Dept. of Mech. Eng., Nat. Sun Yat-Sen Univ., Kaohsiung.
IEEE Trans Image Process. 1995;4(9):1213-22. doi: 10.1109/83.413166.
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.
六边形网格在图像处理和机器视觉等相关领域的许多方面一直优于更为传统的矩形网格系统。然而，六边形网格的数学背景的系统发展却明显缺乏。本文的目的是研究六边形网格上的几何变换。变换矩阵的公式是在一个对称的六边形坐标系中进行的。本文定义了一组新的三角函数，以方便进行旋转变换。还提出了一种将任意点舍入到最近的六边形网格点的快速算法。
