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ednmpt_c

Table of contents
 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

```   ednmpt_c ( Ellipsoid normal vector to surface point )

void ednmpt_c ( SpiceDouble         a,
SpiceDouble         b,
SpiceDouble         c,
ConstSpiceDouble    normal [3],
SpiceDouble         point  [3] )

```

#### Abstract

```   Return the unique point on an ellipsoid's surface where the
outward normal direction is a given vector.
```

#### Required_Reading

```   None.
```

#### Keywords

```   ELLIPSOID
GEOMETRY
NORMAL

```

#### Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
a          I   Length of the ellipsoid semi-axis along the X-axis.
b          I   Length of the ellipsoid semi-axis along the Y-axis.
c          I   Length of the ellipsoid semi-axis along the Z-axis.
normal     I   Outward normal direction.
point      O   Point where outward normal is parallel to `normal'.
```

#### Detailed_Input

```   a           is the length of the semi-axis of the ellipsoid
that is parallel to the X-axis of the body-fixed
coordinate system.

b           is the length of the semi-axis of the ellipsoid
that is parallel to the Y-axis of the body-fixed
coordinate system.

c           is the length of the semi-axis of the ellipsoid
that is parallel to the Z-axis of the body-fixed
coordinate system.

normal      is a non-zero vector. The unique point on the
ellipsoid at which `normal' is an outward normal vector
is sought.
```

#### Detailed_Output

```   point       is the unique point on the ellipsoid at which `normal'
is an outward normal vector.

`point' is a 3-vector giving the body-fixed coordinates
of a point on the ellipsoid. In body-fixed coordinates,
the semi-axes of the ellipsoid are aligned with the X,
Y, and Z-axes of the coordinate system.
```

#### Parameters

```   None.
```

#### Exceptions

```   1)  If any of the semi-axis lengths is non-positive, the error
SPICE(BADAXISLENGTH) is signaled by a routine in the call tree of
this routine.

2)  If any of the semi-axis lengths underflows to zero when divided by
the largest semi-axis length, the error SPICE(AXISUNDERFLOW) is
signaled by a routine in the call tree of this routine.

3)  If `normal' is the zero vector, the error SPICE(ZEROVECTOR)
is signaled by a routine in the call tree of this routine.

4)  If the input pass the above checks but lead to a divide-by-zero error
or to a computing an invalid argument of a fractional exponential
expression, the error SPICE(DEGENERATECASE) is signaled by a routine
in the call tree of this routine.
```

#### Files

