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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This observation is crucial to understand! If it is closer to the former then include the former point on the line, if the latter then the latter. To answer this, evaluate the line function at the midpoint between these two points:.

It is an incremental error algorithm. The Bresenham algorithm can be interpreted as slightly modified digital differential analyzer using 0. Computer graphics algorithms Digital geometry.

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 means that it is still important.

A description of the line drawing routine was accepted for presentation at the ACM national convention in Denver, Colorado. In the following pseudocode sample plot x,y plots the pixel centered at coordinates x,y and abs returns absolute value:.

The algorithm is used in hardware such as plotters and in the graphics chips of modern graphics cards.

### Bresenham’s line algorithm – Wikipedia

The big advantage of this algorithm is that, it uses only integer calculations. Bresenham’s line algorithm is an algorithm that determines the points of an n -dimensional brexenham that should be selected in order to form a close approximation to a straight line between two points. The principle of using an incremental error in place of division operations has other applications in graphics.

The algorithm can be extended to cover gradients between 0 and -1 by checking whether y needs to increase or decrease i. However, as mentioned above this is only for drawung 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.

## Line Generation Algorithm

It can also be found in many software graphics libraries. The black point 3, 2. It is a basic element in graphics. Bresenham’s algorithm was later extended to produce circles, the resulting algorithms being ‘Bresenham’s circle algorithm and midpoint circle algorithm. The adjacent image shows the blue point 2,2 chosen to be on the line with two candidate points in srawing 3,2 and 3,3. 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 alternative method allows for integer-only arithmetic, which is generally faster than using floating-point arithmetic. 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 for a line to draw a line based on the idea of accumulation of error. Mid-point algorithm is due to Bresenham which was modified by Pitteway and Van Aken. If the intersection point Q is closest to the point N then N is considered as algkrithm next point; otherwise E.

The result of this plot is shown to the right. It is one of the earliest algorithms developed in the field of computer graphics. Retrieved 20 December This article needs bresenha, citations for verification. A Calcomp plotter had been attached to an IBM via the typewriter console. The point 2,2 is on the line.

## Bresenham’s line algorithm

If the intersection point Q of the line with the vertical line connecting E and N is below M, then take E as the next point; otherwise take N as the next point. 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. In other projects Wikimedia Commons. The voxel heightmap software-rendering engines seen in some PC games also used this principle. Now you need to decide whether to put the next point at E or N.

You can use these to make a simple decision about which pixel is closer to the mathematical line. Moving across the x axis in unit intervals and at each step choose between two different y coordinates. The value of the line function at this midpoint is the sole determinant of which point should be chosen.

Because the algorithm is algoriithm simple, it is often implemented in either the firmware or the graphics hardware of modern graphics cards. Please help improve this article by adding citations to reliable sources. 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 simple decision is based on the difference between the two pixel positions.

It is possible to use this technique to calculate the U,V co-ordinates during raster scan of texture mapped polygons [ citation needed ].

For example, as shown in the following illustration, from position 2, drawng you need to choose between alorithm, 3 and 3, 4. Simplifying this expression yields:. If the error becomes greater than 0.

### Computer Graphics Line Generation Algorithm

In Bresenham wrote: Notice that the points 2,1 bressnham 2,3 are on opposite sides of the line and f x,y evaluates to positive or negative. I happily agreed, and they printed it in The plotting can be viewed by plotting at the intersection of lines blue circles or filling in pixel boxes yellow squares. The label “Bresenham” is used today for a family of algorithms extending or modifying Bresenham’s original algorithm.

To derive the alternative method, define the difference to be as follows:.

To draw a line, you need two points between which you can draw a line. Views Read Edit View history. Regardless, the plotting is the same. This page was last edited on 16 Octoberat