\name{akimaInterp}


\alias{akimaInterp}
\alias{akimaInterpp}


\title{Bivariate Spline Interpolation}


\description{
    
    Interpolates bivariate data sets using Akima 
    spline interpolation. 
    
}
    

\usage{      
akimaInterp(x, y = NULL, z = NULL, gridPoints = 21,
    xo = seq(min(x), max(x), length = gridPoints),
    yo = seq(min(y), max(y), length = gridPoints), extrap = FALSE)
    
akimaInterpp(x, y = NULL, z = NULL, xo, yo, extrap = FALSE)
}


\arguments{
  
    \item{x, y, z}{
        for \code{akimaInterp} the arguments \code{x} and \code{y} are 
        two numeric vectors of grid pounts, and \code{z} is a numeric 
        matrix or any other rectangular object which can be transformed 
        by the function \code{as.matrix} into a matrix object.  
        For \code{akimaInterpp} we  consider either three numeric vectors 
        of equal length or if  \code{y} and \code{z} are NULL, a list with 
        entries \code{x}, \code{y}, \code{z}, or named data frame with 
        \code{x} in the first, \code{y} in the second, and \code{z} in 
        the third column. 
        }
    \item{gridPoints}{
        an integer value specifying the number of grid points in \code{x} 
        and \code{y} direction.
        } 
    \item{xo, yo}{
        for \code{akimaInterp}
        two numeric vectors of data points spanning the grid, and
        for \code{akimaInterpp}
        two numeric vectors of data points building pairs for pointwise
        interpolation.
        }
    \item{extrap}{
        a logical, if \code{TRUE} then the data points are extrapolated.
        }
    
}


\details{

    Two options are available gridded and pointwise interpolation. 
    
    \code{akimaInterp} is a function wrapper to the \code{interp} 
    function provided by the contributed R package \code{akima}.
    The Fortran code of the Akima spline interpolation routine was
    written by H. Akima.
    
    Linear surface fitting and krige surface fitting are provided by
    the functions \code{linearInterp} and \code{krigeInterp}.
    
}


\note{

    IMPORTANT: The contributed package \code{akima} is not in the 
    dependence list of the DESCRIPTION file due to license conditions.
    The Rmetrics user has to load this package from the CRAN server on 
    his own responsibility, please check the license conditions.

}
       
    
\value{

    \code{akimaInterp} 
    
    returns a list with at least three entries, \code{x}, \code{y} 
    and \code{z}. Note, that the returned values, can be directly 
    used by the  \code{persp} and \code{contour} 3D plotting methods.
    \cr
    
    \code{akimaInterpp} 
    
    returns a data.frame with columns \code{"x"}, \code{"y"}, 
    and \code{"z"}.
    
}


\seealso{

    \code{\link{linearInterp}}, 
    \code{\link{krigeInterp}}.
    
}


\references{

    Akima H., 1978,
    \emph{A Method of Bivariate Interpolation and Smooth Surface Fitting for 
    Irregularly Distributed Data Points},
    ACM Transactions on Mathematical Software 4, 149-164.

    Akima H., 1996,
    \emph{Algorithm 761: Scattered-Data Surface Fitting that has the Accuracy 
    of a Cubic Polynomial},
    ACM Transactions on Mathematical Software 22, 362-371. 
    
    
}


\examples{ 
## akimaInterp -
   # Akima Interpolation:    
   if (require(akima)) {
     set.seed(1953)
     x = runif(999) - 0.5
     y = runif(999) - 0.5
     z = cos(2*pi*(x^2+y^2))
     ans = akimaInterp(x, y, z, gridPoints = 41, extrap = FALSE)
     persp(ans, theta = -40, phi = 30, col = "steelblue",
        xlab = "x", ylab = "y", zlab = "z")
     contour(ans)
   }
}


\keyword{programming}