Approximate Fitting of a Circular Arc When Two Points Are Known

TL;DR

This paper presents an efficient method for fitting circular arcs when one or two points are known, improving computational complexity for applications like polyline compression and noise filtering.

Contribution

It introduces a novel approach to circular arc fitting with known points, achieving O(1) complexity, extending previous eigenvector-based methods.

Findings

Efficient arc fitting when two points are known.

Applicable to polyline compression and noise filtering.

Improves computational complexity of arc fitting algorithms.

Abstract

The task of approximating points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, the development of algorithms that perform a significant amount of circular arcs fitting requires an efficient way of fitting circular arcs with complexity O(1). The elegant solution to this task based on an eigenvector problem for a square nonsymmetrical matrix is described in [1]. For the compression algorithm described in [2], it is necessary to solve this task when two points on the arc are known. This paper describes a different approach to efficiently fitting the arcs and solves the task when one or two points are known.