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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A line connects two points.

Bresenham’s line algorithm – Wikipedia

Mid-point algorithm is due to Bresenham which was modified by Pitteway and Van Aken. The label “Bresenham” is used today for a family of algorithms extending or modifying Bresenham’s original algorithm. Now you need to decide whether to put the next point at E or N.

This can be chosen by identifying the intersection point Q closest to the point N or E. The Bresenham algorithm can be interpreted as slightly modified digital differential analyzer using 0. In the following pseudocode sample plot x,y plots the pixel centered at coordinates x,y and abs returns absolute value:.

The big advantage of this algorithm is that, it uses only integer calculations. The plotting can be viewed by plotting at the intersection of lines blue circles or filling in pixel boxes yellow squares.

Line Generation Algorithm

From Wikipedia, the free encyclopedia. This page was last edited on 16 Octoberat Computer graphics algorithms Digital geometry. The algorithm can be extended to cover gradients between 0 and -1 by checking whether y needs to increase or decrease i.


For example, as shown in the following illustration, from position 2, 3 you need to choose between 3, 3 and 3, 4.

If the error becomes greater than 0. Line Generation Algorithm Advertisements. Moving across the x axis in unit intervals and at each step choose between two different y coordinates. Digital Differential Analyzer DDA algorithm is the simple line generation algorithm which is explained step by step here.

To derive Bresenham’s algorithm, two steps must be taken. This observation is crucial to understand! Remember, the coordinate changes occur along the x axis in unit steps, so you can do everything with integer calculations. Bresenham also published a Run-Slice as opposed to the Run-Length computational algorithm.

Unsourced material may be challenged and removed. Programs in those days were freely exchanged among corporations so Calcomp Jim Newland and Calvin Hefte had copies. 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.

The result of this plot is shown to the right. While algorithms such as Wu’s algorithm are also frequently used in modern computer graphics because they can support antialiasingthe speed and simplicity of Bresenham’s line algorithm ,ine that it is still important. The algorithm is used in hardware such as plotters and in the graphics chips of modern graphics cards.

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. An extension to the original algorithm may be used for drawing circles. A description of the line drawing routine was accepted for presentation at the ACM national convention in Denver, Colorado.


The point 2,2 is on the line. The Bresenham algorithm is another incremental scan conversion algorithm. It is one of the earliest algorithms developed in the field of computer graphics. It is possible to use this technique to calculate the U,V co-ordinates during raster scan of texture mapped polygons [ citation bresenhqm ].

By using this site, you agree to the Terms of Use and Privacy Policy. It is commonly used to draw line primitives in a bitmap image e. It can also be found in many software graphics libraries.

Bresenham’s line algorithm

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 general equation of the line through the endpoints is given by:. However, as mentioned above this is only for octant zero, that is lines starting at the origin with a gradient between 0 and 1 where x increases by exactly 1 per iteration and y increases by 0 or 1. It was a year in which no proceedings were published, only the agenda of speakers and topics in an issue of Communications of the ACM.

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This decision can be generalized by accumulating the error. Bresenham’s algorithm chooses the integer y corresponding to the pixel center that is closest to bresenhham ideal fractional y for the same x ; on successive columns y can remain the same or increase by 1.