Methods for Rapidly Processing Angular Masks of Next-Generation Galaxy Surveys

TL;DR

This paper introduces a divide-and-conquer approach to efficiently process large angular masks in galaxy surveys, significantly speeding up computations and enabling conversions between mask formats, with implementation in the mangle software.

Contribution

It presents a novel divide-and-conquer method for handling large spherical polygon masks, reducing computational complexity and enabling format conversions, implemented in the mangle software.

Findings

Reduces O(N^2) tasks to O(N) for mask processing.

Enables fast point-in-polygon queries on the sphere.

Provides efficient conversion between angular mask formats.

Abstract

As galaxy surveys become larger and more complex, keeping track of the completeness, magnitude limit, and other survey parameters as a function of direction on the sky becomes an increasingly challenging computational task. For example, typical angular masks of the Sloan Digital Sky Survey contain about N=300,000 distinct spherical polygons. Managing masks with such large numbers of polygons becomes intractably slow, particularly for tasks that run in time O(N^2) with a naive algorithm, such as finding which polygons overlap each other. Here we present a "divide-and-conquer" solution to this challenge: we first split the angular mask into predefined regions called "pixels," such that each polygon is in only one pixel, and then perform further computations, such as checking for overlap, on the polygons within each pixel separately. This reduces O(N^2) tasks to O(N), and also reduces the important task of determining in which polygon(s) a point on the sky lies from O(N) to O(1), resulting in significant computational speedup. Additionally, we present a method to efficiently convert any angular mask to and from the popular HEALPix format. This method can be generically applied to convert to and from any desired spherical pixelization. We have implemented these techniques in a new version of the mangle software package, which is freely available at http://space.mit.edu/home/tegmark/mangle/, along with complete documentation and example applications. These new methods should prove quite useful to the astronomical community, and since mangle is a generic tool for managing angular masks on a sphere, it has the potential to benefit terrestrial mapmaking applications as well.