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Index Page edpnt_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

       edpnt_c ( Ellipsoid point  )

       void edpnt_c  ( ConstSpiceDouble    p      [3],
                       SpiceDouble         a,
                       SpiceDouble         b,
                       SpiceDouble         c,
                       SpiceDouble         ep     [3] )

#### Abstract

       Scale a point so that it lies on the surface of a specified
       triaxial ellipsoid that is centered at the origin and aligned
       with the Cartesian coordinate axes.

#### Required_Reading

       None.

#### Keywords

       ELLIPSOID
       GEOMETRY
       MATH

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       p          I   A point in three-dimensional space.
       a          I   Semi-axis length in the X direction.
       b          I   Semi-axis length in the Y direction.
       c          I   Semi-axis length in the Z direction.
       ep         O   Point on ellipsoid.

#### Detailed_Input

       p           is a non-zero point in three-dimensional space.

       a,
       b,
       c           are, respectively, the semi-axis lengths of a triaxial
                   ellipsoid in the X, Y, and Z directions. The axes of
                   the ellipsoid are aligned with the axes of the
                   Cartesian coordinate system.

#### Detailed_Output

       ep          is the result of scaling the input point `p' so that
                   it lies on the surface of the triaxial ellipsoid
                   defined by the input semi-axis lengths.

#### Parameters

       None.

#### Exceptions

       1)  If any of the target ellipsoid's semi-axis lengths is non-positive,
           the error SPICE(INVALIDAXES) is signaled by a routine in the call
           tree of this routine.

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

       3)  If the level surface parameter of the input point underflows, the
           error SPICE(POINTTOOSMALL) is signaled by a routine in the call tree
           of this routine.

#### Files

       None.

#### Particulars

       This routine efficiently computes the ellipsoid surface point
       corresponding to a specified ray emanating from the origin.
       Practical examples of this computation occur in the CSPICE
       routines latsrf_c and srfrec_c.

#### 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) Find the surface intercept point on an ellipsoid having radii

              ( 3, 2, 1 )

          of the ray emanating from the origin and having direction
          vector

              ( 1, 1, 1 )

          Example code begins here.

          /.
             Program edpnt_ex1
          ./
          #include <math.h>
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             SpiceDouble          a;
             SpiceDouble          b;
             SpiceDouble          c;
             SpiceDouble          v      [3];
             SpiceDouble          ep     [3];
             SpiceDouble          level;

             a = 3.0;
             b = 2.0;
             c = 1.0;

             vpack_c ( 1.0, 1.0, 1.0, v );

             edpnt_c ( v, a, b, c, ep );

             printf( "EP    =  %17.14f %17.14f %17.14f\n", ep[0], ep[1], ep[2] );

             /.
             Verify that `ep' is on the ellipsoid.
             ./
             level =   pow( (ep[0]/a), 2 ) + pow( (ep[1]/b), 2 )
                     + pow( (ep[2]/c), 2 );

             printf( "LEVEL =  %17.14f\n", level );

             return ( 0 );
          }

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

          EP    =   0.85714285714286  0.85714285714286  0.85714285714286
          LEVEL =   1.00000000000000

#### 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

       scale point to lie on ellipsoid

#### Link to routine edpnt_c source file edpnt_c.c

    Fri Dec 31 18:41:05 2021