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interp.surface.FFT<-function( obj, M){
#a
z<- obj$z
m1<- nrow( z)
m2<- ncol( z)
#Require that m1 and m2 are odd
if( (m1%%2 != 1) | (m2%%2 != 1)){
cat( m1, m2, fill=TRUE)
stop("Need an odd number of grid points for FFT interp method")
}
zf<- fft( z)
# refined grid sizes
N1<- M*m1
N2<- M*m2
temp<- matrix( 0, N1,N2)
# this stuffing is touchy and that is why the odd
# number of grid values is needed.
n1<- (m1-1)/2
n2<- (m2-1)/2
temp[1:(n1+1), 1:(n2+1)]<- zf[ 1:(n1+1), 1:(n2+1)]
temp[1:(n1+1), N2-(n2-1):0]<- zf[ 1:(n1+1), (n2+2):m2]
temp[N1-(n1-1):0, 1:(n2+1)]<- zf[(n1+2):m1, 1:(n2+1)]
temp[N1-(n1-1):0, N2-(n2-1):0]<- zf[(n1+2):m1, (n2+2):m2]
look<- Re(fft( temp, inverse=TRUE))/ (m1*m2)
# trim interpolated array to be within bounds of source image
look<- look[1: (N1 - M +1), 1: (N2 - M +1) ]
xOut<- seq(obj$x[1], obj$x[m1], length.out=(N1 - M +1) )
yOut<- seq(obj$y[1], obj$y[m2], length.out=(N2 - M +1) )
out<- list( x= xOut, y=yOut, z=look )
return(out)
}
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