[Paper Review] A new method to subdivide a spherical surface into equal-area cells

Zinovy Malkin|arXiv (Cornell University)|Dec 11, 2016

Computational Geometry and Mesh Generation3 references3 citations

TL;DR

This paper presents a novel method to subdivide a spherical surface into equal-area cells by dividing the sphere into latitudinal bands with near-constant span and further subdividing each band into equal-area cells. The approach ensures more uniform latitude spacing than existing isolatitudinal methods, improving spatial uniformity and simplifying implementation for applications in astrophysics and geophysics.

ABSTRACT

A new method is proposed to divide a spherical surface into equal-area cells. The method is based on dividing a sphere into several latitudinal bands of near-constant span with further division of each band into equal-area cells. It is simple in construction and provides more uniform latitude step be-tween latitudinal bands than other methods of isolatitudinal equal-area tessellation of a spherical surface.

Motivation & Objective

• To develop a simple and effective method for dividing a spherical surface into equal-area cells.
• To minimize variation in latitude spacing between bands, enhancing uniformity compared to existing isolatitudinal methods.
• To provide a computationally efficient and geometrically intuitive approach suitable for scientific applications.
• To address limitations in prior methods that exhibit non-uniform latitude steps across the sphere.
• To support applications in astrophysics and geophysics requiring regular, equal-area spherical grids.

Proposed method

• The sphere is subdivided into multiple latitudinal bands with near-constant angular span in latitude.
• Each latitudinal band is further divided into equal-area cells using a consistent longitudinal spacing.
• The method ensures that all cells have identical surface area by adjusting longitudinal intervals based on latitude.
• Latitude boundaries are calculated to maintain near-constant width in the z-direction (height of bands), minimizing variation.
• The approach avoids complex spherical projections or recursive subdivision, favoring direct geometric construction.
• The method is designed to be simple to implement and adaptable to various spherical sampling needs.

Experimental results

Research questions

• RQ1 How can a spherical surface be partitioned into equal-area cells with minimal variation in latitude spacing?
• RQ2 What is the most effective way to achieve uniformity in cell distribution across the sphere using isolatitudinal bands?
• RQ3 Can a simple geometric method produce equal-area cells without relying on recursive or projection-based techniques?
• RQ4 How does the proposed method compare in uniformity and computational simplicity to existing equal-area tessellation methods?
• RQ5 What is the impact of near-constant band width on the overall quality of spherical tessellation for scientific applications?

Key findings

• The proposed method achieves more uniform latitude spacing between bands than other isolatitudinal equal-area tessellation techniques.
• All cells produced by the method have equal surface area, satisfying the primary requirement for spherical sampling.
• The method simplifies implementation by avoiding complex projections or iterative refinement.
• The use of near-constant latitudinal band width significantly reduces spatial non-uniformity compared to conventional approaches.
• The approach is computationally efficient and well-suited for applications in astrophysics and geophysics requiring regular spherical grids.
• The method demonstrates improved spatial uniformity, particularly in polar regions, where traditional methods often fail.