Evaluates a basis for the harmonic polynomials in x and y
of degree less than or equal to n.
Usage
harmonic(x, y, n)
Arguments
x
Vector of x coordinates
y
Vector of y coordinates
n
Maximum degree of polynomial
Details
This function computes a basis for the harmonic polynomials
in two variables x and y up to a given degree n
and evaluates them at given x,y locations.
It can be used in model formulas (for example in
the model-fitting functions
lm,glm,gam and ppm) to specify a
linear predictor which is a harmonic function.
A function f(x,y) is harmonic if
(d/dx)^2 f + (d/dy)^2 f = 0.
The harmonic polynomials of degree less than or equal to
n have a basis consisting of 2 n functions.
This function was implemented on a suggestion of P. McCullagh
for fitting nonstationary spatial trend to point process models.
Value
A data frame with 2 * n columns giving the values of the
basis functions at the coordinates. Each column is labelled by an
algebraic expression for the corresponding basis function.