cspice_nvp2pl

 Abstract I/O Examples Particulars Required Reading Version Index_Entries

#### Abstract

```
CSPICE_NVC2PL constructs a SPICE plane from a normal vector and a point
on the plane.

```

#### I/O

```
Given:

normal   [3,1] = size(normal); double = class(normal)

point    [3,1] = size(point); double = class(point)

are, respectively, a normal vector and point that
define a plane in three-dimensional space.  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 - point, normal >  =  0.

the call:

plane = cspice_nvp2pl( normal, point )

returns:

plane   a structure describing a SPICE plane defined by
'normal' and 'point'

[1,1] = size(plane); struct = class(plane)

The structure has the fields:

normal:     [3,1] = size(normal); double = class(normal)
constant:   [1,1] = size(constant); double = class(constant)

```

#### Examples

```
Any numerical results shown for this example may differ between
platforms as the results depend on the SPICE kernels used as input
and the machine specific arithmetic implementation.

%
% Define a normal vector from a plane and a
% point in a plane.
%
normal = [ -1.;  5.;   -3.5 ];
point  = [  9.; -0.65; -12. ];

%
% Create a plane from the vectors.
%
plane = cspice_nvp2pl( normal, point );

%
% Calculate a point in the plane, and
% two spanning vectors in the plane such that
% the point and spanning are mutually orthogonal.
%
[point, span1, span2] = cspice_pl2psv( plane )

%
% Test point, span1, and span2 orthogonality. The dot
% products of any two vectors should equal zero to
% within round-off.
%
fprintf( 'dot( point, span1) = %18.15e\n', dot( point, span1) )
fprintf( 'dot( point, span2) = %18.15e\n', dot( point, span2) )
fprintf( 'dot( span1, span2) = %18.15e\n', dot( span1, span2) )

Matlab outputs:

point =

-7.777777777777776e-01
3.888888888888888e+00
-2.722222222222222e+00

span1 =

0
5.734623443633283e-01
8.192319205190405e-01

span2 =

9.868415319342446e-01
1.324619505952006e-01
-9.272336541664042e-02

dot( point, span1) = 0.000000000000000e+00
dot( point, span2) = 5.551115123125783e-17
dot( span1, span2) = 0.000000000000000e+00

```

#### Particulars

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

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

cspice_nvc2pl ( Normal vector and constant to plane )
cspice_nvp2pl ( Normal vector and point to plane    )
cspice_psv2pl ( Point and spanning vectors to plane )

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

cspice_pl2nvc ( Plane to normal vector and constant )
cspice_pl2nvp ( Plane to normal vector and point    )
cspice_pl2psv ( 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.

```

#### Required Reading

```
For important details concerning this module's function, please refer to
the CSPICE routine nvp2pl_c.

MICE.REQ
PLANES.REQ

```

#### Version

```
-Mice Version 1.0.1, 27-AUG-2012, EDW (JPL)

Edited I/O section to conform to NAIF standard for Mice documentation.

-Mice Version 1.0.0, 30-DEC-2008, EDW (JPL)

```

#### Index_Entries

```
normal vector and point to plane

```
`Wed Apr  5 18:00:33 2017`