polyCub-package: Cubature over Polygonal Domains

In WastlM/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:

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.

Author(s)

Sebastian Meyer

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.

WastlM/polyCub documentation built on July 18, 2024, 1:38 p.m.