pltvol_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

```   SpiceDouble pltvol_c ( SpiceInt           nv,
ConstSpiceDouble   vrtces[],
SpiceInt           np,
ConstSpiceInt      plates[] )
```

#### Abstract

```
Compute the volume of a three-dimensional region bounded by a
collection of triangular plates.
```

```
None.
```

```
DSK
GEOMETRY
MATH
TOPOGRAPHY

```

#### Brief_I/O

```
Variable  I/O  Description
--------  ---  --------------------------------------------------
nv         I   Number of vertices.
vrtces     I   Array of vertices.
np         I   Number of triangular plates.
plates     I   Array of plates.

The function returns the volume of the spatial region bounded
by the plates.
```

#### Detailed_Input

```
nv             is the number of vertices comprising the plate
model.

vrtces         is an array containing the plate model's vertices.
Elements

vrtces[i-1]
vrtces[i-1]
vrtces[i-1]

are, respectively, the X, Y, and Z components of
the ith vertex, where `i' ranges from 1 to `nv'.

This routine doesn't associate units with the
vertices.

np             is the number of triangular plates comprising the
plate model.

plates         is an array containing 3-tuples of integers
representing the model's plates. The elements of
`plates' are vertex indices. The vertex indices are
1-based: vertices have indices ranging from 1 to
`nv'. The elements

plates[i-1]
plates[i-1]
plates[i-1]

are, respectively, the indices of the vertices
comprising the ith plate.

Note that the order of the vertices of a plate is
significant: the vertices must be ordered in the
positive (counterclockwise) sense with respect to
the outward normal direction associated with the
plate. In other words, if v1, v2, v3 are the
vertices of a plate, then

( v2 - v1 )  x  ( v3 - v2 )

points in the outward normal direction. Here
"x" denotes the vector cross product operator.

```

#### Detailed_Output

```
The function returns the volume of the spatial region bounded
by the plates.

If the components of the vertex array have length unit L, then the
output volume has units

3
L
```

```
None.
```

#### Exceptions

```
1) The input plate model must define a spatial region with
a boundary. This routine does not check the inputs to
verify this condition. See the Restrictions section below.

2) If the number of vertices is less than 4, the error
SPICE(TOOFEWVERTICES) is signaled.

3) If the number of plates is less than 4, the error
SPICE(TOOFEWPLATES) is signaled.

4) If any plate contains a vertex index outside of the range

[1, nv]

the error SPICE(INDEXOUTOFRANGE) will be signaled.
```

```
None.
```

#### Particulars

```
This routine computes the volume of a spatial region bounded by
a set of triangular plates. If the plate set does not actually
form the boundary of a spatial region, the result of this routine
is invalid.

Examples:

Valid inputs
------------
Tetrahedron
Box
Tiled ellipsoid
Two disjoint boxes

Invalid inputs
--------------
Single plate
Tiled ellipsoid with one plate removed
Two boxes with intersection having positive volume

```

#### Examples

```
The numerical results shown for these examples may differ across
platforms. The results depend on the SPICE kernels used as input
(if any), the compiler and supporting libraries, and the machine
specific arithmetic implementation.

1) Compute the volume of the pyramid defined by the four
triangular plates whose vertices are the 3-element
subsets of the set of vectors

( 0, 0, 0 )
( 1, 0, 0 )
( 0, 1, 0 )
( 0, 0, 1 )

Example code begins here.

/.
PROGRAM EX1
./

/.
Compute the volume of a plate model representing the pyramid
with one vertex at the origin and the other vertices
coinciding with the standard basis vectors.
./

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

int main()
{
/.
Local constants
./
#define NVERT           4
#define NPLATE          4

/.
Local variables
./
SpiceDouble             vol;

/.
Let the notation

< A, B >

denote the dot product of vectors A and B.

The plates defined below lie in the following planes,
respectively:

Plate 1:    { P :  < P, (-1,  0,  0) > = 0 }
Plate 2:    { P :  < P, ( 0, -1,  0) > = 0 }
Plate 3:    { P :  < P, ( 0,  0, -1) > = 0 }
Plate 4:    { P :  < P, ( 1,  1,  1) > = 1 }

./
SpiceDouble             vrtces[NVERT ] =

{ { 0.0, 0.0, 0.0 },
{ 1.0, 0.0, 0.0 },
{ 0.0, 1.0, 0.0 },
{ 0.0, 0.0, 1.0 }  };

SpiceInt                plates[NPLATE] =

{ { 1, 4, 3 },
{ 1, 2, 4 },
{ 1, 3, 2 },
{ 2, 3, 4 }  };

vol = pltvol_c( NVERT, vrtces, NPLATE, plates );

printf ( "Expected volume =      1/6\n"        );
printf ( "Computed volume  =   %24.17e\n", vol );

return ( 0 );
}

When this program was executed on a PC/Linux/gcc 64-bit platform,
the output was:

Expected volume =      1/6
Computed volume  =    1.66666666666666657e-01
```

#### Restrictions

```
1) The plate collection must describe a surface and enclose a
volume such that the divergence theorem (see ) is
applicable.
```

#### Literature_References

```
  Calculus, Vol. II. Tom Apostol. John Wiley & Sons, 1969.
```

#### Author_and_Institution

```
N.J. Bachman    (JPL)
```

#### Version

```
-CSPICE Version 1.0.0, 24-OCT-2016 (NJB)
```

#### Index_Entries

```
compute plate model volume
```
`Wed Apr  5 17:54:40 2017`