Geometric transformations on the hexagonal grid

Author

Her, Innchyn

Author_Institution

Dept. of Mech. Eng., Nat. Sun Yat-Sen Univ., Kaohsiung, Taiwan

Volume

4

Issue

9

fYear

1995

fDate

9/1/1995 12:00:00 AM

Firstpage

1213

Lastpage

1222

Abstract

The hexagonal grid has long been known to be superior to the more traditional rectangular grid system in many aspects in image processing and machine vision related fields. However, systematic developments of the mathematical backgrounds for the hexagonal grid are conspicuously lacking. The purpose of this paper is to study geometric transformations on the hexagonal grid. Formulations of the transformation matrices are carried out in a symmetrical hexagonal coordinate frame. A trio of new trigonometric functions are defined in this paper to facilitate the rotation transformations. A fast algorithm for rounding an arbitrary point to the nearest hexagonal grid point is also presented

Keywords

computational geometry; computer vision; image processing; matrix algebra; fast algorithm; geometric transformations; hexagonal grid; image processing; machine vision; rotation transformations; rounding; symmetrical hexagonal coordinate frame; transformation matrices; trigonometric functions; Digital images; Equations; Graphics; Grid computing; Image processing; Machine vision; Mathematics; Mechanical engineering; Symmetric matrices;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/83.413166

Filename

413166