Cubature over Polygonal Domains
Description
The following methods for cubature (numerical integration)
over polygonal domains are currently implemented:
the two-dimensional midpoint rule as a simple wrapper around
as.im.function() from package spatstat (Baddeley and Turner, 2005),
the product Gauss cubature by Sommariva and Vianello (2007),
an adaptive cubature for isotropic functions via line integrate()
along the boundary (Meyer and Held, 2014),
and quasi-exact methods specific to the integration of the
bivariate Gaussian density over polygonal and circular domains
(based on formulae from the Abramowitz and Stegun (1972) handbook).
For cubature over simple hypercubes, the packages "cubature" and
"R2Cuba" are more appropriate.