polyCub.midpoint

a polygonal integration domain.
It can be any object coercible to the <pkg>spatstat</pkg> class
<code>"<a href="/link/owin?package=polyCub&version=0.5-1&to=spatstat" rd-options="spatstat" data-mini-rdoc="spatstat::owin">owin</a>"</code> (via <code><a href="/link/as.owin?package=polyCub&version=0.5-1&to=spatstat" rd-options="spatstat" data-mini-rdoc="spatstat::as.owin">as.owin</a></code>).

polyregion

a two-dimensional real function.
As its first argument it must take a coordinate matrix, i.e., a
numeric matrix with two columns, and it must return a numeric vector of
length the number of coordinates.

width and height of the pixels (squares),
see <code><a href="/link/as.mask?package=polyCub&version=0.5-1&to=spatstat" rd-options="spatstat" data-mini-rdoc="spatstat::as.mask">as.mask</a></code>.

number of subdivisions in each dimension,
see <code><a href="/link/as.mask?package=polyCub&version=0.5-1&to=spatstat" rd-options="spatstat" data-mini-rdoc="spatstat::as.mask">as.mask</a></code>.

dimyx

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

plot

The surface is converted to a binary pixel image
using the <code><a href="/link/as.im.function?package=polyCub&version=0.5-1&to=spatstat" rd-options="spatstat" data-mini-rdoc="spatstat::as.im.function">as.im.function</a></code> method from package
<pkg>spatstat</pkg> (Baddeley and Turner, 2005).
The integral under the surface is then approximated as the
sum over (pixel area * f(pixel midpoint)).

spatial

math

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.

polyCub.midpoint: Two-Dimensional Midpoint Rule

Description

Usage

Arguments

Value

References

See Also

Examples