Procedure

   void nvc2pl_c ( ConstSpiceDouble     normal[3],
                   SpiceDouble          constant,
                   SpicePlane        *  plane     ) 

Abstract

 
   Make a CSPICE plane from a normal vector and a constant. 
 

Required_Reading

 
   PLANES 
 

Keywords

 
   GEOMETRY 
   MATH 
   PLANE 
 

Brief_I/O

 
   Variable  I/O  Description 
   --------  ---  -------------------------------------------------- 
   normal, 
   constant   I   A normal vector and constant defining a plane. 
   plane      O   A CSPICE plane structure representing the plane. 
 

Detailed_Input

 
   normal, 
   constant       are, respectively, a normal vector and constant
                  defining a plane.  normal need not be a unit vector.
                  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. 
 

Detailed_Output

 
   plane          is a CSPICE plane structure that represents the 
                  geometric plane defined by normal and constant. 
 

Parameters

 
   None. 
 

Exceptions

 
   1)  If the input vector normal is the zero vector, the error 
       SPICE(ZEROVECTOR) is signalled. 
 

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 ) 
 
   Any of these last three routines may be used to convert this 
   routine's output, plane, to another representation of a 
   geometric plane. 
 

Examples

 
   1)  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

 
   No checking is done to prevent arithmetic overflow. 
 

Literature_References

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

Author_and_Institution

 
   N.J. Bachman   (JPL) 
 

Version

 
   -CSPICE Version 1.0.1, 02-NOV-2009 (NJB)

      Corrected header typo.

   -CSPICE Version 1.0.0, 01-MAR-1999 (NJB)

Index_Entries

 
   normal vector and constant to plane 
 

Link to routine nvc2pl_c source file nvc2pl_c.c