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pltar_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

pltar_c ( Compute area of plate set )

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

Abstract

Compute the total area of a collection of triangular plates.

DSK

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 total area of the set of plates.

Detailed_Input

nv          is the number of vertices comprising the plate
set.

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 set.

plates      is an array containing 3-tuples of integers
representing the set of 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 total area of the input set of plates.
Each plate contributes the area of the triangle defined by the
plate's vertices.

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

2
L

None.

Exceptions

1)  If the number of plates is less than 0, the error
SPICE(BADPLATECOUNT) is signaled by a routine in the call tree
of this routine.

2)  If the number of plates is positive and the number of vertices
is less than 3, the error SPICE(TOOFEWVERTICES) is signaled by
a routine in the call tree of this routine.

3)  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.

None.

Particulars

This routine computes the total area of a set of triangular
plates. The plates need not define a closed surface.

Examples of valid plate sets:

Tetrahedron
Box
Tiled ellipsoid
Tiled ellipsoid with one plate removed
Two disjoint boxes
Two boxes with intersection having positive volume
Single plate
Empty plate set

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 area 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 pltar_ex1

Compute the area 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             area;

/.
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 }  };

area = pltar_c( NVERT, vrtces, NPLATE, plates );

printf ( "Expected area  =    (3 + sqrt(3)) / 2\n"
"               =    0.23660254037844384e+01\n" );
printf ( "Computed area  =   %24.17e\n", area            );

return ( 0 );
}

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

Expected area  =    (3 + sqrt(3)) / 2
=    0.23660254037844384e+01
Computed area  =    2.36602540378443837e+00

None.

None.

Author_and_Institution

N.J. Bachman        (JPL)
J. Diaz del Rio     (ODC Space)

Version

-CSPICE Version 1.0.1, 04-AUG-2021 (JDR)

Edited the header to comply with NAIF standard.

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

Index_Entries

compute plate model area
Fri Dec 31 18:41:10 2021