Trilinear Interpolation in a 3D Array

Interpolate within a 3D array, using the trilinear approximation.

Usage

approx3d(x, y, z, f, xout, yout, zout)

Arguments

x

vector of x values for grid (must be equi-spaced)

y

vector of y values for grid (must be equi-spaced)

z

vector of z values for grid (must be equi-spaced)

f

matrix of rank 3, with the gridded values mapping to the x values (first index of f), etc.

xout

vector of x values for output.

yout

vector of y values for output (length must match that of xout).

zout

vector of z values for output (length must match that of xout).

Value

A vector of interpolated values (or NA values), with length matching that of xout.

Details

Trilinear interpolation is used to interpolate within the f array, for those (xout, yout and zout) triplets that are inside the region specified by x, y and z. Triplets that lie outside the range of x, y or z result in NA values.

Author

Dan Kelley and Clark Richards

Examples

# set up a grid
library(oce)
n <- 5
x <- seq(0, 1, length.out = n)
y <- seq(0, 1, length.out = n)
z <- seq(0, 1, length.out = n)
f <- array(1:n^3, dim = c(length(x), length(y), length(z)))
# interpolate along a diagonal line
m <- 100
xout <- seq(0, 1, length.out = m)
yout <- seq(0, 1, length.out = m)
zout <- seq(0, 1, length.out = m)
approx <- approx3d(x, y, z, f, xout, yout, zout)
# graph the results
plot(xout, approx, type = "l")
points(xout[1], f[1, 1, 1])
points(xout[m], f[n, n, n])