Fast exact digital differential analyzer for circle generation

TL;DR

This paper introduces a new two-step digital differential analyzer algorithm for circle generation that is both computationally efficient and maximally accurate, achieving exactness up to round-off errors.

Contribution

A novel fast two-step numerical scheme for circle generation that outperforms traditional DDAs in accuracy while maintaining low computational cost.

Findings

Algorithm is as cheap as simple one-step DDAs

Generates circles with maximal accuracy up to round-off errors

Based on explicit midpoint rule for improved precision

Abstract

In the first part of the paper we present a short review of applications of digital differential analyzers (DDA) to generation of circles showing that they can be treated as one-step numerical schemes. In the second part we present and discuss a novel fast algorithm based on a two-step numerical scheme (explicit midpoint rule). Although our algorithm is as cheap as the simplest one-step DDA algoritm (and can be represented in terms of shifts and additions), it generates circles with maximal accuracy, i.e., it is exact up to round-off errors.