A chronological and mathematical overview of digital circle generation algorithms – introducing efficient 4- and 8-connected circles

Abstract

Circles are one of the basic drawing primitives for computers and while the naive way of setting up an equation for drawing circles is simple, implementing it in an efficient way using integer arithmetic has resulted in quite a few different algorithms. We present a short chronological overview of the most important publications of such digital circle generation algorithms. Bresenham is often assumed to have invented the first all integer circle algorithm. However, there were other algorithms published before his first official publication, which did not use floating point operations. Furthermore, we present both a 4- and an 8-connected all integer algorithm. Both of them proceed without any multiplication, using just one addition per iteration to compute the decision variable, which makes them more efficient than previously published algorithms.

Keywords:

• digital circle drawing
• all integer arithmetic
• connectivity
• Bresenham
• midpoint and Michener circle

2010 AMS Subject Classifications:

• 65S05
• 68U05

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

A. Hast http://orcid.org/0000-0003-1054-2754

Notes

1. This information was obtained through a private communication with James C. Michener through Ingrid B. Carlbom.