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pl2nvc_c
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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 pl2nvc_c ( ConstSpicePlane   * plane,
                   SpiceDouble         normal[3],
                   SpiceDouble       * constant  ) 

Abstract

 
   Return a unit normal vector and constant that define a specified 
   plane. 
 

Required_Reading

 
   PLANES 
 

Keywords

 
   GEOMETRY 
   MATH 
   PLANE 
 

Brief_I/O

 
   Variable  I/O  Description 
   --------  ---  -------------------------------------------------- 
   plane      I   A CSPICE plane. 
   normal, 
   constant   O   A normal vector and constant defining the 
                  geometric plane represented by plane. 
 

Detailed_Input

 
   plane          is a CSPICE plane. 
 

Detailed_Output

 
   normal, 
   constant       are, respectively, a unit normal vector and 
                  constant that define the geometric plane 
                  represented by plane.  Let the symbol < a, b > 
                  indicate the inner product of vectors a and b; 
                  then the geometric plane is the set of vectors x 
                  in three-dimensional space that satisfy 
 
                     < x,  normal >  =  constant. 
 
                  normal is a unit vector.  constant is the distance of 
                  the plane from the origin; 
 
                     constant * normal 
 
                  is the closest point in the plane to the origin. 
 

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)  Given a point in a plane and a normal vector, find the distance 
       of the plane from the origin.  We make a `plane' from the point
       and normal, then convert the plane to a unit normal and constant.
       The constant is the distance of the plane from the origin. 
 
          nvp2pl_c ( normal, point,  &plane    ); 
          pl2nvc_c ( &plane, normal, &constant ); 
 
 
   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 1.0.1, 06-FEB-2003 (EDW)

       Trivial correction to header docs.

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

Index_Entries

 
   plane to normal vector and constant 
 
Wed Apr  5 17:54:40 2017