polyCub.SV: Product Gauss Cubature over Polygonal Domains

Description

Product Gauss cubature over polygons as proposed by Sommariva and Vianello (2007).

Usage

polyCub.SV(polyregion, f, ..., nGQ = 20, alpha = NULL,
    rotation = FALSE, plot = FALSE)

Arguments

polyregion

a polygonal integration domain. The following classes are supported: "owin", "gpc.poly", "SpatialPolygon

two-dimensional function to be integrated. As its first argument the function must take a coordinate matrix, i.e. a numeric matrix with two columns.

...

further arguments for f.

nGQ

degree of the one-dimensional Gauss-Legendre quadrature rule (default: 20). See gauss.quad in package statmod, on which this function depends.

plot

logical indicating if an illustrative plot of the numerical integration should be produced.

alpha

base-line of the (rotated) polygon at $x = \alpha$ (see Sommariva and Vianello (2007) for an explication). If NULL (default), the midpoint of the x-range of the polygon is chosen if no rotation is performed, and otherwise

rotation

logical (default: FALSE) or a list of points "P" and "Q" describing the preferred direction. If TRUE, the polygon is rotated according to the vertices "P" and "Q", which

Value

The approximated value of the integral of f over polyregion.

References

A. Sommariva and M. Vianello (2007). Product Gauss cubature over polygons based on Green's integration formula. Bit Numerical Mathematics, 47 (2), 441-453.

Examples

Run this code

# see example(polyCub)

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