A Simple Circle Discretization Algorithm With Applications

TL;DR

This paper presents a straightforward algorithm for discretizing circles into points with a built-in dimensional tolerance, aiding in CNC toolpath generation for applications like helix machining.

Contribution

It introduces a simple circle discretization method that incorporates a dimensional tolerance, improving control over point density in CNC programming.

Findings

Efficient circle discretization with controlled point density

Applicable to CNC toolpath generation for complex curves

Reduces program size while maintaining smoothness

Abstract

In CNC manufacturing,there often arises the need to create G-Code programs which require the calculation of discrete x-y coordinate pairs(2D).An example of this situation is when the programmer needs to create a program to machine a helix(or thread).The required toolpath will be a set of points on a helix curve.The problem now entails calculating the number of points along this curve.Too few points and the toolpath will not be smooth.Too many points and the program becomes too big.This article will serve to provide a simple way to divide a circle into discrete points,with a notion of "dimensional tolerance" built into the algorithm.