void nvc2pl_c ( ConstSpiceDouble normal[3],
SpiceDouble constant,
SpicePlane * plane )
Make a CSPICE plane from a normal vector and a constant.
PLANES
GEOMETRY
MATH
PLANE
Variable I/O Description
  
normal,
constant I A normal vector and constant defining a plane.
plane O A CSPICE plane structure representing the plane.
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 threedimensional space that satisfy
< x, normal > = constant.
plane is a CSPICE plane structure that represents the
geometric plane defined by normal and constant.
None.
1) If the input vector normal is the zero vector, the error
SPICE(ZEROVECTOR) is signalled.
None.
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.
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 );
No checking is done to prevent arithmetic overflow.
[1] `Calculus and Analytic Geometry', Thomas and Finney.
N.J. Bachman (JPL)
CSPICE Version 1.0.1, 02NOV2009 (NJB)
Corrected header typo.
CSPICE Version 1.0.0, 01MAR1999 (NJB)
normal vector and constant to plane
