Arithmetic and Fourier transform for the PYXIS multi-resolution digital Earth model

This paper investigates a multi-resolution digital Earth model called PYXIS,which was developed by PYXIS Innovation Inc.The PYXIS hexagonal grids employ an efficient hierarchical labeling scheme for addressing pixels.We provide a recursive definition of the PYXIS grids,a systematic approach to the labeling,an algorithm to add PYXIS labels,and a discussion of the discrete Fourier transform on PYXIS grids.