To draw a line, you need two points between which you can draw a line. The Bresenham algorithm is another incremental scan conversion algorithm. The big . E Claridge, School of Computer Science, The University of Birmingham. DERIVATION OF THE BRESENHAM’S LINE ALGORITHM. Assumptions: ○ input: line. The basic ”line drawing” algorithm used in computer graphics is Bresenham’s example, in which we wish to draw a line from (0,0) to (5,3) in device space.

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An extension to the original algorithm may be used for drawing circles. Retrieved 20 December Notice that the points 2,1 and 2,3 are on opposite sides of the line and f x,y evaluates to positive or negative.

The big advantage of this algorithm is that, it uses only integer calculations. Mid-point algorithm is due to Bresenham which was modified by Pitteway and Van Aken.

It can also be found in many software graphics libraries.

The Bresenham Line-Drawing Algorithm

Computer graphics algorithms Digital geometry. Digital Differential Analyzer DDA algorithm is the simple line generation algorithm which is explained step by step here. Articles needing additional references from August All articles needing additional references All articles with unsourced statements Articles with unsourced statements from September Articles with unsourced statements from December All Wikipedia articles needing clarification Wikipedia articles needing clarification from May Commons category link is on Wikidata Articles with example pseudocode.

To derive the alternative method, define the difference to be as follows:. A description of the line drawing routine was accepted for presentation at the ACM national convention in Denver, Colorado. Please help improve this article by adding citations to reliable sources.


It is a basic element in graphics. Programs in those days were freely exchanged among corporations so Calcomp Jim Newland and Calvin Hefte had copies. The plotting can be viewed by plotting at the intersection of dfawing blue circles or filling in pixel boxes yellow squares.

Bresenham’s line algorithm – Wikipedia

This is a function of only x and it would be useful to make this equation written as a function of both x and y. This decision can be generalized by accumulating the error. A line connects two points. Retrieved from ” https: The first step is transforming the equation of a line from the typical slope-intercept form into something different; and then using this new equation drading a line to draw a line based on the idea of accumulation of error.

From Wikipedia, the free encyclopedia. You would like the point that is closer to the original line. Moving across the x axis in unit intervals and at each step choose between two different y coordinates.

All of the derivation for the algorithm is done. By switching the x and y axis an implementation for positive or negative steep gradients can be written as. This article needs additional citations for verification.

Line Generation Algorithm

It should be noted that everything about this form involves only integers if x and y are integers since the constants are necessarily integers. This simple decision is based on the difference between the two pixel positions. In low level implementation which access the video memory directly it would be typical for the special cases of vertical and horizontal lines to be handled separately as they can be highly optimised.


The Bresenham algorithm is another incremental scan conversion algorithm. It is an incremental error algorithm. The algorithm is used in hardware such as plotters and in the graphics chips of modern graphics cards. The drawong 2,2 is on the line.

In Bresenham wrote: To draw a line, you need two points between which you can draw a line. This can be chosen by identifying the intersection point Q closest to the point N or E.

If the intersection point Q of the line with the vertical line connecting E drawlng N is below M, then take E as the next point; otherwise take N as the next point. The general equation of the line through the endpoints is given by:.

This alternative method allows for integer-only arithmetic, which is generally faster than using floating-point arithmetic. Since all of this is about the sign of the accumulated difference, then everything can be multiplied algogithm 2 with no consequence.

Regardless, the plotting is the same. This observation is very important in the remainder of the derivation. The principle of using an incremental error in lien of division operations has other applications in graphics.