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polyCub

Cubature over Polygonal Domains

Numerical integration of continuously differentiable functions f(x,y) over simple closed polygonal domains. The following cubature methods are implemented: product Gauss cubature (Sommariva and Vianello, 2007, <doi:10.1007/s10543-007-0131-2>), the simple two-dimensional midpoint rule (wrapping 'spatstat.geom' functions), adaptive cubature for radially symmetric functions via line integrate() along the polygon boundary (Meyer and Held, 2014, <doi:10.1214/14-AOAS743>, Supplement B), and integration of the bivariate Gaussian density based on polygon triangulation. For simple integration along the axes, the 'cubature' package is more appropriate.

Functions (20)

checkintrfr

Check the Integral of r f_r(r)

circleCub.Gauss

Integration of the Isotropic Gaussian Density over Circular Domains

coerce-gpc-methods

Conversion between polygonal "owin" and "gpc.poly"

coerce-sp-methods

Coerce "SpatialPolygons" to "owin"

dotprod

Dot/Scalar Product of Two Vectors

gpclibPermit

gpclib License Acceptance

isClosed

Check if Polygon is Closed

isScalar

Checks if Argument is Scalar

plot_polyregion

Plots a Polygonal Domain (of Various Classes)

plotpolyf

Plot Polygonal Domain on Image of Bivariate Function

polyCub

Wrapper Function for the Various Cubature Methods

polyCub-package

Cubature over Polygonal Domains

polyCub.SV

Product Gauss Cubature over Polygonal Domains

polyCub.exact.Gauss

Quasi-Exact Cubature of the Bivariate Normal Density

polyCub.iso

Cubature of Isotropic Functions over Polygonal Domains

polyCub.midpoint

Two-Dimensional Midpoint Rule

polygauss

Calculate 2D Nodes and Weights of the Product Gauss Cubature

sfg2gpc

Convert polygonal "sfg" to "gpc.poly"

vecnorm

Euclidean Vector Norm (Length)

xylist

Convert Various Polygon Classes to a Simple List of Vertices

polyCub

Cubature over Polygonal Domains

v0.8.0
GPL-2
Authors
Sebastian Meyer [aut, cre, trl] (<https://orcid.org/0000-0002-1791-9449>), Leonhard Held [ths], Michael Hoehle [ths]
Initial release
2021-01-26

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