## SPH_4PNT

Given four 3-dimensional points, the SPH_4PNT procedure returns the center and radius necessary to define the unique sphere passing through those points.

This routine is written in the IDL language. Its source code can be found in the file `sph_4pnt.pro` in the `lib` subdirectory of the IDL distribution.

### Syntax

SPH_4PNT, X, Y, Z, Xc, Yc, Zc, R [, /DOUBLE]

### Arguments

#### X, Y, Z

4-element floating-point or double-precision vectors containing the X, Y, and Z coordinates of the points.

#### Xc, Yc, Zc

Named variables that will contain the sphere's center X, Y, and Z coordinates.

#### R

A named variable that will contain the sphere's radius.

### Keywords

#### DOUBLE

Set this keyword to force computations to be done in double-precision arithmetic.

### Examples

Find the center and radius of the unique sphere passing through the points: (1, 1, 0), (2, 1, 2), (1, 0, 3), (1, 0, 1):

```; Define the floating-point vectors containing the x, y and z
; coordinates of the points:
X = [1, 2, 1, 1] + 0.0
Y = [1, 1, 0, 0] + 0.0
Z = [0, 2, 3, 1] + 0.0

; Compute sphere's center and radius:
SPH_4PNT, X, Y, Z, Xc, Yc, Zc, R

; Print the results:
PRINT, Xc, Yc, Zc, R
```

IDL prints:

```-0.500000      2.00000      2.00000      2.69258
```

### Version History

Introduced: Pre 4.0