void pltexp_c ( ConstSpiceDouble iverts[3][3],
SpiceDouble delta,
SpiceDouble overts[3][3] )
Expand a triangular plate by a specified amount. The expanded
plate is co-planar with, and has the same orientation as, the
original. The centroids of the two plates coincide.
DSK
MATH
GEOMETRY
TOPOGRAPHY
Variable I/O Description
-------- --- --------------------------------------------------
iverts I Vertices of the plate to be expanded.
delta I Fraction by which the plate is to be expanded.
overts O Vertices of the expanded plate.
iverts is an array containing three vertices of a triangular
plate. Each vertex is a three-dimensional vector. The
elements
iverts[i][j], j = 0 ... 2
are, respectively, the X, Y, and Z components of the
ith vertex.
delta is a fraction by which the plate is to be scaled.
Scaling is done so that the scaled plate has the
following properties:
- it is co-planar with the input plate
- its centroid coincides with that of the input
plate
- its sides remain parallel to the corresponding
sides of the input plate
- the distance of each vertex from the centroid is
(1+delta) times the corresponding distance for
the input plate
overts is an array containing three vertices of the triangular
plate resulting from scaling the input plate.
If `ctroid' is the centroid (the average of the vertices)
of the input plate, then the ith vertex of `overts'
overts[i][j], j = 0 ... 2
is equal to
ctroid[j] + (1+delta)*( iverts[i][j] - ctroid[j] ),
j = 0 ... 2
None.
Error free.
None.
This routine supports "greedy" ray-plate intercept algorithms.
Such algorithms attempt to ensure that false negatives---in which
an intersection is not found due to round-off error---do not
occur. In such an algorithm, the plate of interest is expanded
slightly before the intersection test is performed.
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) Expand an equilateral triangle that lies in the plane
{ (x,y,z) : z = 7 }
Use an expansion fraction of 1.0; this doubles the size of
the plate.
Example code begins here.
/.
Example program pltexp_ex1
./
#include <stdio.h>
#include <math.h>
#include "SpiceUsr.h"
int main()
{
/.
Local variables
./
SpiceDouble delta;
SpiceDouble iverts[3][3];
SpiceDouble overts[3][3];
SpiceDouble s;
s = sqrt( 3.0 ) / 2.0;
vpack_c ( s, -0.5, 7.0, iverts[0] );
vpack_c ( 0.0, 1.0, 7.0, iverts[1] );
vpack_c ( -s, -0.5, 7.0, iverts[2] );
delta = 1.0;
pltexp_c ( iverts, delta, overts );
printf ( "\n"
"Vertices of input plate: \n"
" I1 = %20.12f %20.12f %20.12f\n"
" I2 = %20.12f %20.12f %20.12f\n"
" I3 = %20.12f %20.12f %20.12f\n",
iverts[0][0], iverts[0][1], iverts[0][2],
iverts[1][0], iverts[1][1], iverts[1][2],
iverts[2][0], iverts[2][1], iverts[2][2] );
printf ( "\n"
"Vertices of output plate: \n"
" O1 = %20.12f %20.12f %20.12f\n"
" O2 = %20.12f %20.12f %20.12f\n"
" O3 = %20.12f %20.12f %20.12f\n\n",
overts[0][0], overts[0][1], overts[0][2],
overts[1][0], overts[1][1], overts[1][2],
overts[2][0], overts[2][1], overts[2][2] );
return ( 0 );
}
When this program was executed on a PC/Linux/gcc/64-bit
platform, the output was:
Vertices of input plate:
I1 = 0.866025403784 -0.500000000000 7.000000000000
I2 = 0.000000000000 1.000000000000 7.000000000000
I3 = -0.866025403784 -0.500000000000 7.000000000000
Vertices of output plate:
O1 = 1.732050807569 -1.000000000000 7.000000000000
O2 = 0.000000000000 2.000000000000 7.000000000000
O3 = -1.732050807569 -1.000000000000 7.000000000000
Note that the height of the plate is unchanged, but the vectors
from the centroid to the vertices have doubled in length.
None.
None.
N.J. Bachman (JPL)
-CSPICE Version 1.0.0, 29-FEB-2016 (NJB)
expand triangular plate
Link to routine pltexp_c source file pltexp_c.c
|