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vlcom_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

vlcom_c ( Vector linear combination, 3 dimensions )

void vlcom_c ( SpiceDouble        a,
ConstSpiceDouble   v1[3],
SpiceDouble        b,
ConstSpiceDouble   v2[3],
SpiceDouble        sum[3] )

#### Abstract

Compute a vector linear combination of two double precision,
3-dimensional vectors.

None.

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.
sum        O   Linear vector combination a*v1 + b*v2.

#### 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.

#### Detailed_Output

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

a * v1 + b * v2

None.

Error free.

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]

No error checking is performed to guard against numeric overflow.

#### Examples

The numerical results shown for these examples 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 want to generate a sequence of points representing
an elliptical footprint, from the known semi-major
and semi-minor axes.

Example code begins here.

/.
Program vlcom_ex1
./
#include <math.h>
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local variables.
./
SpiceDouble          step;
SpiceDouble          theta;
SpiceDouble          vector [3];

SpiceInt             i;

/.
Let `smajor' and `sminor' be the two known semi-major and
semi-minor axes of our elliptical footprint.
./
SpiceDouble          smajor [3] = { 0.070115, 0.0,        0.0 };

SpiceDouble          sminor [3] = { 0.0,       0.035014,  0.0 };

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

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

vlcom_c ( cos(theta), smajor, sin(theta), sminor, vector );

printf( "%2d: %9.6f %9.6f %9.6f\n",
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  0.000000
1:  0.064778  0.013399  0.000000
2:  0.049579  0.024759  0.000000
3:  0.026832  0.032349  0.000000
4:  0.000000  0.035014  0.000000
5: -0.026832  0.032349  0.000000
6: -0.049579  0.024759  0.000000
7: -0.064778  0.013399  0.000000
8: -0.070115  0.000000  0.000000
9: -0.064778 -0.013399 -0.000000
10: -0.049579 -0.024759 -0.000000
11: -0.026832 -0.032349 -0.000000
12: -0.000000 -0.035014 -0.000000
13:  0.026832 -0.032349  0.000000
14:  0.049579 -0.024759  0.000000
15:  0.064778 -0.013399  0.000000

2) As a second example, suppose that U and V are orthonormal
vectors that form a basis of a plane. Moreover suppose that we
wish to project a vector X onto this plane.

Example code begins here.

/.
Program vlcom_ex2
./
#include <math.h>
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local variables.
./
SpiceDouble          puv    [3];
SpiceDouble          v      [3];

/.
Let `x' be an arbitrary 3-vector
./
SpiceDouble          x      [3] = { 4.0, 35.0, -5.0 };

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

v[0] =  sqrt(2.0)/2.0;
v[1] = -sqrt(2.0)/2.0;
v[2] =  0.0;

/.
Compute the projection of `x' onto this 2-dimensional
plane in 3-space.
./
vlcom_c ( vdot_c ( x, u ), u, vdot_c ( x, v ), v, puv );

/.
Display the results.
./
printf( "Input vector             :  %5.1f %5.1f %5.1f\n",
x[0], x[1], x[2] );
printf( "Projection into 2-d plane:  %5.1f %5.1f %5.1f\n",
puv[0], puv[1], puv[2] );

return ( 0 );
}

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

Input vector             :    4.0  35.0  -5.0
Projection into 2-d plane:  -15.5  15.5  -5.0

#### 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.

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, 13-AUG-2021 (JDR)