| pltvol_c |
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Table of contents
Procedure
pltvol_c ( Compute volume of plate model )
SpiceDouble pltvol_c ( SpiceInt nv,
ConstSpiceDouble vrtces[][3],
SpiceInt np,
ConstSpiceInt plates[][3] )
AbstractCompute the volume of a three-dimensional region bounded by a collection of triangular plates. Required_ReadingDSK KeywordsDSK GEOMETRY MATH TOPOGRAPHY Brief_I/OVARIABLE 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][0]
vrtces[i-1][1]
vrtces[i-1][2]
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][0]
plates[i-1][1]
plates[i-1][2]
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
ParametersNone. 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 by a routine in the call tree of
this routine.
3) If the number of plates is less than 4, the error SPICE(TOOFEWPLATES)
is signaled by a routine in the call tree of this routine.
4) If any plate contains a vertex index outside of the range
[1, nv]
the error SPICE(INDEXOUTOFRANGE) is signaled by a routine in the call
tree of this routine.
FilesNone. 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 this example 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 pltvol_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 ][3] =
{ { 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][3] =
{ { 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 Mac/Intel/cc/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 [1]) is
applicable.
Literature_References[1] T. Apostol, "Calculus, Vol. II," John Wiley & Sons, 1969. Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) Version
-CSPICE Version 1.0.1, 13-APR-2021 (JDR)
Edited the header to comply with NAIF standard.
-CSPICE Version 1.0.0, 24-OCT-2016 (NJB)
Index_Entriescompute plate model volume |
Fri Dec 31 18:41:10 2021