polyCub (version 0.5-0)

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

Description

Calculate 2D Nodes and Weights of the Product Gauss Cubature

Usage

polygauss(xy, nw_MN, alpha = NULL, rotation = FALSE, engine = "C")

Arguments

xy

list with elements "x" and "y" containing the polygon vertices in anticlockwise order (otherwise the result of the cubature will have a negative sign) with first vertex not repeated at the end (like owin.ob

nw_MN

unnamed list of nodes and weights of one-dimensional Gauss quadrature rules of degrees $N$ and $M=N+1$ (as returned by gauss.quad): list(s_M, w_M, s_N, w_N).

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

engine

character string specifying the implementation to use. Up to polyCub version 0.4-3, the two-dimensional nodes and weights were computed by R functions and these are still available by setting engine = "R". The new C-implementation is

References

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