Procedure

   void nvp2pl_c ( ConstSpiceDouble    normal[3],
                   ConstSpiceDouble    point [3],
                   SpicePlane        * plane     ) 

Abstract

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

Required_Reading

 
   PLANES 
 

Keywords

 
   GEOMETRY 
   MATH 
   PLANE 
 

Brief_I/O

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

Detailed_Input

 
   normal, 
   point 
                  are, respectively, a normal vector and point that 
                  define a plane in three-dimensional space.  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 - point, normal >  =  0. 
 

Detailed_Output

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

Parameters

 
   None. 
 

Exceptions

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

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)  Project a vector v orthogonally onto a plane defined by point 
       and normal.  proj is the projection we want; it is the 
       closest vector in the plane to v. 
 
          nvp2pl_c ( normal,  point,   &plane ); 
          vprjp_c  ( v,       &plane,  proj   );
 
 
   2)  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 output constant 
       is (according to the specification of pl2nvc_c) the distance of 
       the plane from the origin. 
 
          nvp2pl_c ( normal,  point,  &plane   ); 
          pl2nvc_c ( &plane,  normal, constant );
          
 

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

 
   normal vector and point to plane 
 

Link to routine nvp2pl_c source file nvp2pl_c.c