| pl2nvc_c |
|
Table of contents
Procedure
pl2nvc_c ( Plane to normal vector and constant )
void pl2nvc_c ( ConstSpicePlane * plane,
SpiceDouble normal[3],
SpiceDouble * konst )
AbstractReturn a unit normal vector and constant that define a specified plane. Required_ReadingPLANES KeywordsGEOMETRY 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_Inputplane 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.
ParametersNone. 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.
FilesNone. 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 [3];
SpiceDouble vec [3];
/.
Define the plane with a vector normal to the plan
and a point in the plane.
./
SpiceDouble normal [3] = { -1.0, 5.0, -3.5 };
SpiceDouble point [3] = { 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[0], vec[1], vec[2] );
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 [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
RestrictionsNone. Literature_References
[1] G. Thomas and R. Finney, "Calculus and Analytic Geometry,"
7th Edition, Addison Wesley, 1988.
Author_and_InstitutionN.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.
Edited the header to comply with NAIF standard. Added complete code
examples.
-CSPICE Version 1.0.1, 06-FEB-2003 (EDW)
Trivial correction to header docs.
-CSPICE Version 1.0.0, 05-MAR-1999 (NJB)
Index_Entriesplane to normal vector and constant |
Fri Dec 31 18:41:10 2021