# ncl_c_csa3s - Man Page

cubic spline approximation, simple entry for three-dimensional input, gridded output

## Function Prototype

```float *c_csa3s(int, float [], float [], float [], float [], int [], int, int,
int, float [], float [], float [], int *);```

## Synopsis

```float *c_csa3s (int n, float xi[], float yi[], float zi[],
float ui[], int knots[3], int nxo, int nyo,
int nzo, float xo[], float yo[], float zo[],
int *ier);```

## Description

n

(integer,input) The number of input data points. It must be  that n is greater than 3 and, depending  on the size of knots below, n may have to be larger.

xi

(real, input) An array dimensioned for n containing the X coordinate  values for the input function.

yi

(real, input) An array dimensioned for n containing the Y coordinate  values for the input function.

zi

(real, input) An array dimensioned for n containing the Z coordinate  values for the input function.

ui

(real, input) An array containing the functional values of  the input function -- ui[k] is the functional value at (xi[k], yi[k], zi[k]) for k=0,n-1.

knots

(integer, input) The number of knots to be used  in constructing the approximation spline. knots[0], knots[1] and knots[2] must each be at least 4. The  larger the value for knots, the closer the approximated curve will come  to passing through the input function values.

nxo

(integer, input) The number of X coordinate  values to be calculated for the output surface.

nyo

(integer, input) The number of Y coordinate  values to be calculated for the output surface.

nzo

The number of Z coordinate values to be calculated for the output grid.

xo

(real, input) An array dimensioned for nxo containing the X coordinates of the output grid.

yo

(real, output) An array dimensioned for nyo containing the Y coordinates of the output grid.

zo

(real, output) An array dimensioned for nzo containing the Z coordinates of the output grid.

ier

(pointer to integer, output) An error return value.  If *ier is returned as 0, then no errors were  detected. If *ier is non-zero, then refer to the error list in the error  table for details.

## Usage

c_csa3s is called to find an approximating cubic spline for  three-dimensional input data. If you want to weight the input  data values, calculate derivatives, or handle data sparse areas specially, then you will need to use c_csa3xs.

c_csa3s returns a pointer to a linear array of data that is the approximation spline stored in row-major order. That is, if out is declared as

`  float *out;`

and we set:

`  out = c_csa3s(n, x, y, z, u, nx, ny, nz, xo, yo, zo, &ier);`

then out[nz*ny*i + nz*j + k] is the approximation function value  at coordinate point (xo[i], yo[j], zo[k]) for 0 <= i < nx, 0 <= j < ny, and 0 <= k < nz. The space  for out is allocated internal to c_csa3s and is nx*ny*nz floats in size.

## Access

To use c_csa3s, load the NCAR Graphics library ngmath.