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vlcom3_c

 Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input Detailed_Output Parameters Exceptions Files Particulars Examples Restrictions Literature_References Author_and_Institution Version Index_Entries

#### Procedure

```   vlcom3_c ( Vector linear combination, 3 dimensions )

void vlcom3_c ( SpiceDouble        a,
ConstSpiceDouble   v1 [3],
SpiceDouble        b,
ConstSpiceDouble   v2 [3],
SpiceDouble        c,
ConstSpiceDouble   v3 [3],
SpiceDouble        sum[3]  )

```

#### Abstract

```   Compute the vector linear combination of three double precision
3-dimensional vectors.
```

```   None.
```

#### Keywords

```   VECTOR

```

#### Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
a          I   Coefficient of `v1'.
v1         I   Vector in 3-space.
b          I   Coefficient of `v2'.
v2         I   Vector in 3-space.
c          I   Coefficient of `v3'.
v3         I   Vector in 3-space.
sum        O   Linear vector combination a*v1 + b*v2 + c*v3.
```

#### Detailed_Input

```   a           is the double precision scalar variable that multiplies
`v1'.

v1          is an arbitrary, double precision 3-dimensional vector.

b           is the double precision scalar variable that multiplies
`v2'.

v2          is an arbitrary, double precision 3-dimensional vector.

c           is the double precision scalar variable that multiplies
`v3'.

v3          is a double precision 3-dimensional vector.
```

#### Detailed_Output

```   sum         is the double precision 3-dimensional vector which
contains the linear combination

a * v1 + b * v2 + c * v3
```

#### Parameters

```   None.
```

#### Exceptions

```   Error free.
```

#### Files

```   None.
```

#### Particulars

```   The code reflects precisely the following mathematical expression

For each value of the index `i', from 0 to 2:

sum[i] = a * v1[i] + b * v2[i] + c * v3[i]

No error checking is performed to guard against numeric overflow.
```

#### Examples

```   The numerical results shown for this example may differ across
platforms. The results depend on the SPICE kernels used as
input, the compiler and supporting libraries, and the machine
specific arithmetic implementation.

1) Suppose you have an instrument with an elliptical field
of view described by its angular extent along the semi-minor
and semi-major axes.

The following code example demonstrates how to create
16 vectors aiming at visualizing the field-of-view in
three dimensional space.

Example code begins here.

/.
Program vlcom3_ex1
./
#include <math.h>
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local parameters.

Define the two angular extends, along the semi-major
(u) and semi-minor (v) axes of the elliptical field
./
#define MAXANG       0.07
#define MINANG       0.035

/.
Local variables.
./
SpiceDouble          a;
SpiceDouble          b;
SpiceDouble          step;
SpiceDouble          theta;
SpiceDouble          vector [3];
SpiceInt             i;

/.
Let `u' and `v' be orthonormal 3-vectors spanning the
focal plane of the instrument, and `z' its
boresight.
./
SpiceDouble          u      [3] = { 1.0,  0.0,  0.0 };
SpiceDouble          v      [3] = { 0.0,  1.0,  0.0 };
SpiceDouble          z      [3] = { 0.0,  0.0,  1.0 };

/.
Find the length of the ellipse's axes. Note that
we are dealing with unitary vectors.
./
a = tan ( MAXANG );
b = tan ( MINANG );

/.
Compute the vectors of interest and display them
./
theta = 0.0;
step  = twopi_c() / 16;

for ( i = 0; i < 16; i++ )
{

vlcom3_c ( 1.0, z, a * cos(theta), u, b * sin(theta), v, vector );

printf( "%2d: %9.6f %9.6f %9.6f\n",
(int)i, vector[0], vector[1], vector[2] );

theta = theta + step;

}

return ( 0 );
}

When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:

0:  0.070115  0.000000  1.000000
1:  0.064777  0.013399  1.000000
2:  0.049578  0.024759  1.000000
3:  0.026832  0.032349  1.000000
4:  0.000000  0.035014  1.000000
5: -0.026832  0.032349  1.000000
6: -0.049578  0.024759  1.000000
7: -0.064777  0.013399  1.000000
8: -0.070115  0.000000  1.000000
9: -0.064777 -0.013399  1.000000
10: -0.049578 -0.024759  1.000000
11: -0.026832 -0.032349  1.000000
12: -0.000000 -0.035014  1.000000
13:  0.026832 -0.032349  1.000000
14:  0.049578 -0.024759  1.000000
15:  0.064777 -0.013399  1.000000
```

#### Restrictions

```   1)  No error checking is performed to guard against numeric
overflow or underflow. The user is responsible for insuring
that the input values are reasonable.
```

#### Literature_References

```   None.
```

#### Author_and_Institution

```   N.J. Bachman        (JPL)
J. Diaz del Rio     (ODC Space)
W.L. Taber          (JPL)
E.D. Wright         (JPL)
```

#### Version

```   -CSPICE Version 1.1.1, 10-AUG-2021 (JDR)

code example.

```   linear combination of three 3-dimensional vectors
`Fri Dec 31 18:41:14 2021`