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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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 everything can be multiplied by 2 with no consequence.

### Computer Graphics Line Generation Algorithm

All of the derivation for the algorithm is done. Programs in those days were freely exchanged among corporations so Calcomp Jim Newland and Calvin Hefte had copies.

The black point 3, 2. This page was last edited on 16 Octoberat 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. To draw a line, you need two points between which you can draw a line.

## Line Generation Algorithm

Line Generation Algorithm Advertisements. The Bresenham algorithm is another incremental scan conversion algorithm.

Bresenham’s algorithm was later extended to produce circles, the resulting algorithms being ‘Bresenham’s circle algorithm and midpoint circle algorithm. Unsourced material may be challenged and removed. To answer this, evaluate the line function at the midpoint between these two points:. 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 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. Notice that the points 2,1 and 2,3 are on opposite sides of the line and f x,y evaluates to drawibg or negative. Since we know bresenahm column, xthe pixel’s row, yis given by rounding this quantity to the nearest integer:. A line splits a plane into halves and the half-plane that has a negative f x,y can be called the negative half-plane, and the other half can be called the positive half-plane.

The voxel heightmap software-rendering engines seen in some PC games also used this principle. It can also be found in many software graphics libraries. To derive Bresenham’s algorithm, two steps must be taken.

This can be chosen by identifying the intersection point Q closest to the point N or E. The plotting can be viewed by plotting at the intersection of crawing blue circles or filling in pixel boxes yellow squares. The principle of using an incremental error in place of division operations has other applications in graphics.

Computer graphics algorithms Digital geometry. Retrieved 20 December This simple decision is based on the difference between the two pixel positions. The algorithm can be extended to cover gradients between 0 and -1 by checking whether y needs to increase or decrease i. 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.

It should be noted that everything about this form involves only integers if x and y are integers since the constants are necessarily integers. It is an incremental error algorithm. Drasing can use these to make a simple decision about which pixel is closer to the mathematical line.

August Learn how and when to remove this template message. Remember, the coordinate changes occur darwing the x axis in unit steps, so you can do everything with integer calculations. This article needs additional citations for verification. It is commonly used to draw line primitives in a bitmap image e.

The point 2,2 is on the line. It is a basic element in graphics. Now you need lune decide whether to put the next point at E or N.

Retrieved from ” https: Bresenham also published a Run-Slice as opposed to the Run-Length computational algorithm.

## Bresenham’s line algorithm

Views Read Edit View history. If the intersection point Q is closest to the point N then N is considered as the next point; otherwise E. An extension to the original algorithm may be used for drawing circles.

A Calcomp plotter had been attached to an IBM via the typewriter console. The label “Bresenham” is lline today for a family of algorithms extending or modifying Bresenham’s original algorithm.