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# dspnt3

Interpolates 3D data at specified points.

## Prototype

```	function dspnt3 (
x  [*] : numeric,
y  [*] : numeric,
z  [*] : numeric,
u      : numeric,
xo [*] : numeric,
yo [*] : numeric,
zo [*] : numeric
)

return_val [dimsizes(xo) * dimsizes(yo) * dimsizes(zo)] :  float or double
```

## Arguments

x

A 1D array of length npts containing the X coordinates of the points where interpolation is desired.

y

A 1D array of length npts containing the Y coordinates of the points where interpolation is desired.

z

A 1D array of length npts containing the Z coordinates of the points where interpolation is desired.

u

An array of any dimensionality (last dimension must be npts) containing the functional values of the input data. Element u(...,i) is the value of the input function at coordinate (x(i), y(i), z(i)) for i = 0, npts - 1.

xo

A 1D array of length m containing the X coordinates of the output data grid. The values in xo may be in any order and m can be equal to one.

yo

A 1D array of length m containing the Y coordinates of the output data grid. The values in yo may be in any order and m can be equal to one.

zo

A 1D array of length m containing the Z coordinates of the output data grid. The values in zo may be in any order and m can be equal to one.

## Return value

Returns a floating point array dimensioned as N x m x m x m, where N represents all but the last dimension of u. The return value type is double if u is of type double.

## Description

This function performs interpolation from sets of 3D data at a list of specified points.

This function must allocate its output arrays in advance.

This function is part of the Dsgrid package which implements a simple inverse distance weighted interpolation algorithm. No missing values are allowed.

## Examples

Example 1

```begin

NUM = 1000
NX  = 21
NY  = 21
NZ  = 21
RAND_MAX = 32767.0

xi = new((/NUM/), float)
yi = new((/NUM/), float)
zi = new((/NUM/), float)
u  = new((/NUM/), float)

xo = new((/NX/), float)
yo = new((/NY/), float)
zo = new((/NZ/), float)
output = new((/NX, NY, NZ/), float)

xmin = -2.0
ymin = -2.0
zmin = -2.0
xmax =  2.0
ymax =  2.0
zmax =  2.0

;
; Create random data in three space and define a function.
;
rand1 = new((/NUM/), float)
rand2 = new((/NUM/), float)
rand3 = new((/NUM/), float)
srand(1)
do i = 0, NUM - 1
rand1(i) = rand()
rand2(i) = rand()
rand3(i) = rand()
end do
xi = xmin + (xmax - xmin) * (rand1 / RAND_MAX)
yi = ymin + (ymax - ymin) * (rand2 / RAND_MAX)
zi = zmin + (zmax - zmin) * (rand3 / RAND_MAX)

u = (xi * xi) + (yi * yi) + (zi * zi)
;
; Create the output grid.
;
ii = fspan(0, 20.0, 21)
xo = xmin + (ii / (NX - 1)) * (xmax - xmin)
yo = ymin + (ii / (NY - 1)) * (ymax - ymin)
zo = zmin + (ii / (NZ - 1)) * (zmax - zmin)

do i = 0, NX - 1
do j = 0, NY - 1
do k = 0, NZ - 1
u(i, j, k) = dspnt3(xi, yi, zi, u, xo(i), yo(j), zo(k))
end do
end do
end do
end
```