Estimation of systematic errors of discrete line approximation by triangular tessellation and marching squares algorithm

Piotr Bobrowski

doi:10.1016/j.micron.2020.102966

Estimation of systematic errors of discrete line approximation by triangular tessellation and marching squares algorithm

Micron. 2021 Feb:141:102966. doi: 10.1016/j.micron.2020.102966. Epub 2020 Nov 5.

Author

Piotr Bobrowski¹

Affiliation

¹ Institute of Metallurgy and Materials Science of Polish Academy of Sciences, 25 Reymonta Str., PL-30-059 Krakow, Poland. Electronic address: p.bobrowski@imim.pl.

PMID: 33221525
DOI: 10.1016/j.micron.2020.102966

Abstract

This paper presents methods to calculate the length overestimation errors which are being made when approximating a discrete line by edges of triangular tessellation and marching squares algorithm. The maximum error and its average value are 15.47 % and 10.27 % for the triangular tessellation, while for the marching squares approach they are 8.24 % and 5.49 %, respectively. Mathematical calculations were compared with experimental results obtained by the Electron Backscatter Diffraction technique showing their usefulness as correction coefficients to obtain more accurate boundary length estimates.

Keywords: EBSD; Grain boundary length; Marching squares; Triangular tessellation.