Optimal Compression of a Polyline with Segments and Arcs

TL;DR

This paper presents an efficient method for compressing polylines into minimal segments and arcs, focusing on reducing complexity in arc fitting and subdivision to optimize the approximation within a tolerance.

Contribution

It introduces a novel approach that minimizes the number of segments and arcs in polyline compression by optimizing subdivision and arc fitting checks.

Findings

Achieves minimal segment and arc count in polyline compression

Reduces computational complexity in arc fitting process

Provides an effective subdivision strategy for polyline approximation

Abstract

This paper describes an efficient approach to constructing a resultant polyline with a minimum number of segments and arcs. While fitting an arc can be done with complexity O(1) (see [1] and [2]), the main complexity is in checking that the resultant arc is within the specified tolerance. There are additional tests to check for the ends and for changes in direction (see [3, section 3] and [4, sections II.C and II.D]). However, the most important part in reducing complexity is the ability to subdivide the polyline in order to limit the number of arc fittings [2]. The approach described in this paper finds a compressed polyline with a minimum number of segments and arcs.