String Art: Circle Drawing Using Straight Lines

TL;DR

This paper presents an algorithm that generates circle images using straight lines and intersection points, optimized for speed and suitable for string art applications, though with some pixel accuracy limitations.

Contribution

It introduces a novel parallelizable algorithm utilizing straight lines and parabolic arcs to approximate circle drawing, optimized with integer arithmetic.

Findings

Algorithm is parallelizable and uses integer arithmetic for speed.

Suitable for string art circle generation despite pixel errors.

Potential limitations in accuracy for larger circles.

Abstract

An algorithm to generate the locus of a circle using the intersection points of straight lines is proposed. The pixels on the circle are plotted independent of one another and the operations involved in finding the locus of the circle from the intersection of straight lines are parallelizable. Integer only arithmetic and algorithmic optimizations are used for speedup. The proposed algorithm makes use of an envelope to form a parabolic arc which is consequent transformed into a circle. The use of parabolic arcs for the transformation results in higher pixel errors as the radius of the circle to be drawn increases. At its current state, the algorithm presented may be suitable only for generating circles for string art.