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nvc2pl_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

```   nvc2pl_c ( Normal vector and constant to plane )

void nvc2pl_c ( ConstSpiceDouble     normal[3],
SpiceDouble          konst,
SpicePlane        *  plane     )

```

#### Abstract

```   Make a SPICE plane from a normal vector and a constant.
```

```   PLANES
```

#### Keywords

```   GEOMETRY
MATH
PLANE

```

#### Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
normal,
konst      I   A normal vector and constant defining a plane.
plane      O   A SPICE plane structure representing the plane.
```

#### Detailed_Input

```   normal,
konst       are, respectively, a normal vector and constant
defining a plane. normal need not be a unit vector.
Let the symbol < a, b > indicate the inner product of
vectors a and b; then the geometric plane is the set
of vectors x in three-dimensional space that satisfy

< x,  normal >  =  konst.
```

#### Detailed_Output

```   plane       is a SPICE plane structure that represents the
geometric plane defined by `normal' and `konst'.
```

#### Parameters

```   None.
```

#### Exceptions

```   1)  If the input vector `normal' is the zero vector, the error
SPICE(ZEROVECTOR) is signaled.
```

#### Files

```   None.
```

#### Particulars

```   CSPICE geometry routines that deal with planes use the `plane'
data type to represent input and output planes. This data type
makes the routine interfaces simpler and more uniform.

The CSPICE routines that produce SPICE planes from data that
define a plane are:

nvc2pl_c ( Normal vector and constant to plane )
nvp2pl_c ( Normal vector and point to plane    )
psv2pl_c ( Point and spanning vectors to plane )

The CSPICE routines that convert SPICE planes to data that
define a plane are:

pl2nvc_c ( Plane to normal vector and constant )
pl2nvp_c ( Plane to normal vector and point    )
pl2psv_c ( Plane to point and spanning vectors )

Any of these last three routines may be used to convert this
routine's output, `plane', to another representation of a
geometric plane.
```

#### 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) Construct a SPICE plane from a normal vector and a constant.

Example code begins here.

/.
Program nvc2pl_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{
/.
Local variables.
./
SpiceDouble          konst;
SpicePlane           plane;
SpiceDouble          okonst;
SpiceDouble          onorml [3];

/.
Set the normal vector and the constant defining the
plane.
./
SpiceDouble          normal [3] = { 1.0, 1.0, 1.0 };

konst = 23.0;

printf( "Inputs:\n" );
printf( "   Normal vector: %11.7f %11.7f %11.7f\n",
normal[0], normal[1], normal[2] );
printf( "   Constant     : %11.7f\n", konst );
printf( " \n" );

/.
Make a SPICE plane from `normal' and `konst'.
`normal' need not be a unit vector.
./
nvc2pl_c ( normal, konst, &plane );

/.
Print the results.
./
pl2nvc_c ( &plane, onorml, &okonst );
printf( "Generated plane:\n" );
printf( "   Normal vector: %11.7f %11.7f %11.7f\n",
onorml[0], onorml[1], onorml[2] );
printf( "   Constant     : %11.7f\n", okonst );

return ( 0 );
}

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

Inputs:
Normal vector:   1.0000000   1.0000000   1.0000000
Constant     :  23.0000000

Generated plane:
Normal vector:   0.5773503   0.5773503   0.5773503
Constant     :  13.2790562

2) Apply a linear transformation represented by a matrix to
a plane represented by a normal vector and a constant.

Find a normal vector and constant for the transformed plane.

Example code begins here.

/.
Program nvc2pl_ex2
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local variables.
./
SpicePlane           plane;
SpiceDouble          m      [3][3];
SpiceDouble          point  [3];
SpiceDouble          span1  [3];
SpiceDouble          span2  [3];
SpiceDouble          tkonst;
SpiceDouble          tnorml [3];
SpicePlane           tplane;
SpiceDouble          tpoint [3];
SpiceDouble          tspan1 [3];
SpiceDouble          tspan2 [3];

/.
Set the normal vector and the constant defining the
initial plane.
./
SpiceDouble          normal [3] = {
-0.1616904, 0.8084521, -0.5659165 };
SpiceDouble          konst      = 4.8102899;

/.
Define a transformation matrix to the right-handed
reference frame having the +i unit vector as primary
axis, aligned to the original frame's +X axis, and
the -j unit vector as second axis, aligned to the +Y
axis.
./
SpiceDouble          axdef  [3] = { 1.0,  0.0,  0.0 };
SpiceDouble          plndef [3] = { 0.0, -1.0,  0.0 };

twovec_c ( axdef, 1, plndef, 2, m );

/.
Make a SPICE plane from `normal' and `konst', and then
find a point in the plane and spanning vectors for the
plane.  `normal' need not be a unit vector.
./
nvc2pl_c ( normal, konst, &plane );
pl2psv_c ( &plane, point, span1, span2 );

/.
Apply the linear transformation to the point and
spanning vectors.  All we need to do is multiply
these vectors by `m', since for any linear
transformation T,

T ( point  +  t1 * span1     +  t2 * span2 )

=  T (point)  +  t1 * T(span1)  +  t2 * T(span2),

which means that T(point), T(span1), and T(span2)
are a point and spanning vectors for the transformed
plane.
./
mxv_c ( m, point, tpoint );
mxv_c ( m, span1, tspan1 );
mxv_c ( m, span2, tspan2 );

/.
Make a new SPICE plane `tplane' from the
transformed point and spanning vectors, and find a
unit normal and constant for this new plane.
./
psv2pl_c (  tpoint, tspan1, tspan2, &tplane );
pl2nvc_c ( &tplane, tnorml, &tkonst );

/.
Print the results.
./
printf( "Unit normal vector: %11.7f %11.7f %11.7f\n",
tnorml[0], tnorml[1], tnorml[2] );
printf( "Constant          : %11.7f\n", tkonst );

return ( 0 );
}

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

Unit normal vector:  -0.1616904  -0.8084521   0.5659165
Constant          :   4.8102897
```

#### Restrictions

```   1)  No checking is done to prevent arithmetic overflow.
```

#### Literature_References

```   [1]  G. Thomas and R. Finney, "Calculus and Analytic Geometry,"
```

#### Author_and_Institution

```   N.J. Bachman        (JPL)
J. Diaz del Rio     (ODC Space)
```

#### Version

```   -CSPICE Version 1.1.0, 24-AUG-2021 (JDR)

examples.

Changed the input argument name "constant" to "konst" for
consistency with other routines.

-CSPICE Version 1.0.1, 02-NOV-2009 (NJB)

```   normal vector and constant to plane
`Fri Dec 31 18:41:10 2021`