polyCub() is the main entry point of the package.
It is a wrapper around the specific cubature methods listed below.polyCub.midpoint:as.im.function method from package
spatstat (Baddeley and Turner, 2005).
The integral is then obtained as the sum over
(pixel area * f(pixel midpoint)).
polyCub.SV:polyCub.iso:integrate() along the polygon boundary, see Meyer and Held
(2014, Supplement B, Section 2.4).
polyCub.exact.Gauss:tristrip of package
gpclib) and appropriate evaluations of
pmvnorm from package mvtnorm.
Note that there is also a function circleCub.Gauss
to perform integration of the isotropic Gaussian density over
circular domains.
See Section 3.2 of Meyer (2010) for a more detailed description and benchmark experiment of some of the above cubature methods (and others).
Baddeley, A. and Turner, R. (2005). spatstat: an R package for analyzing spatial point patterns. Journal of Statistical Software, 12 (6), 1-42.
Meyer, S. (2010). Spatio-Temporal Infectious Disease Epidemiology based on Point Processes. Master's Thesis, LMU Munich. Available as http://epub.ub.uni-muenchen.de/11703/.
Meyer, S. and Held, L. (2014). Power-law models for infectious disease spread. The Annals of Applied Statistics, 8 (3), 1612-1639. DOI-Link: http://dx.doi.org/10.1214/14-AOAS743, http://arxiv.org/abs/1308.5115
Sommariva, A. and Vianello, M. (2007). Product Gauss cubature over polygons based on Green's integration formula. Bit Numerical Mathematics, 47 (2), 441-453.