```   None.
```

#### Particulars

```   This routine can be used to determine the distance between an
ellipsoid and a non-intersecting plane. This distance computation
supports computation of terminator points on an ellipsoid.
```

#### 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) Choose a triaxial ellipsoid with three unequal semi-axis
lengths. Pick several vectors; find the points on the
ellipsoid where the respective outward normals are parallel to
those vectors.

Check the results: at each point, a computed outward normal
vector should have very small angular separation from the
input vector. Also, the point should be on the surface of the
ellipsoid. The ellipsoid can be thought of as a level surface
of the function

2        2         2
f(x, y, z) = (x/a)  + (y/b)  +  (z/c)

where `a', `b', `c' are the semi-axis lengths of the ellipsoid.
Specifically, the ellipsoid is the set

{ (x, y, z) : f(x, y, z)  =  1 }

We can evaluate F at a point to determine whether that point
is close to the ellipsoid's surface.

Example code begins here.

/.
Program ednmpt_ex1
./
#include <math.h>
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local variables
./
SpiceDouble          a;
SpiceDouble          b;
SpiceDouble          c;
SpiceDouble          normal [3];
SpiceDouble          point  [3];
SpiceDouble          xnorml [3];

/.
Initialize the ellipsoid semi-axes.
./
a = 10.0;
b =  5.0;
c =  2.0;

/.
Pick several vectors; find the points
on the ellipsoid where the respective
outward normals are parallel to those
vectors; check the results.
./
vpack_c ( 0.0, 0.0, 3.0, xnorml );
ednmpt_c ( a, b, c, xnorml, point );
surfnm_c ( a, b, c, point, normal );

printf( " \n" );
printf( "Semi-axis lengths:    %13.8f %13.8f %13.8f\n", a, b, c );
printf( "Input vector:         %13.8f %13.8f %13.8f\n",
xnorml[0], xnorml[1], xnorml[2] );
printf( "Point:                %13.8f %13.8f %13.8f\n",
point[0], point[1], point[2] );
printf( "Outward normal:       %13.8f %13.8f %13.8f\n",
normal[0], normal[1], normal[2] );
printf( "Angular error (rad):  %13.8f\n",
vsep_c ( normal, xnorml ) );
printf( "Off-surface error:    %13.8f\n",
pow( (point[0]/a), 2 ) + pow( (point[1]/b), 2 )
+ pow( (point[2]/c), 2 ) - 1 );
printf( " \n" );

vpack_c ( 15.0, -7.0, 3.0, xnorml );
ednmpt_c ( a, b, c, xnorml, point );
surfnm_c ( a, b, c, point, normal );

printf( "Semi-axis lengths:    %13.8f %13.8f %13.8f\n", a, b, c );
printf( "Input vector:         %13.8f %13.8f %13.8f\n",
xnorml[0], xnorml[1], xnorml[2] );
printf( "Point:                %13.8f %13.8f %13.8f\n",
point[0], point[1], point[2] );
printf( "Outward normal:       %13.8f %13.8f %13.8f\n",
normal[0], normal[1], normal[2] );
printf( "Angular error (rad):  %13.8f\n",
vsep_c ( normal, xnorml ) );
printf( "Off-surface error:    %13.8f\n",
pow( (point[0]/a), 2 ) + pow( (point[1]/b), 2 )
+ pow( (point[2]/c), 2 ) - 1 );
printf( " \n" );

vpack_c ( 15.0, -7.0, 3.0, xnorml );
ednmpt_c ( a, b, c, xnorml, point );
surfnm_c ( a, b, c, point, normal );

printf( "Semi-axis lengths:    %13.8f %13.8f %13.8f\n", a, b, c );
printf( "Input vector:         %13.8f %13.8f %13.8f\n",
xnorml[0], xnorml[1], xnorml[2] );
printf( "Point:                %13.8f %13.8f %13.8f\n",
point[0], point[1], point[2] );
printf( "Outward normal:       %13.8f %13.8f %13.8f\n",
normal[0], normal[1], normal[2] );
printf( "Angular error (rad):  %13.8f\n",
vsep_c ( normal, xnorml ) );
printf( "Off-surface error:    %13.8f\n",
pow( (point[0]/a), 2 ) + pow( (point[1]/b), 2 )
+ pow( (point[2]/c), 2 ) - 1 );
printf( " \n" );

vpack_c ( a/2, b/2, c/2, xnorml );
ednmpt_c ( a, b, c, xnorml, point );
surfnm_c ( a, b, c, point, normal );

printf( "Semi-axis lengths:    %13.8f %13.8f %13.8f\n", a, b, c );
printf( "Input vector:         %13.8f %13.8f %13.8f\n",
xnorml[0], xnorml[1], xnorml[2] );
printf( "Point:                %13.8f %13.8f %13.8f\n",
point[0], point[1], point[2] );
printf( "Outward normal:       %13.8f %13.8f %13.8f\n",
normal[0], normal[1], normal[2] );
printf( "Angular error (rad):  %13.8f\n",
vsep_c ( normal, xnorml ) );
printf( "Off-surface error:    %13.8f\n",
pow( (point[0]/a), 2 ) + pow( (point[1]/b), 2 )
+ pow( (point[2]/c), 2 ) - 1 );
printf( " \n" );

return ( 0 );
}

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

Semi-axis lengths:      10.00000000    5.00000000    2.00000000
Input vector:            0.00000000    0.00000000    3.00000000
Point:                   0.00000000    0.00000000    2.00000000
Outward normal:          0.00000000    0.00000000    1.00000000
Angular error (rad):     0.00000000
Off-surface error:       0.00000000

Semi-axis lengths:      10.00000000    5.00000000    2.00000000
Input vector:           15.00000000   -7.00000000    3.00000000
Point:                   9.73103203   -1.13528707    0.07784826
Outward normal:          0.89165745   -0.41610681    0.17833149
Angular error (rad):     0.00000000
Off-surface error:       0.00000000

Semi-axis lengths:      10.00000000    5.00000000    2.00000000
Input vector:           15.00000000   -7.00000000    3.00000000
Point:                   9.73103203   -1.13528707    0.07784826
Outward normal:          0.89165745   -0.41610681    0.17833149
Angular error (rad):     0.00000000
Off-surface error:       0.00000000

Semi-axis lengths:      10.00000000    5.00000000    2.00000000
Input vector:            5.00000000    2.50000000    1.00000000
Point:                   9.69412864    1.21176608    0.07755303
Outward normal:          0.88045091    0.44022545    0.17609018
Angular error (rad):     0.00000000
Off-surface error:       0.00000000
```

#### Restrictions

```   None.
```

#### Literature_References

```   None.
```

#### Author_and_Institution

```   J. Diaz del Rio     (ODC Space)
```

#### Version

```   -CSPICE Version 1.0.0, 08-FEB-2021 (JDR)
```

#### Index_Entries

```   point on an ellipsoid having given surface normal
```
`Fri Dec 31 18:41:05 2021`