bresenham s circle drawing algorithm with flowchart
#1

Hi am Abhishek i would like to get details on bresenham s circle drawing algorithm with flowchart.
my mail id is ajaries07[at]gmail.com
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#2

Bresenham's line algorithm is an algorithm that determines the points of an n-dimensional raster that should be selected in order to form a close approximation to a straight line between two points. It is commonly used to draw line primitives in a bitmap image (e.g. on a computer screen), as it uses only integer addition, subtraction and bit shifting, all of which are very cheap operations in standard computer architectures. It is an incremental error algorithm. It is one of the earliest algorithms developed in the field of computer graphics. An extension to the original algorithm may be used for drawing circles.

While algorithms such as Wu's algorithm are also frequently used in modern computer graphics because they can support antialiasing, the speed and simplicity of Bresenham's line algorithm means that it is still important. The algorithm is used in hardware such as plotters and in the graphics chips of modern graphics cards. It can also be found in many software graphics libraries. Because the algorithm is very simple, it is often implemented in either the firmware or the graphics hardware of modern graphics cards.

The label "Bresenham" is used today for a family of algorithms extending or modifying Bresenham's original algorithm.
Bresenham's line algorithm is named after Jack Elton Bresenham who developed it in 1962 at IBM. In 2001 Bresenham wrote.

I was working in the computation lab at IBM's San Jose development lab. A Calcomp plotter had been attached to an IBM 1401 via the 1407 typewriter console. [The algorithm] was in production use by summer 1962, possibly a month or so earlier. Programs in those days were freely exchanged among corporations so Calcomp (Jim Newland and Calvin Hefte) had copies. When I returned to Stanford in Fall 1962, I put a copy in the Stanford comp center library. A description of the line drawing routine was accepted for presentation at the 1963 ACM national convention in Denver, Colorado. 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. A person from the IBM Systems Journal asked me after I made my presentation if they could publish the paper. I happily agreed, and they printed it in 1965.

Bresenham's algorithm was later extended to produce circles, the resulting algorithm being sometimes known as either Bresenham's circle algorithm or midpoint circle algorithm
The common conventions will be used:

the top-left is (0,0) such that pixel coordinates increase in the right and down directions (e.g. that the pixel at (7,4) is directly above the pixel at (7,5)), and
that the pixel centers have integer coordinates.
The endpoints of the line are the pixels at {\displaystyle (x_{0},y_{0})} (x_{0},y_{0}) and {\displaystyle (x_{1},y_{1})} (x_{1},y_{1}), where the first coordinate of the pair is the column and the second is the row.

The algorithm will be initially presented only for the octant in which the segment goes down and to the right ( {\displaystyle x_{0}\leq x_{1}} x_{0}\leq x_ and {\displaystyle y_{0}\leq y_{1}} y_{0}\leq y_{1}), and its horizontal projection {\displaystyle x_{1}-x_{0}} x_{1}-x_{0} is longer than the vertical projection {\displaystyle y_{1}-y_{0}} y_{1}-y_{0} (the line has a negative slope whose absolute value is less than 1). In this octant, for each column x between {\displaystyle x_{0}} x_{0} and {\displaystyle x_{1}} x_{1}, there is exactly one row y (computed by the algorithm) containing a pixel of the line, while each row between {\displaystyle y_{0}} y_{0} and {\displaystyle y_{1}} y_{1} may contain multiple rasterized pixels.
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