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vprjp_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

```   vprjp_c ( Vector projection onto plane )

void vprjp_c ( ConstSpiceDouble    vin   [3],
ConstSpicePlane   * plane,
SpiceDouble         vout  [3] )

```

#### Abstract

```   Project a vector onto a specified plane, orthogonally.
```

```   PLANES
```

#### Keywords

```   GEOMETRY
MATH
PLANE
VECTOR

```

#### Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
vin        I   Vector to be projected.
plane      I   A SPICE plane onto which `vin' is projected.
vout       O   Vector resulting from projection.
```

#### Detailed_Input

```   vin         is a 3-vector that is to be orthogonally projected
onto a specified plane.

plane       is a SPICE plane that represents the geometric
plane onto which `vin' is to be projected.

The normal vector component of a SPICE plane has
unit length.
```

#### Detailed_Output

```   vout        is the vector resulting from the orthogonal
projection of `vin' onto `plane'. `vout' is the closest
point in the specified plane to `vin'.
```

#### Parameters

```   None.
```

#### Exceptions

```   1)  If the normal vector of the input plane does not have unit
length (allowing for round-off error), the error
SPICE(NONUNITNORMAL) is signaled by a routine in the call tree
of this routine.
```

#### Files

```   None.
```

#### Particulars

```   Projecting a vector `vin' orthogonally onto a plane can be thought
of as finding the closest vector in the plane to `vin'. This
"closest vector" always exists; it may be coincident with the
original vector.

Two related routines are vprjpi_c, which inverts an orthogonal
projection of a vector onto a plane, and vproj_c, which projects
a vector orthogonally onto another vector.
```

#### Examples

```   The numerical results shown for this example 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) Find the closest point in the ring plane of a planet to a
spacecraft located at a point (in body-fixed coordinates).

Example code begins here.

/.
Program vprjp_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{
/.
Local variables.
./
SpiceDouble          proj   [3];
SpicePlane           ringpl;

/.
Set the spacecraft location and define the normal
vector as the normal to the equatorial plane, and
the origin at the body/ring center.
./
SpiceDouble          scpos  [3] = { -29703.16955,
879765.72163,
-137280.21757 };

SpiceDouble          norm   [3] = { 0.0, 0.0, 1.0 };

SpiceDouble          orig   [3] = { 0.0, 0.0, 0.0 };

/.
Create the plane structure.
./
nvp2pl_c ( norm, orig, &ringpl );

/.
Project the position vector onto the ring plane.
./
vprjp_c ( scpos, &ringpl, proj );

printf( "Projection of S/C position onto ring plane:\n" );
printf( "%17.5f %16.5f %16.5f\n", proj[0], proj[1], proj[2] );

return ( 0 );
}

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

Projection of S/C position onto ring plane:
-29703.16955     879765.72163          0.00000
```

#### Restrictions

```   1)  It is recommended that the input plane be 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 )

In any case the input plane must have a unit length normal
vector and a plane constant consistent with the normal
vector.
```

#### Literature_References

```   [1]  G. Thomas and R. Finney, "Calculus and Analytic Geometry,"
7th Edition, Addison Wesley, 1988.
```

#### Author_and_Institution

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

#### Version

```   -CSPICE Version 1.0.2, 24-AUG-2021 (JDR) (NJB)

Edited the header to comply with NAIF standard. Added complete
code example.

Added entry #1 to -Exceptions section, and entry #1 to -Restrictions.

-CSPICE Version 1.0.1, 01-FEB-2017 (BVS)

Typo fix: pnv2pl_c -> nvp2pl_c.

-CSPICE Version 1.0.0, 05-MAR-1999 (NJB)
```

#### Index_Entries

```   vector projection onto plane
```
`Fri Dec 31 18:41:15 2021`