polyCub-package | R Documentation |

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.

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.

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")}

`vignette("polyCub")`

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

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