Procedure

     EDPNT ( Ellipsoid point  )

     SUBROUTINE EDPNT ( P, A, B, C, EP )

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

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION      P  ( 3 )
     DOUBLE PRECISION      A
     DOUBLE PRECISION      B
     DOUBLE PRECISION      C
     DOUBLE PRECISION      EP ( 3 )

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.

     2)  If P is the zero vector, the error SPICE(ZEROVECTOR) is
         signaled.

     3)  If the level surface parameter of the input point
         underflows, the error SPICE(POINTTOOSMALL) is signaled.

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 SPICELIB
     routines LATSRF and SRFREC.

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
              IMPLICIT NONE

              CHARACTER*(*)         FMT1
              PARAMETER           ( FMT1 = '(A,F18.14)'  )

              CHARACTER*(*)         FMT3
              PARAMETER           ( FMT3 = '(A,3F18.14)' )

              DOUBLE PRECISION      A
              DOUBLE PRECISION      B
              DOUBLE PRECISION      C
              DOUBLE PRECISION      V      ( 3 )
              DOUBLE PRECISION      EP     ( 3 )
              DOUBLE PRECISION      LEVEL

              A = 3.D0
              B = 2.D0
              C = 1.D0

              CALL VPACK ( 1.D0, 1.D0, 1.D0, V )

              CALL EDPNT ( V, A, B, C, EP )

              WRITE (*,FMT3) 'EP    = ', EP

        C
        C     Verify that EP is on the ellipsoid.
        C
              LEVEL = (EP(1)/A)**2 + (EP(2)/B)**2 + (EP(3)/C)**2

              WRITE (*,FMT1) 'LEVEL = ', LEVEL

              END


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


        EP    =   0.85714285714286  0.85714285714286  0.85714285714286
        LEVEL =   1.00000000000000

Restrictions

     None.

Literature_References

     None.

Author_and_Institution

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

Version

    SPICELIB Version 2.0.1, 09-JUL-2020 (JDR)

        Minor edits to the header and code example.

    SPICELIB Version 2.0.0, 19-APR-2016 (NJB) (EDW)