polyCub-package: Cubature over Polygonal Domains

In polyCub: Cubature over Polygonal Domains

Cubature over Polygonal Domains

Description

The R package polyCub implements cubature (numerical integration) over polygonal domains. It solves the problem of integrating a continuously differentiable function f(x,y) over simple closed polygons.

Details

polyCub provides the following cubature methods, which can either be called explicitly or via the generic polyCub function:

polyCub.SV:

General-purpose product Gauss cubature (Sommariva and Vianello, 2007)

polyCub.midpoint:

Simple two-dimensional midpoint rule based on as.im.function from spatstat.geom (Baddeley et al., 2015)

polyCub.iso:

Adaptive cubature for radially symmetric functions via line integrate() along the polygon boundary (Meyer and Held, 2014, Supplement B, Section 2.4).

A brief description and benchmark experiment of the above cubature methods can be found in the vignette("polyCub").

There is also polyCub.exact.Gauss, intended to accurately (but slowly) integrate the bivariate Gaussian density; however, this implementation is disabled as of polyCub 0.9.0: it needs a reliable implementation of polygon triangulation. Meyer (2010, Section 3.2) discusses and compares some of these methods.

References

Baddeley, A., Rubak, E. and Turner, R. (2015). Spatial Point Patterns: Methodology and Applications with R. Chapman and Hall/CRC Press, London.

Meyer, S. (2010). Spatio-Temporal Infectious Disease Epidemiology based on Point Processes. Master's Thesis, LMU Munich. Available as https://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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/14-AOAS743")}

Sommariva, A. and Vianello, M. (2007). Product Gauss cubature over polygons based on Green's integration formula. BIT Numerical Mathematics, 47 (2), 441-453. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s10543-007-0131-2")}

See Also

vignette("polyCub")

For the special case of a rectangular domain along the axes (e.g., a bounding box), the cubature package is more appropriate.

polyCub documentation built on Oct. 25, 2023, 5:07 p.m.