polygauss

list with elements <code>"x"</code> and <code>"y"</code> containing the
polygon vertices in <em>anticlockwise</em> order (otherwise the result of the
cubature will have a negative sign) with first vertex not repeated at the
end (like <code>owin.object$bdr</code>

unnamed list of nodes and weights of one-dimensional Gauss
quadrature rules of degrees $N$ and $M=N+1$ (as returned by
<code><a href="/link/gauss.quad?package=polyCub&version=0.5-1&to=statmod" rd-options="statmod" data-mini-rdoc="statmod::gauss.quad">gauss.quad</a></code>): <code>list(s_M, w_M, s_N, w_N)</code>.

nw_MN

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

alpha

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

rotation

character string specifying the implementation to use.
Up to <pkg>polyCub</pkg> version 0.4-3, the two-dimensional nodes and weights
were computed by Rfunctions and these are still available by setting
<code>engine = "R"</code>.
The new C-implementation i

engine

Calculate 2D Nodes and Weights of the Product Gauss Cubature

internal

A package providing methods for cubature (numerical integration)
             over polygonal domains.
             Currently, four cubature methods are implemented:
             the two-dimensional midpoint rule as a simple wrapper around
             as.im.function() from package spatstat (Baddeley and Turner, 2005),
             the product Gauss cubature by Sommariva and Vianello (2007),
             an adaptive cubature for isotropic functions via line integrate()
             along the boundary (Meyer and Held, 2014),
             and quasi-exact methods specific to the integration of the
             bivariate Gaussian density over polygonal and circular domains
             (based on formulae from the Abramowitz and Stegun (1972) handbook).
             For cubature over simple hypercubes, the packages "cubature" and
             "R2Cuba" are more appropriate.

polygauss: Calculate 2D Nodes and Weights of the Product Gauss Cubature

Description

Usage

Arguments

References