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pl2nvc_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

pl2nvc_c ( Plane to normal vector and constant )

void pl2nvc_c ( ConstSpicePlane   * plane,
SpiceDouble         normal,
SpiceDouble       * konst     )

Abstract

Return a unit normal vector and constant that define a specified
plane.

PLANES

GEOMETRY
MATH
PLANE

Brief_I/O

VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
plane      I   A SPICE plane.
normal,
konst      O   A normal vector and constant defining the
geometric plane represented by `plane'.

Detailed_Input

plane       is a SPICE plane.

Detailed_Output

normal,
konst       are, respectively, a unit normal vector and
constant that define the geometric plane
represented by `plane'. 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.

`normal' is a unit vector. `konst' is the distance of
the plane from the origin;

konst * normal

is the closest point in the plane to the origin.

None.

Exceptions

Error free.

1)  The input plane MUST have been created by one of the CSPICE
routines

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

Otherwise, the results of this routine are unpredictable.

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 )

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) Determine the distance of a plane from the origin, and
confirm the result by calculating the dot product (inner
product) of a vector from the origin to the plane and a
vector in that plane.

The dot product between these two vectors should be zero,
to double precision round-off, so orthogonal to that
precision.

Example code begins here.

/.
Program pl2nvc_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

SpiceDouble          konst;
SpicePlane           plane;
SpiceDouble          plnvec ;
SpiceDouble          vec    ;

/.
Define the plane with a vector normal to the plan
and a point in the plane.
./
SpiceDouble          normal  = { -1.0,  5.0,   -3.5 };
SpiceDouble          point   = { 9.0, -0.65, -12.0 };

/.
Create the SPICE plane from the normal and point.
./
nvp2pl_c ( normal, point, &plane );

/.
Calculate the normal vector and constant defining
the plane. The constant value is the distance from
the origin to the plane.
./
pl2nvc_c ( &plane, normal, &konst );
printf( "Distance to the plane: %11.7f\n", konst );

/.
Confirm the results. Calculate a vector
from the origin to the plane.
./
vscl_c ( konst, normal, vec );
printf( "Vector from origin   : %11.7f %11.7f %11.7f\n",
vec, vec, vec );
printf( " \n" );

/.
Now calculate a vector in the plane from the
location in the plane defined by `vec'.
./
vsub_c ( vec, point, plnvec );

/.
These vectors should be orthogonal.
./
printf( "dot product          : %11.7f\n", vdot_c ( plnvec, vec ) );

return ( 0 );
}

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

Distance to the plane:   4.8102899
Vector from origin   :  -0.7777778   3.8888889  -2.7222222

dot product          :  -0.0000000

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 pl2nvc_ex2
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

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

/.
Set the normal vector and the constant defining the
initial plane.
./
SpiceDouble          normal  = {
-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   = { 1.0,  0.0,  0.0 };
SpiceDouble          plndef  = { 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, tnorml, tnorml );
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

None.

Literature_References

  G. Thomas and R. Finney, "Calculus and Analytic Geometry,"

Author_and_Institution

N.J. Bachman        (JPL)
J. Diaz del Rio     (ODC Space)
E.D. Wright         (JPL)

Version

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

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