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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Because the algorithm is very simple, it is often implemented in either the firmware or dfawing graphics hardware of modern graphics cards. Alternatively, the difference between points can be used instead of evaluating f x,y at midpoints. It is a basic element in graphics. The point 2,2 is on the line.

Programs in those days were freely exchanged among corporations so Calcomp Jim Newland and Calvin Hefte had copies.

Bresenham’s algorithm was later extended to produce circles, the resulting algorithms being ‘Bresenham’s circle algorithm and midpoint circle algorithm.

It can also be found in many software graphics libraries. Line Generation Algorithm Advertisements. The black point 3, 2. This decision can be generalized by accumulating the error. The result of this plot is shown to the right. By switching the x and y axis an implementation for positive or negative steep gradients can be written as.

Line Generation Algorithm

Retrieved 20 December In the following pseudocode sample plot x,y plots the pixel centered at coordinates x,y and abs returns absolute value:. Since all of this is about the sign of the accumulated difference, then lins can be multiplied by 2 with no consequence. For example, as shown in the following illustration, from position 2, 3 you need to choose between 3, 3 and 3, 4.


To draw a line, you need two points between which you can draw a line.

Remember, the coordinate changes occur along the x axis in unit steps, so you can do everything with integer calculations. Since we know the column, xthe pixel’s row, yis given by rounding this quantity to the nearest integer:.

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. The big advantage of this algorithm is that, it uses only integer calculations. It is possible to use this technique to calculate the U,V co-ordinates during raster scan of texture mapped polygons [ citation needed ].

Bresenham’s algorithm chooses the integer y xlgorithm to the pixel center that is closest to the ideal fractional y for the same x ; on successive columns y can remain the same or increase by 1. It was a year in which no proceedings were published, only the agenda of speakers and topics dtawing an issue of Communications of the ACM.

This alternative method allows for integer-only arithmetic, which is generally faster than using floating-point arithmetic. If the error becomes greater than 0.

Bresenham’s line algorithm

Retrieved from ” https: Now you need to decide whether to put the next point at E or N. 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 rdawing this equation written as a function of both x and y.


A line connects two points. It is one of the earliest algorithms developed in the field of computer graphics. Bresenham also published a Run-Slice as opposed to the Run-Length computational algorithm.

The adjacent image shows the blue point 2,2 chosen to be on the line with two candidate points in green 3,2 and 3,3.

The Bresenham Line-Drawing Algorithm

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.

The value of the line function at this midpoint is the sole determinant of which point should be chosen. An extension to the original algorithm may be used for drawing circles.

The principle of using an incremental error in place of division operations has other applications in graphics.

I happily agreed, and they printed it in To answer rdawing, evaluate the line function at the midpoint between these two points:.

Regardless, the plotting is the same. This article needs additional citations for verification.