A scheme to deal accurately and efficiently with complex angular masks in galaxy surveys

This paper presents a scheme to deal accurately and efficiently with complex angular masks, such as occur typically in galaxy surveys. An angular mask is taken to be an arbitrary union of arbitrarily weighted angular regions bounded by arbitrary numbers of edges. The restrictions on the mask are (i) that each edge must be part of some circle on the sphere (but not necessarily a great circle), and (ii) that the weight within each subregion of the mask must be constant. The scheme works by resolving a mask into disjoint polygons, convex angular regions bounded by arbitrary numbers of edges. The polygons may be regarded as the ‘pixels’ of a mask, with the feature that the pixels are allowed to take a rather general shape, rather than following some predefined regular pattern. Among other things, the scheme includes facilities to compute the spherical harmonics of the angular mask, and Data-Random 〈DR〉 and Random-Random 〈RR〉 angular integrals. A software package mangle which implements this scheme, along with complete software documentation, is available at http://casa.colorado.edu/~ajsh/mangle/.