The following table defines the precise meaning of terms used in the context of the mangle software. For example, the most general angular region that mangle can handle is a mask, as defined in the table.

Definition of terms, in alphabetical order
term definition
boundary A set of edges bounding a polygon.
cap A spherical disk, a region above a circle on the unit sphere.
circle A line of constant latitude with respect to some arbitrary polar axis on the unit sphere.
edge An edge is part of a circle. A polygon is enclosed by its edges.
great circle A line of zero latitude with respect to some arbitrary polar axis on the unit sphere. A great circle is a circle, but a circle is not necessarily a great circle.
group The circles of a polygon partition into groups: two circles are friends, belonging to the same group, if they intersect (anywhere, not necessarily inside the polygon), and friends of friends are friends.
mask The union of an arbitrary number of weighted polygons.
pixel A special polygon that specifies some predefined region on the sky. Once a mask has been pixelized, each polygon in the mask is guaranteed to overlap with exactly one pixel.
polygon The intersection of an arbitrary number of caps.
rectangle A special kind of polygon, a rectangular polygon bounded by lines of constant longitude and latitude.
vertex A point of intersection of two circles. A vertex of a polygon is a point where two of its edges meet.
weight The weight assigned to a polygon. The spherical harmonics of a mask is the sum of the spherical harmonics of its polygons, each weighted according to its weight. A weight of 1 is the usual weight. A weight of 0 signifies an empty polygon, a hole. In general the weight may be some arbitrary positive or negative real number.