Approximation of Discs by Octagons on Pixel-Plane via Jaccards Proximity Criterion: Theoretical Approach and Experimental Results Analysis

TL;DR

This paper investigates how well octagons can approximate discs on pixel grids using Jaccard's distance, providing theoretical insights and experimental results to evaluate approximation quality.

Contribution

It introduces a method for approximating discs with octagons on pixel planes using Jaccard's proximity criterion, supported by both theoretical analysis and experimental data.

Findings

Jaccard's distance effectively measures approximation quality

Experimental results include a comprehensive table of distances

Properties of octagon approximations are analyzed

Abstract

In the present paper we study approximation of discs by octagons on the pixel plane. To decide which octagon approximates better the given disc we use Jaccard's distance. The table of Jaccard's distances (calculated by a software created for these purposes) are presented at the end of the paper. The results for proximity are given in the form of a graph. Some properties of considered octagons are also studied