y2 - y1).

1.  Now plot the initial coordinates in (x, y) format. 

1. Next, the x coordinate will be incremented by 1 and the increment for y coordinate will be found by this formula: 'y = y + m'. 

1. By following the third step again and again until the final coordinates are reached, the line will be drawn. 

Here, the division and floating point calculation is used to get a more precise movement. Since these are not used in the Bresenham line drawing algorithm, that is why it becomes Faster. 

This is why the Bresenham line drawing algorithm is better known as the Bresenham line tracer algorithm, as tracing a line requires less precision, so this algorithm can be used in place of other algorithms. 

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Final Words

The Bresenham line drawing algorithm is a great algorithm, but due to less precision, it is better known for tracing lines instead of drawing them. However, Bresenham is not only limited to drawing straight lines. After its first development, the algorithm was extended to drawing circles and other shapes by making some changes.