Index Page pl2psv_c

A B C D E F G H I J K L M N O P Q R S T U V W X

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

       void pl2psv_c ( ConstSpicePlane  * plane,
                       SpiceDouble        point[3],
                       SpiceDouble        span1[3],
                       SpiceDouble        span2[3]  )

#### Abstract

       Return a point and two orthogonal spanning vectors that generate
       a specified plane.

#### Required_Reading

       PLANES

#### Keywords

       GEOMETRY
       MATH
       PLANE

#### Brief_I/O

       Variable  I/O  Description
       --------  ---  --------------------------------------------------
       plane      I   A CSPICE plane.
       point,
       span1,
       span2      O   A point in the input plane and two vectors
                      spanning the input plane.

#### Detailed_Input

       plane          is a CSPICE plane that represents the geometric
                      plane defined by point, span1, and span2.

#### Detailed_Output

       point,
       span1,
       span2          are, respectively, a point and two orthogonal
                      spanning vectors that generate the geometric plane
                      represented by plane.  The geometric plane is the
                      set of vectors

                         point   +   s * span1   +   t * span2

                      where s and t are real numbers.  point is the
                      closest point in the plane to the origin; this
                      point is always a multiple of the plane's normal
                      vector.  span1 and span2 are an orthonormal pair
                      of vectors.  point, span1, and span2 are mutually
                      orthogonal.

#### Parameters

       None.

#### Exceptions

       Error free.

       1)  The input plane MUST have been created by one of the CSPICE
           routines

              nvc2pl_c ( Normal vector and constant to plane )
              nvp2pl_c ( Normal vector and point to plane    )
              psv2pl_c ( Point and spanning vectors to plane )

           Otherwise, the results of this routine are unpredictable.

#### Files

       None.

#### Particulars

       CSPICE geometry routines that deal with planes use the `plane'
       data type to represent input and output planes.  This data type
       makes the subroutine interfaces simpler and more uniform.

       The CSPICE routines that produce CSPICE planes from data that
       define a plane are:

          nvc2pl_c ( Normal vector and constant to plane )
          nvp2pl_c ( Normal vector and point to plane    )
          psv2pl_c ( Point and spanning vectors to plane )

       The CSPICE routines that convert CSPICE planes to data that
       define a plane are:

          pl2nvc_c ( Plane to normal vector and constant )
          pl2nvp_c ( Plane to normal vector and point    )
          pl2psv_c ( Plane to point and spanning vectors )

#### Examples

       1)  Find the intersection of a plane and the unit sphere.  This
           is a geometry problem that arises in computing the
           intersection of a plane and a triaxial ellipsoid.  The
           CSPICE routine inedpl_c computes this intersection, but this
           example does illustrate how to use this routine.

              /.
              The geometric plane of interest will be represented
              by the CSPICE plane plane in this example.

              The intersection circle will be represented by the
              vectors center, v1, and v2; the circle is the set
              of points

                 center  +  cos(theta) v1  +  sin(theta) v2,

              where theta is in the interval (-pi, pi].

              The logical variable found indicates whether the
              intersection is non-empty.

              The center of the intersection circle will be the
              closest point in the plane to the origin.  This
              point is returned by pl2psv_c.  The distance of the
              center from the origin is the norm of center.
              ./

              pl2psv_c  ( &plane, center, span1, span2 );

              dist = vnorm_c ( center )

              /.
              The radius of the intersection circle will be

                      ____________
                  _  /          2
                   \/  1 - dist

              since the radius of the circle, the distance of the
              plane from the origin, and the radius of the sphere
              (1) are the lengths of the sides of a right triangle.

              ./

              found = ( dist <= 1.0 );

              if ( found )
              {
                 radius = sqrt ( 1.0 - pow(dist,2) );

                 vscl_c ( radius, span1, v1 );
                 vscl_c ( radius, span2, v2 ) ;
              }

       2)  Apply a linear transformation represented by the matrix m to
           a plane represented by the normal vector n and the constant c.
           Find a normal vector and constant for the transformed plane.

              /.
              Make a CSPICE plane from n and c, and then find a
              point in the plane and spanning vectors for the
              plane.  n need not be a unit vector.
              ./
              nvc2pl_c ( n,       c,     &plane         );
              pl2psv_c ( &plane,  point,  span1,  span2 );

              /.
              Apply the linear transformation to the point and
              spanning vectors.  All we need to do is multiply
              these vectors by m, since for any linear
              transformation T,

                    T ( point  +  t1 * span1     +  t2 * span2 )

                 =  T (point)  +  t1 * T(span1)  +  t2 * T(span2),

              which means that T(point), T(span1), and T(span2)
              are a point and spanning vectors for the transformed
              plane.
              ./

              mxv_c ( m, point, tpoint );
              mxv_c ( m, span1, tspan1 );
              mxv_c ( m, span2, tspan2 );

              /.
              Make a new CSPICE plane tplane from the
              transformed point and spanning vectors, and find a
              unit normal and constant for this new plane.
              ./

              psv2pl_c ( tpoint,   tspan1,  tspan2,   &tplane );
              pl2nvc_c ( &tplane,  tn,      &tc               );

#### Restrictions

       None.

#### Literature_References

       [1] `Calculus and Analytic Geometry', Thomas and Finney.

#### Author_and_Institution

       N.J. Bachman   (JPL)

#### Version

       -CSPICE Version 1.0.0, 05-MAR-1999 (NJB)

#### Index_Entries

       plane to point and spanning vectors

#### Link to routine pl2psv_c source file pl2psv_c.c

    Wed Apr  5 17:54:40 2017